Teat Bank For Physics for Scientists and Engineers 11th Edition By Raymond A. Serway, John W. Jewett

Teat Bank For Physics for Scientists and Engineers 11e Raymond A. Serway, John W. Jewett, Vahé Peroomian Chapter 1-44 Chapter 1 Physics and Measurement 1. The density of an object is defined as a. the volume occupied by each unit of mass. b. the amount of mass for each unit of volume. c. the weight of each unit of volume. d. the amount of the substance that has unit volume and unit mass. e. the amount of the substance that contains as many particles as 12 grams of the carbon-12 isotope.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 1.1 Standards of Length, Mass, and Time HAS VARIABLES: False 23

3

2. One mole of the carbon-12 isotope contains 6.022 × 10 atoms. What volume in m would be needed to store one mole of cube-shaped children's blocks 2.00 cm long on each side? a. 4.8 × 1018 b. 1.2 × 1022 c. 6.0 × 1023 d. 1.2 × 1024 e. 4.8 × 1024 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 1.1 Standards of Length, Mass, and Time HAS VARIABLES: False 3. John and Linda are arguing about the definition of density. John says an object with a greater mass than another also has a greater density. Linda says it is impossible to compare the densities of the two objects without also knowing their volumes. Which one, if either, is correct? a. They are both wrong. b. John is correct, but Linda is wrong. c. John is wrong, but Linda is correct. d. They are both correct. e. There is not enough information given to determine who is correct.

ANSWER: c POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 1.1 Standards of Length, Mass, and Time HAS VARIABLES: False 4. The standard kilogram is a platinum-iridium cylinder 39 mm in height and 39 mm in diameter. What is the density of the material?

3 ANSWER: 21 464 kg/m POINTS: 2 DIFFICULTY: Average REFERENCES: 1.1 Standards of Length, Mass, and Time HAS VARIABLES: False 5. A 2.00-m by 3.00-m plate of aluminum has a mass of 324 kg. What is the thickness of the plate? (The density of 3 3 aluminum is 2.70 × 10 kg/m .)

ANSWER: 2.00 cm POINTS: 2 DIFFICULTY: Average REFERENCES: 1.1 Standards of Length, Mass, and Time HAS VARIABLES: False 6. What is the mass of air in a room that measures 5.0 m × 8.0 m × 3.0 m? (The density of air is 1/800 that of water).

ANSWER: 150 kg POINTS: 2 DIFFICULTY: Average REFERENCES: 1.1 Standards of Length, Mass, and Time HAS VARIABLES: False 7. The term

occurs in Bernoulli's equation, with ρ being the density of a fluid and v its speed. The dimensions of

this term are what? a. M-1L5T2 b. MLT2 c. ML-1T-2 d. M-1L9T-2 e. M-1L3T-2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 1.3 Dimensional Analysis HAS VARIABLES: False 8. Which of the following quantities has the same dimensions as kinetic energy, -2

?

-1

Note: [a] = [g] = LT ; [h] = L and [v] = LT . a. ma b. mvx Copyright Cengage Learning. Powered by Cognero.

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c. mvt d. mgh e. mgt ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 1.3 Dimensional Analysis HAS VARIABLES: False -1

9. The quantity with the same units as force times time, Ft, with dimensions MLT is what? a. mv b. mvr c. mv2r d. ma e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 1.3 Dimensional Analysis HAS VARIABLES: False 10. The equation for the change of position of a train starting at x = 0 m is given by

. What are the

dimensions of b? a. T−3 b. LT−3 c. LT−2 d. LT−1 e. L−1T−1 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 1.3 Dimensional Analysis HAS VARIABLES: False 11. Spike claims that dimensional analysis shows that the correct expression for change in velocity,

, is

, where m is mass, t is time, and F is the magnitude of force. Carla says that can't be true because the dimensions of force are

. Which one, if either, is correct?

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a.

Spike, because

.

b.

Spike, because

.

c.

Carla, because

.

d.

Carla, because

.

e.

Spike, because the dimensions of force are

.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 1.3 Dimensional Analysis HAS VARIABLES: False

12. Which one of the quantities below has dimensions equal to

?

a. mv b. mv2 c.

d. mrv e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 1.3 Dimensional Analysis HAS VARIABLES: False -1

13. Which quantity has dimensions equal to [MLT ]. a. mr b. mvr c. ma d. mat

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e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 1.3 Dimensional Analysis HAS VARIABLES: False 14. If each frame of a motion picture film is 2 cm high, and 24 frames go by in a second, estimate how many frames are needed to show a two-hour-long movie. a. 1 400 b. 25 000 c. 50 000 d. 170 000 e. This cannot be determined without knowing how many reels were used.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 1.4 Conversion of Units HAS VARIABLES: False 15. The basic function of a carburetor of an automobile is to atomize the gasoline and mix it with air to promote rapid 3 combustion. As an example, assume that 30 cm of gasoline is atomized into N spherical droplets, each with a radius of −5 2.0 × 10 m. What is the total surface area of these N spherical droplets?

2 ANSWER: 45 000 cm POINTS: 3 DIFFICULTY: Challenging REFERENCES: 1.4 Conversion of Units HAS VARIABLES: False

16. Which of the following products of ratios gives the conversion factor to convert miles per hour

second

to meters per

?

a. b. c. d.

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e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 1.4 Conversion of Units HAS VARIABLES: False

17. Which of the following products of ratios gives the conversion factors to convert meters per second

per hour

to miles

?

a. b. c. d. e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 1.4 Conversion of Units HAS VARIABLES: False 18. One U.S. fluid gallon contains a volume of 231 cubic inches. How many liters of gasoline would you have to buy in 3 3 Canada to fill a 14-gallon tank? (Note: 1 L = 10 cm .) a. 53 b. 21 c. 14 d. 8.0 e. 4.0 ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 1.4 Conversion of Units HAS VARIABLES: False 2

19. The standard exam page is 8.50 inches by 11.0 inches. What is its area in cm ?

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a. 19.5 b. 36.8 c. 93.5 d. 237 e. 603 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 1.4 Conversion of Units HAS VARIABLES: False 20. A standard exam page is 8.5 inches by 11 inches. What is the volume of an exam booklet that is 2.0 mm thick? a. 1.9 × 104 mm3. b. 4.7 × 104 mm3. c. 1.2 × 105 mm3. d. 3.1 × 105 mm3. e. 3.1 × 103 mm3.

ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 1.4 Conversion of Units HAS VARIABLES: False 21. Which quantity can be converted from the English system to the metric system by the conversion factor ? a. feet per second b. feet per hour c. miles per second d. miles per hour e. miles per minute ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 1.4 Conversion of Units HAS VARIABLES: False 22. If you drove day and night without stopping for one year without exceeding the legal highway speed limit in the United States, the maximum number of miles you could drive would be closest to a. 8 700. b. 300 000. c. 500 000. d. 1 000 000. e. 32 000 000.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 1.5 Estimates and Order-of-Magnitude Calculations HAS VARIABLES: False 23. At the end of a year, a motor car company announces that sales of a pickup truck are down 43% for the year. If sales continue to decrease by 43% in each succeeding year, how long will it take for sales to decrease to zero? a. 1 year b. 2 years c. 3 years d. 4 years e. More than four years ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 1.5 Estimates and Order-of-Magnitude Calculations HAS VARIABLES: False 24. One number has three significant figures and another number has four significant figures. How many significant figures will their product have? a. One b. Three c. Four d. Seven e. Twelve ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 1.6 Significant Figures HAS VARIABLES: False 25. A rectangle has a length of 1.323 m and a width of 4.16 m. Using significant figure rules, what is the area of this rectangle? a. 5.503 68 m2 b. 5.503 7 m2 c. 5.504 m2 d. 5.50 m2 e. 5.5 m2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 1.6 Significant Figures HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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Instructions: On occasion, the notation

= [A, θ] will be a shorthand notation for

.

1. The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are (r, 67.4°). What is the value of the polar coordinate r in this case? a. 1.92 b. 4.62 c. 12.0 d. 13.0 e. More information is needed.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 2.1 Coordinate Systems HAS VARIABLES: False 2. In what quadrant are both the sine and tangent negative? a. 1st b. 2nd c. 3rd d. 4th e. This cannot happen.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.1 Coordinate Systems HAS VARIABLES: False 3. The vector has components +5 and +7 along the x and y axes, respectively. Along a set of axes rotated 90 degrees counterclockwise relative to the original axes, the vector's components are a. −7; −5. b. 7; −5. c. −7; 5. d. 7; 5. e. 7; 0.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.3 Vector and Scalar Quantities HAS VARIABLES: False Instructions: On occasion, the notation

= [A, θ] will be a shorthand notation for

.

4. A student decides to spend spring break by driving 50 miles due east, then 50 miles 30 degrees south of east, then 50 miles 30 degrees south of that direction, and to continue to drive 50 miles deviating by 30 degrees each time until he returns to his original position. How far will he drive, and how many vectors must he sum to calculate his displacement? a. 0, 0 Copyright Cengage Learning. Powered by Cognero.

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b. 0, 8 c. 0, 12 d. 400 mi, 8 e. 600 mi, 12 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 2.4 Basic Vector Arithmetic HAS VARIABLES: False 5. The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true?

a. b. c. d. e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.4 Basic Vector Arithmetic HAS VARIABLES: False 6. When three vectors, , , and are placed head to tail, the vector sum same magnitude, the angle between the directions of any two adjacent vectors is what? a. 30° b. 60° c. 90° d. 120° e. 150° ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.4 Basic Vector Arithmetic HAS VARIABLES: False Instructions: On occasion, the notation

= [A, θ] will be a shorthand notation for

. If the vectors all have the

.

Exhibit 2-3 Copyright Cengage Learning. Powered by Cognero.

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The vectors

,

, and

are shown below.

Use this exhibit to answer the following question(s).

7. Refer to Exhibit 2-3. Which diagram below correctly represents a. b.

c.

?

d.

e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 2.4 Basic Vector Arithmetic HAS VARIABLES: False 8. Refer to Exhibit 2-3. Which diagram below correctly represents a. b.

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?

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c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 2.4 Basic Vector Arithmetic HAS VARIABLES: False Instructions: On occasion, the notation

= [A, θ] will be a shorthand notation for

.

Exhibit 2-4 The diagram below shows the path taken by a sailboat tacking sideways because it cannot sail directly into the wind.

Use this exhibit to answer the following question(s).

9. Refer to Exhibit 2-4. The total distance it travels is a. 1000 m. b. 1732 m. c. 2000 m. d. 6298 m. e. 8000 m.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.4 Basic Vector Arithmetic HAS VARIABLES: False 10. Refer to Exhibit 2-4. The total displacement of the sailboat, the vector sum of its displacements OB, BC, CD, and DE, is Copyright Cengage Learning. Powered by Cognero.

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a. 1732 m, East. b. 2000 m, Northeast. c. 6298 m, East. d. 8000 m, Southeast. e. 8000 m, East.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.4 Basic Vector Arithmetic HAS VARIABLES: False = [A, θ] will be a shorthand notation for

Instructions: On occasion, the notation 11. Dana says any vector

can be represented as the sum of two vectors:

. . Ardis says any vector

can be

represented as the difference of two vectors: . Which one, if either, is correct? a. They are both wrong: every vector is unique. b. Dana is correct: Any vector can be represented as a sum of components and not as a difference. c. Ardis is correct: Any vector can be represented as a difference of vector components and not as a sum. d.

They are both correct: A difference of vectors is a sum . e. They are both wrong: Vectors can be moved as long as they keep the same magnitude and direction.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 2.4 Basic Vector Arithmetic HAS VARIABLES: False 12. Given two non-zero vectors, a. b.

, such that

, the sum

satisfies

. .

c.

.

d. e.

and

. .

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 2.4 Basic Vector Arithmetic HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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Instructions: On occasion, the notation

= [A, θ] will be a shorthand notation for

13. If = [15, 80°] and , what is the magnitude of a. 15 b. 35 c. 32 d. 5.0 e. 23 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 14. Vectors

and

are shown. What is the magnitude of a vector

.

?

if

?

a. 46 b. 10 c. 30 d. 78 e. 90 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 15. If and , what is the magnitude of the vector a. 42 b. 22 c. 64 d. 90 e. 13 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

?

Page 14

16. If and , what is the direction of the vector a. −49° b. −41° c. −90° d. +49° e. +21° ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False

?

17. If = [10 m, 30°] and = [25 m, 130°], what is the magnitude of the sum of these two vectors? a. 20 m b. 35 m c. 15 m d. 25 m e. 50 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 18. If = [10 m, 30°] and = [25 m, 130°], what is the direction of the sum of these two vectors? a. 17° b. 73° c. 107° d. 163° e. 100° ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 19. A vector,

, when added to the vector

has a magnitude equal to that of a. 3.2 b. 6.3 c. 9.5 d. 18 e. 5 ANSWER: a

, yields a resultant vector which is in the positive y direction and

. What is the magnitude of

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?

Page 15

POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 20. If vector

is added to vector

, the result is

. If

is subtracted from

, the result is

. What is the

magnitude of ? a. 5.1 b. 4.1 c. 5.4 d. 5.8 e. 8.2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 21. If

= [2.5 cm, 80°], i.e., the magnitude and direction of

are 2.5 cm and 80°,

= [3.5 cm, 120°], and

,

what is the direction of (to the nearest degree)? a. 247° b. 235° c. 243° d. 216° e. 144° ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 22. If vector

is added to vector

, the result is

. If

is subtracted from

, the result is

. What is the

direction of (to the nearest degree)? a. 225° b. 221° c. 230° d. 236° e. 206° ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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23. A vector

is added to

. The resultant vector is in the positive x direction and has a magnitude equal to

. What is the magnitude of ? a. 11 b. 5.1 c. 7.1 d. 8.3 e. 12.2 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 24. A vector

is added to

. The resultant vector is in the positive x direction and has a magnitude equal to

that of . What is the direction of ? a. 74° b. 100° c. −81° d. −62° e. 106° ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 25. If two collinear vectors

and

are added, the resultant has a magnitude equal to 4.0. If

is subtracted from

, the

is subtracted from

, the

resultant has a magnitude equal to 8.0. What is the magnitude of ? a. 2.0 b. 3.0 c. 4.0 d. 5.0 e. 6.0 ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 26. If two collinear vectors

and

are added, the resultant has a magnitude equal to 4.0. If

resultant has a magnitude equal to 8.0. What is the magnitude of a. 2.0 b. 3.0 Copyright Cengage Learning. Powered by Cognero.

?

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c. 4.0 d. 5.0 e. 6.0 ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 27. When vector

is added to vector

, which has a magnitude of 5.0, the vector representing their sum is perpendicular

to

and has a magnitude that is twice that of . What is the magnitude of a. 2.2 b. 2.5 c. 4.5 d. 5.0 e. 7.0 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False

?

28. Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What distance separates the two oases? a. 15 km b. 48 km c. 28 km d. 53 km e. 55 km ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 29. Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What is the direction from the first oasis to the second oasis? a. 21° N of W b. 39° W of N c. 69° N of W d. 51° W of N e. 42° W of N ANSWER: d POINTS: 3 DIFFICULTY: Challenging Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False Instructions: On occasion, the notation

= [A, θ] will be a shorthand notation for

.

Exhibit 2-1 The three forces shown act on a particle.

Use this exhibit to answer the following question(s).

30. Refer to Exhibit 2-1. What is the magnitude of the resultant of these three forces? a. 27.0 N b. 33.2 N c. 36.3 N d. 23.8 N e. 105 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 31. Refer to Exhibit 2-1. What is the direction of the resultant of these three forces? a. 35° b. 45° c. 65° d. 55° e. 85° ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False Instructions: On occasion, the notation 32. If vector

is added to vector

= [A, θ] will be a shorthand notation for

, the result is a third vector that is perpendicular to

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. and has a magnitude equal to 3 .

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What is the ratio of the magnitude of to that of ? a. 1.8 b. 2.2 c. 3.2 d. 1.3 e. 1.6 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False Instructions: On occasion, the notation

= [A, θ] will be a shorthand notation for

.

Exhibit 2-2 A child starts at one corner of a cubical jungle gym in a playground and climbs up to the diagonally opposite corner. The original corner is the coordinate origin, and the x, y and z axes are oriented along the jungle gym edges. The length of each side is 2 m.

Use this exhibit to answer the following question(s).

33. Refer to Exhibit 2-2. The child's displacement is: a. b. c. d. e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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34. Refer to Exhibit 2-2. What is the child’s distance from her starting position? a. 2.8 m b. 3.5 m c. 6.0 m d. 6.9 m e. 12.0 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False Instructions: On occasion, the notation

= [A, θ] will be a shorthand notation for

.

35. The displacement of the tip of the 10-cm-long minute hand of a clock between 12:15 A.M. and 12:45 P.M. is what? a. 10 cm, 90° b. 10 cm, 180° c. 10 cm, 4 500° d. 20 cm, 180° e. 20 cm, 540° ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 36. Given that

and

, what is

?

a. b. c. d. e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False

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Page 21

37. Given that

and

, what is

?

a. b. c. d. e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 38. Given that

and

, what is

?

a. b. c. d. e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 39. Which statement is true about the unit vectors , , and ? a. Their directions are defined by a left-handed coordinate system. b. The angle between any two is 90 degrees. c. Each has a length of 1 m. d.

If is directed east and is directed south, points up out of the surface. e. All of the above.

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Page 22

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False = [A, θ] will be a shorthand notation for

Instructions: On occasion, the notation

40. Anthony has added the vectors listed below and gotten the result

a. b.

He lost the minus sign in vector He read the

in

as

. . What errors has he made?

.

.

c.

He lost the minus sign in vector . d. All of the above are correct. e. Only (a) and (b) above are correct.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 41. Adding vectors and by the graphical method gives the same result for + and + . If both additions are done graphically from the same origin, the resultant is the vector that goes from the tail of the first vector to the tip of the second vector, i.e., it is represented by a diagonal of the parallelogram formed by showing both additions in the same figure. Note that a parallelogram has 2 diagonals. Keara says that the sum of two vectors by the parallelogram method is . Shamu says it is . Both used the parallelogram method, but one used the wrong diagonal. Which one of the vector pairs below contains the original two vectors? a. ; b. c. d. e.

; ; ; ;

ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

Page 23

42. The vector has components +5 and +7 along the x and y axes, respectively. If the vector is now rotated 90 degrees counterclockwise relative to the original axes, the vector's components are now a. −7; −5. b. 7; −5. c. −7; 5. d. 7; 5. e. 7; 0.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 43. Two vectors starting at the same origin have equal and opposite x components. Is it possible for the two vectors to be perpendicular to each other? Justify your answer.

ANSWER: Yes. If the y components are of the right magnitudes, the angle can be 90 degrees. (This will occur if and A = B tan θ1.)

POINTS: 3 DIFFICULTY: Challenging REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 44. A vector starts at coordinate (3.0, 4.0) and ends at coordinate (−2.0, 16.0). What are the magnitude and direction of this vector?

ANSWER: 13.0 m, 113°.

POINTS: 2 DIFFICULTY: Average REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 45. What two vectors are each the same magnitude as and perpendicular to ANSWER: and .

?

POINTS: 3 DIFFICULTY: Challenging REFERENCES: 2.5 Components of a Vector and Unit Vectors HAS VARIABLES: False 46. Two vectors

and

are given by

and

. If these two vectors are drawn starting at

the same point, what is the angle between them? a. 106° b. 102° c. 110° d. 113° Copyright Cengage Learning. Powered by Cognero.

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e. 97° ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 47. If

, and the angle between

and

(when the two are drawn starting from the same point)

is 60°, what is the scalar product of these two vectors? a. −13 b. +13 c. +37 d. −37 e. 73 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 48. If vectors

and

have magnitudes 12 and 15, respectively, and the angle between the two when they are drawn

starting from the same point is 110°, what is the scalar product of these two vectors? a. −76 b. −62 c. −90 d. −47 e. −170 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 49. If vectors

and

have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is −100,

what is the magnitude of the sum of these two vectors? a. 6.6 b. 4.6 c. 8.3 d. 9.8 e. 7.6 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 50. If the scalar product of two vectors,

and , is equal to −3.5, if

, and the angle between the two vectors

when they are drawn starting from the same point is equal to 130°, what is the magnitude of ? a. 2.1 b. 2.5 c. 2.3 d. 2.7 e. 3.1 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 51. If

,

,

, what is the angle between the two vectors when they are drawn starting

from the same point? a. 118° b. 107° c. 112° d. 103° e. 77° ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 52. Two vectors

and

The scalar product of

are given by and

and

is +18. The z component of

. The scalar product of

and a third vector

is −16.

is 0. What is the magnitude of ?

a. 7.8 b. 6.4 c. 3.6 d. 5.0 e. 4.8 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 53. If

= 10,

= 15, and α = 130°, determine the scalar product of the two vectors shown.

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a. +96 b. −96 c. +51 d. −51 e. −35 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 54. If

= 5.0,

= 8.0, and α = 30°, determine the scalar product of the two vectors shown.

a. −35 b. +35 c. −20 d. +20 e. +40 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 55. If

= 6.0,

a. +19 b. +23 c. −19 d. −23 e. +30 ANSWER:

= 5.0, and α = 40°, determine the scalar product of the two vectors shown.

d

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POINTS: 2 DIFFICULTY: Average REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 56. If the scalar (dot) product of two vectors is negative, it means that a. there was a calculator error. b. the angle between the vectors is less than 90 degrees. c. the angle between the vectors is 90 degrees. d. the angle between the vectors is greater than 270 degrees. e. the angle between the vectors is between 90 and 180 degrees.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 57. Each of two vectors,

and

, lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and

the dot product of the two vectors is

. Which possibility is correct?

a.

and

b.

lies along the positive x axis.

c.

and

d.

lies along the negative x axis.

lies along the negative y axis.

e.

lies along the positive y axis.

lies along the negative y axis.

both lie along the positive x axis. lies along the negative x axis.

both lie along the positive y axis.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 58. Each of two vectors,

and

, lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and

the dot product of the two vectors is

. Which possibility is correct?

a.

and

b.

lies along the positive x axis.

c.

and

d.

lies along the negative x axis.

lies along the negative y axis.

e.

lies along the positive y axis.

lies along the negative x axis.

ANSWER:

both lie along the positive x axis. lies along the negative x axis.

both lie along the positive y axis.

b

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 2.6 The Scalar Product of Two Vectors HAS VARIABLES: False 59. Two vectors lying in the xy plane are given by the equations

and

. The value of

is

what? a. 19 b. −11 c. −19 d. 11 e. 10 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 2.7 The Vector Product of Two Vectors HAS VARIABLES: False 60. Two vectors lying in the xz plane are given by the equations

and

. The value of

is

what? a. b. c. 7 d. −7 e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 2.7 The Vector Product of Two Vectors HAS VARIABLES: False

2

1. The position of a particle moving along the x axis is given by x = (21 + 22t − 6.0t ) m, where t is in s. What is the average velocity during the time interval t = 1.0 s to t = 3.0 s? a. −6.0 m/s b. −4.0 m/s c. −2.0 m/s d. −8.0 m/s e. 8.0 m/s ANSWER: c POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 2. vx is the velocity of a particle moving along the x axis as shown. If x = 2.0 m at t = 1.0 s, what is the position of the particle at t = 6.0 s?

a. −2.0 m b. +2.0 m c. +1.0 m d. −1.0 m e. 6.0 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 3. To help Kim practice for the Special Olympics, Sally runs beside him for half the required distance. She runs the remaining distance at her regular speed and arrives 90 seconds ahead of Kim. What is the ratio of Sally's regular speed to Kim's speed? Use tKim for Kim's total time. a.

b.

c.

d.

e.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 4. The position of a particle moving along the y axis has a position given by

Is there any time interval during which the particle is not moving? a. Yes, from 0.60 s to 1.00 s. b. Yes, from 0.795 s to 0.805 s. c. Yes, at the time t = 0.80 s. d. No, the velocity is never zero. e. No, an instant is not the same as a time interval.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 3

5. A particle moving along the x axis has a position given by x = 54t − 2.0t m. At the time t = 3.0 s, the speed of the particle is zero. Which statement is correct? a. The particle remains at rest after t = 3.0 s. b. The particle no longer accelerates after t = 3.0 s. c. The particle can be found at positions x < 0 m only when t < 0 s. d. All of the above are correct. e. None of the above is correct.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 6. Two children start at one end of a street, the origin, run to the other end, then head back. On the way, back Joan is ahead of Mike. Which statement is correct about the distances run and the displacements from the origin? a. Joan has run a greater distance and her displacement is greater than Mike's. b. Mike has run a greater distance and his displacement is greater than Joan's. c. Joan has run a greater distance, but her displacement is less than Mike's. d. Mike has run a greater distance, but his displacement is less than Joan's. e. Mike has run a shorter distance, and his displacement is less than Joan's.

ANSWER: c POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 7. A car travels north at 30 m/s for one half hour. It then travels south at 40 m/s for 15 minutes. The total distance the car has traveled and its displacement are a. 18 km; 18 km S. b. 36 km; 36 km S. c. 36 km; 36 km N. d. 90 km; 18 km N. e. 90 km; 36 km N. ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 8. The area under a graph of vx vs. t from t = ti to t = tf represents a. xi. b. xf. c. xf − xi. d. (xi + xf). e. xi + xf.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 9. In 20 minutes, Kara ran 2.40 km on a treadmill facing due east. Relative to the gym, what were her displacement and average velocity during this time interval? a. 0; 0 b. 0; 2.00 m/s c. 2.40 km, east; 0 d. 2.40 km, east; 2.00 m/s, east e. 2.40 km, west; 2.00 m/s, west ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 10. A swimmer swims 20 laps in a north-south facing pool in 7.00 minutes. Her first lap is toward the north. Her displacement and average velocity are Copyright Cengage Learning. Powered by Cognero.

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a. 0; 0. b. 0; 2.38 m/s, south. c. 0; 2.38 m/s, north. d. 1 000 m, south; 2.38 m/s, south. e. 1 000 m, north; 2.38 m/s, north.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 11. A particle is moving at constant velocity. Its position at t = 1.0 s is 3.0 m and its position at t = 4.0 s is 15.0 m. What is the slope of the position-time graph for this particle? a. 0, since this is a constant-velocity situation. b. 4.0 m/s c. 4.0 m/s2 d. 9.0 m/s e. 12 m/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 12. A boat moves at 10.0 m/s relative to the water. If the boat is in a river where the current is 2.0 m/s, how long does it take the boat to make a complete round trip of 1.00 km upstream followed by a 1.00-km trip downstream?

ANSWER: 208 s POINTS: 2 DIFFICULTY: Average REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 13. A speedy tortoise can run with a velocity of 10.0 cm/s and a hare can run 20.0 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.00 minutes. The tortoise wins by a shell (20.0 cm). What was the length of the race?

ANSWER: 12.6 m POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.1 Velocity and Speed of a Particle HAS VARIABLES: False 14. A problem may be solved more easily when alternative representations are used. The best strategy is to formulate representations in an order that assists in understanding the physical principles involved. Of the orders given below, the one that will work best most often is a. pictorial representation, mathematical representation, tabular representation, mental representation. b. pictorial representation, mental representation, mathematical representation, tabular representation. c. mathematical representation, pictorial representation, tabular representation, mental representation.

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d. mathematical representation, tabular representation, mental representation, pictorial representation. e. mental representation, pictorial representation, tabular representation, mathematical representation.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.4 The Analysis Model Approach to Problem-Solving HAS VARIABLES: False 15. A bullet is fired through a board, 14.0 cm thick, with its line of motion perpendicular to the face of the board. If it enters with a speed of 450 m/s and emerges with a speed of 220 m/s, what is the bullet's acceleration as it passes through the board? a. −500 km/s2 b. −550 km/s2 c. −360 km/s2 d. −520 km/s2 e. −275 km/s2 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.5 Acceleration HAS VARIABLES: False 2

3

16. The position of a particle moving along the x axis is given by x = 6.0t − 1.0t , where x is in meters and t in seconds.

What is the position of the particle when it achieves its maximum speed in the positive x direction? a. 24 m b. 12 m c. 32 m d. 16 m e. 2.0 m ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.5 Acceleration HAS VARIABLES: False 3

17. The velocity of a particle moving along the x axis is given for t > 0 by vx = (32.0t − 2.00t ) m/s, where t is in s. What is the acceleration of the particle when (after t = 0) it achieves its maximum displacement in the positive x direction? a. −64.0 m/s2 b. zero c. 128 m/s2 d. 32.0 m/s2 e. −32.0 m/s2 ANSWER: POINTS:

a 3

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DIFFICULTY: Challenging REFERENCES: 3.5 Acceleration HAS VARIABLES: False 3

2

18. The position of a particle as it moves along the x axis is given for t > 0 by x = (t − 3t + 6t) m, where t is in s. Where is the particle when it achieves its minimum speed (after t = 0)? a. 3 m b. 4 m c. 8 m d. 2 m e. 7 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 3.5 Acceleration HAS VARIABLES: False 19. The position of a particle as it moves along the x axis is given by x = 15e of the particle at t = 1.0 s? a. 22 m/s b. 60 m/s c. 8.1 m/s d. 15 m/s e. 35 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 3.5 Acceleration HAS VARIABLES: False

−2t

m, where t is in s. What is the acceleration

3

20. A particle moving along the x axis has a position given by x = (24t – 2.0t ) m, where t is measured in s. What is the magnitude of the acceleration of the particle at the instant when its velocity is zero? a. 24 m/s2 b. zero c. 12 m/s2 d. 48 m/s2 e. 36 m/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 3.5 Acceleration HAS VARIABLES: False 21. At t = 0, a particle is located at x = 25 m and has a velocity of 15 m/s in the positive x direction. The acceleration of the particle varies with time as shown in the diagram. What is the velocity of the particle at t = 5.0 s?

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a. +15 m/s b. −15 m/s c. +30 m/s d. 0 e. −1.2 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 3.5 Acceleration HAS VARIABLES: False 22. At t = 0, a particle is located at x = 25 m and has a velocity of 15 m/s in the positive x direction. The acceleration of the particle varies with time as shown in the diagram. What is the position of the particle at t = 5.0 s?

a. 175 m b. 125 m c. 138 m d. 154 m e. 165 m ANSWER: POINTS: DIFFICULTY: REFERENCES:

d 3 Challenging 3.5 Acceleration

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HAS VARIABLES: False 23. The area under a graph of ax vs. t from t = ti to t = tf represents a. xf − xi. b. vf − vi. c. xavg. d. vavg. e. aavg.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.5 Acceleration HAS VARIABLES: False 2

24. A particle is moving with a constant acceleration of 4.0 m/s . Its speed at t = 1.0 s is 4.0 m/s and at t = 3.0 s it is 12.0 m/s. What is the area under the position-time graph for the interval from t = 1.0 s to t = 3.0 s? a. 8.0 m/s b. 8.0 m c. 12 m d. 16 m e. 16 m/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 3.5 Acceleration HAS VARIABLES: False 25. The position of an object at equal time intervals is shown below:

Which graph below correctly represents position versus time for this object? a. b. c.

d.

ANSWER: POINTS: DIFFICULTY:

e.

e 1 Easy

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REFERENCES: 3.6 Motion Diagrams HAS VARIABLES: False 26. Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below.

Which statement is correct?

a. A has the greatest speed and the greatest acceleration. b. C has decreasing speed. c. D slows down and then speeds up. d. D speeds up and then slows down. e. E has a greater speed than A. ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 3.6 Motion Diagrams HAS VARIABLES: False 27. The small circles in the diagram below represent the positions along the x axis of a body at equal time intervals.

Assume the body moves in a straight line.

This diagram is most likely to describe a. a swimmer swimming laps. b. an exercise on a rowing machine. c. a person on a treadmill. d. a tennis ball during a volley. e. a runner who tripped, fell, rose, and continued racing.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 3.6 Motion Diagrams HAS VARIABLES: False 28. A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5-s time interval. The velocity of the particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this time interval? a. 0.48 m/s2 b. 0.32 m/s2 c. 0.64 m/s2 d. 0.80 m/s2 e. 0.57 m/s2 ANSWER:

b

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POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 6

12

29. A proton moving along the x axis has an initial velocity of 4.0 × 10 m/s and a constant acceleration of 6.0 × 10 2 m/s . What is the velocity of the proton after it has traveled a distance of 80 cm? a. 5.1 × 106 m/s b. 6.3 × 106 m/s c. 4.8 × 106 m/s d. 3.9 × 106 m/s e. 2.9 × 106 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False

30. A particle moving with a constant acceleration has a velocity of 20 cm/s when its position is x = 10 cm. Its position 7.0 s later is x = −30 cm. What is the acceleration of the particle? a. −7.3 cm/s2 b. −8.9 cm/s2 c. −11 cm/s2 d. −15 cm/s2 e. −13 cm/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 31. An automobile moving along a straight track changes its velocity from 40 m/s to 80 m/s in a distance of 200 m. What is the (constant) acceleration of the vehicle during this time? a. 8.0 m/s b. 9.6 m/s c. 12 m/s d. 6.9 m/s e. 0.20 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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32. In 2.0 s, a particle moving with constant acceleration along the x axis goes from x = 10 m to x = 50 m. The velocity at the end of this time interval is 10 m/s. What is the acceleration of the particle? a. +15 m/s2 b. +20 m/s2 c. −20 m/s2 d. −10 m/s2 e. −15 m/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 33. An automobile manufacturer claims that its product will, starting from rest, travel 0.40 km in 9.0 s. What is the magnitude of the constant acceleration required to do this? a. 9.9 m/s2 b. 8.9 m/s2 c. 6.6 m/s2 d. 5.6 m/s2 e. 4.6 m/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 34. An automobile traveling along a straight road increases its speed from 30.0 m/s to 50.0 m/s in a distance of 180 m. If the acceleration is constant, how much time elapses while the auto moves this distance? a. 6.00 s b. 4.50 s c. 3.60 s d. 4.00 s e. 9.00 s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 35. An object moving on the x axis with a constant acceleration increases its x coordinate by 80 m in a time of 5.0 s and has a velocity of +20 m/s at the end of this time. Determine the acceleration of the object during this motion. a. −1.6 m/s2 b. +6.4 m/s2 c. +1.6 m/s2 Copyright Cengage Learning. Powered by Cognero.

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d. −2.0 m/s2 e. −6.4 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 36. An electron, starting from rest and moving with a constant acceleration, travels 2.0 cm in 5.0 ms. What is the magnitude of this acceleration? a. 2.5 km/s2 b. 0.80 km/s2 c. 1.6 km/s2 d. 1.3 km/s2 e. 3.2 km/s2 ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 2

37. A particle starts from rest at xi = 0 and moves for 10 s with an acceleration of +2.0 cm/s . For the next 20 s, the 2 acceleration of the particle is −1.0 cm/s . What is the position of the particle at the end of this motion? a. zero b. +3.0 m c. −1.0 m d. +2.0 m e. −3.0 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 38. When Jim and Rob ride bicycles, Jim can only accelerate at three-quarters the acceleration of Rob. Both start from rest at the bottom of a long, straight road with constant upward slope. If Rob takes 5.0 minutes to reach the top, how much earlier should Jim start in order to reach the top at the same time as Rob? a. 25 s b. 40 s c. 46 s d. 55 s e. 75 s ANSWER: c POINTS: 3 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Challenging REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 39. When starting from rest at the bottom of a straight road with constant upward slope, Joan bicycles to the top 50.0 s ahead of Sally, whose travel time is 5.00 minutes. What is the ratio of Joan's acceleration to Sally's acceleration? a. 0.694 b. 0.833 c. 1.20 d. 1.44 e. 6.00 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 40. Two identical balls are at rest side by side at the bottom of a hill. Some time after ball A is kicked up the hill, ball B is given a kick up the hill. Ball A is headed downhill when it passes ball B headed up the hill. At the instant when ball A passes ball B, a. it has the same position and velocity as ball B. b. it has the same position and acceleration as ball B. c. it has the same velocity and acceleration as ball B. d. it has the same displacement and velocity as ball B. e. it has the same position, displacement and velocity as ball B. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 41. Two identical balls are at rest and side by side at the top of a hill. You let one ball, A, start rolling down the hill. A little later you start the second ball, B, down the hill by giving it a shove. The second ball rolls down the hill along a line parallel to the path of the first ball and passes it. At the instant ball B passes ball A: a. it has the same position and the same velocity as A. b. it has the same position and the same acceleration as A. c. it has the same velocity and the same acceleration as A. d. it has the same displacement and the same velocity as A. e. it has the same position, displacement, and velocity as A. ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 42. The graph below shows the velocity-versus-time graph for a ball. Which explanation best fits the motion of the ball as shown by the graph?

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a. The ball is falling, is caught, and is thrown down with greater velocity. b. The ball is rolling, stops, and then continues rolling. c. The ball is rising, hits the ceiling, and falls down. d. The ball is falling, hits the floor, and bounces up. e. The ball is rising, is caught, and then is thrown down.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False

43. The equation that solves a problem is

. The problem is:

a. What is the initial velocity of a car that goes from rest to 18 m/s in 3.0 s? b. What is the final velocity of a car that goes from rest to 18 m/s in 3.0 s? c. What is the initial velocity of a car that accelerates at 18 m/s for 3.0 s? d. What is the final velocity of a car that accelerates at 3.0 m/s2 over a 6.0-m distance? e. What is the final velocity of a car that accelerates at 3.0 m/s2 over a 3.0-m distance?

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False

44. The equation that solves a problem is

. The problem is:

a. How far above its initial position does a rock travel in 2.0 s when thrown up from a point 40 m above the ground? b. How far below its initial position does a rock travel in 2.0 s when thrown up from a point 40 m above the ground? c. What is the position relative to the ground of a rock thrown up at 3.0 m/s from a roof 20 m above the ground 2.0 s after it is released? d. What is the change in position relative to the ground of a rock thrown up at 3.0 m/s from a roof 20 m above the ground 2.0 s after it is released? e. What is the position relative to the ground of a rock thrown up at 3.0 m/s from a roof 20 m above the ground if its maximum height is 33.6 m?

ANSWER: c POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 45. Dallas says that any change in velocity is directly proportional to the time interval over which the change took place.

Dana says that is true only when the acceleration is constant. Which one, if either, is correct? a. Dana, because it is true only when the acceleration is constant. b. Dallas, because we can define ax, avg so that Δvx = ax, avgΔt. c.

Dallas, because ax, avg is always equal to

.

d. All the above are correct. e. Only (a) and (b) above are correct.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 46. Driver A is cruising along enjoying the fall colors. Driver B starts driving her car at the instant he passes her. Their velocities are shown as functions of time in the graph below. At what instants in time on the graph are drivers A and B side by side?

a. 0 s, 2 s b. 0 s, 4 s c. 2 s, 4 s d. 2 s, 6 s e. 4 s, 6 s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 47. Cart A, of mass m, starts from rest and travels in a straight line with acceleration a. It traverses a distance x in time t.

Cart B, of mass 4m, starts from rest and travels in a straight line with acceleration

. At time t it has traversed the

distance

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a. . b. . c. x. d. 2x. e. 4x.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 48. Cart A, of mass m, starts from rest and travels in a straight line with acceleration a. It reaches velocity v in time t. Cart B, of mass 4m, starts from rest and travels in a straight line with acceleration

. At time t it has reached velocity

a. . b. . c. v. d. 2v. e. 4v.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 2

49. The speed of an object is given by v = 5.00t + 4.00t, where v is in m/s and t is in s. What is the acceleration of the object at t = 2.00 s? a. 5.00 m/s2 b. 9.00 m/s2 c. 10.0 m/s2 d. 14.0 m/s2 e. 24.0 m/s2 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 50. A 50-gram superball traveling at 25.0 m/s is bounced off a brick wall and rebounds at 22.0 m/s. A high-speed camera Copyright Cengage Learning. Powered by Cognero.

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records this event. If the ball is in contact with the wall for 3.50 ms, what is the average acceleration of the ball during this time interval?

2 ANSWER: 13 400 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 51. A bicyclist starts down a hill with an initial speed of 2.0 m/s. She moves down the hill with a constant acceleration, arriving at the bottom of the hill with a speed of 8.0 m/s. If the hill is 12 m long, how long did it take the bicyclist to travel down the hill?

ANSWER: 2.4 s POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 52. A helicopter descends from a height of 600 m with uniform negative acceleration, reaching the ground and coming to rest in 5.00 minutes. Determine the acceleration of the helicopter and its initial velocity.

2 ANSWER: −0.013 3 m/s , −4.0 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 53. A peregrine falcon dives at a pigeon. The falcon starts with zero downward velocity and falls with the acceleration of gravity. If the pigeon is 76.0 m below the initial height of the falcon, how long does it take the falcon to intercept the pigeon?

ANSWER: 3.94 s POINTS: 2 DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 2

54. Starting from rest, a car travels 1 350 meters in 1.00 minute. It accelerated at 1.0 m/s until it reached its cruising speed. Then it drove the remaining distance at constant velocity. What was its cruising speed?

ANSWER: 30 m/s POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 55. A car originally traveling at 30 m/s manages to brake for 5.0 seconds while traveling 125 m downhill. At that point the brakes fail. After an additional 5.0 seconds, it travels an additional 150 m down the hill. What was the acceleration of the car after the brakes failed?

2 ANSWER: 4.0 m/s POINTS:

2

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DIFFICULTY: Average REFERENCES: 3.7 Analysis Model: Particle Under Constant Acceleration HAS VARIABLES: False 2

56. A rocket, initially at rest, is fired vertically with an upward acceleration of 10 m/s . At an altitude of 0.50 km, the engine of the rocket cuts off. What is the maximum altitude it achieves? a. 1.9 km b. 1.3 km c. 1.6 km d. 1.0 km e. 2.1 km ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 57. A ball is thrown vertically upward with an initial speed of 20 m/s. Two seconds later, a stone is thrown vertically (from the same initial height as the ball) with an initial speed of 24 m/s. At what height above the release point will the ball and stone pass each other? a. 17 m b. 21 m c. 18 m d. 27 m e. 31 m ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 58. An object is thrown vertically and has an upward velocity of 18 m/s when it reaches one fourth of its maximum height above its launch point. What is the initial (launch) speed of the object? a. 35 m/s b. 25 m/s c. 30 m/s d. 21 m/s e. 17 m/s ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 59. A stone is thrown from the top of a building with an initial velocity of 20 m/s downward. The top of the building is 60 m above the ground. How much time elapses between the instant of release and the instant of impact with the ground? a. 2.0 s Copyright Cengage Learning. Powered by Cognero.

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b. 6.1 s c. 3.5 s d. 1.6 s e. 1.0 s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 60. An object is thrown downward with an initial (t = 0) speed of 10 m/s from a height of 60 m above the ground. At the same instant (t = 0), a second object is propelled vertically upward from ground level with a speed of 40 m/s. At what height above the ground will the two objects pass each other? a. 53 m b. 41 m c. 57 m d. 46 m e. 37 m ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 2

61. A toy rocket, launched from the ground, rises vertically with an acceleration of 20 m/s for 6.0 s until its motor stops.

Disregarding any air resistance, what maximum height above the ground will the rocket achieve? a. 1.1 km b. 0.73 km c. 1.9 km d. 0.39 km e. 1.5 km ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 62. A rock is thrown downward from an unknown height above the ground with an initial speed of 10 m/s. It strikes the ground 3.0 s later. Determine the initial height of the rock above the ground. a. 44 m b. 14 m c. 74 m d. 30 m e. 60 m ANSWER: c POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 63. A ball thrown vertically from ground level is caught 3.0 s later when it is at its highest point by a person on a balcony which is 14 m above the ground. Determine the initial speed of the ball. a. 19 m/s b. 4.7 m/s c. 10 m/s d. 34 m/s e. 17 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 64. An object is thrown vertically upward such that it has a speed of 25 m/s when it reaches two-thirds of its maximum height above the launch point. Determine this maximum height. a. 64 m b. 48 m c. 32 m d. 96 m e. 75 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 65. The velocity at the midway point of a ball able to reach a height y when thrown with velocity vi at the origin is: a.

b. c.

d. e. gy ANSWER: POINTS: DIFFICULTY: REFERENCES:

c 2 Average 3.8 Freely Falling Objects

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HAS VARIABLES: False 66. A boy on a skateboard skates off a horizontal bench at a velocity of 10 m/s. One-tenth of a second after he leaves the bench, to two significant figures, the magnitudes of his velocity and acceleration are a. 10 m/s; 9.8 m/s2. b. 9.0 m/s; 9.8 m/s2. c. 9.0 m/s; 9.0 m/s2. d. 1.0 m/s; 9.0 m/s2. e. 1.0 m/s; 9.8 m/s2.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 67. A juggler throws two balls to the same height so that one is at the halfway point going up when the other is at the halfway point coming down. At that point a. their velocities and accelerations are equal. b. their velocities are equal but their accelerations are equal and opposite. c. their accelerations are equal but their velocities are equal and opposite. d. their velocities and accelerations are both equal and opposite. e. their velocities are equal to their accelerations.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False 68. A skier leaves a ski jump with a horizontal velocity of 29.4 m/s. The instant before she lands three seconds later, the magnitudes of the horizontal and vertical components of her velocity are a. 0; 29.4 m/s. b. 29.4 m/s; 0. c. 29.4 m/s; 29.4 m/s. d. 29.4 m/s; 41.6 m/s. e. 41.6 m/s; 41.6 m/s.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 3.8 Freely Falling Objects HAS VARIABLES: False

1. The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by

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and

.

The magnitude, in meters, of the plane's displacement from the origin is a. 9.14 × 103. b. 1.61 × 104. c. 1.84 × 104. d. 9.14 × 103t. e. 1.61 × 104t.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 2. A tennis player wants to slam a serve at O so that the ball lands just inside the opposite corner of the court. What should the ratio

be for the initial velocity

? The time t = 0 is the time when the ball is hit by the racket.

a. W/L b. L/W c. d. e.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 3. The position of an object is given by magnitude of the particle’s acceleration? a. 0 m/s2

, where t is in seconds. At t = 2.0 s, what is the

b. 2.0 m/s2 c. 17 m/s2 Copyright Cengage Learning. Powered by Cognero.

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d. 36 m/s2 e. 72 m/s2 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 4. The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by and

.

The plane is most likely a. just touching down. b. in level flight in the air. c. ascending. d. descending. e. taking off.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 5. The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by and

.

The plane is most likely a. just touching down. b. in level flight in the air. c. ascending. d. descending. e. taking off.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 6. The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by Copyright Cengage Learning. Powered by Cognero.

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and

.

The plane is most likely a. just touching down. b. in level flight in the air. c. ascending. d. descending. e. taking off.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 7. The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by and

.

The plane is most likely a. just touching down. b. in level flight in the air. c. ascending. d. descending. e. taking off.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 8. Car A leaves point O at t = 0 and travels a quarter circle counterclockwise at 30.0 m/s to point P. Car B will leave point O and travel to point P at the same speed but in a straight line. The radius of the circle is 100 m. At what time should car B leave point O in order to arrive at point P at the same time as car A? a. At t = 0. b. At t = 0.52 s. c. At t = 4.71 s. d. At t = 4.98 s. e. At t = 5.24 s.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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9. In a location where the train tracks run parallel to a road, a high-speed train traveling at 60 m/s passes a car traveling at 30 m/s. How long does it take for the train to be 180 m ahead of the car? a. 2.0 s b. 3.0 s c. 6.0 s d. 9.0 s e. 18.0 s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 10. In a location where the train tracks run parallel to a road, a high-speed train traveling at 60 m/s passes a car traveling at 30 m/s in the opposite direction. How long does it take for the train to be 180 m away from the car? a. 2.0 s b. 3.0 s c. 6.0 s d. 9.0 s e. 18.0 s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False Exhibit 4-2 Newton approximated motion in a circle as a series of linear motions, as in the polygon below.

Assume that the particle moves at constant speed vA from A to B, and at constant speed vB from B to C. Use this exhibit to answer the following question(s).

11. Refer to Exhibit 4-2. The direction of the change in velocity, a. b.

, at point B, is shown by which arrow?

c. d. e.

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ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 12. Refer to Exhibit 4-2. The direction of the acceleration, a. b.

, at point B, is shown by which arrow?

c. d. e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 13. A car is driven 1 200 m north at 20.0 m/s and then driven 1 600 m east at 25.0 m/s. What are the magnitude and direction of the displacement for this trip? a. 1 400 m, northeast b. 2 000 m, 36.9° north of east c. 2 000 m, 53.1° north of east d. 2 800 m, 36.9° east of north e. 2 800 m, 53.1° east of north ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors HAS VARIABLES: False 14. A car is driven 1 200 m north at 20.0 m/s and then driven 1 600 m east at 25.0 m/s. What is the magnitude of the average velocity for this trip? a. 16.1 m/s b. 22.6 m/s c. 31.3 m/s d. 11.3 m/s e. 62.2 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 4.1 The Position, Velocity, and Acceleration Vectors Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 15. At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane 2 with a constant acceleration of (2.0i − 4.0j) m/s . At the instant the x coordinate of the particle is 15 m, what is the speed of the particle? a. 10 m/s b. 16 m/s c. 12 m/s d. 14 m/s e. 26 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 4.2 Two-Dimensional Motion with Constant Acceleration HAS VARIABLES: False 16. A particle starts from the origin at t = 0 with a velocity of 6.0 m/s and moves in the xy plane with a constant 2

acceleration of (−2.0 + 4.0 ) m/s . At the instant the particle achieves its maximum positive x coordinate, how far is it from the origin? a. 36 m b. 20 m c. 45 m d. 27 m e. 37 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 4.2 Two-Dimensional Motion with Constant Acceleration HAS VARIABLES: False 17. A particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and moves in the xy plane with a 2

constant acceleration of (3.0 − 2.0 ) m/s . At the instant the particle moves back across the x axis (y = 0), what is the value of its x coordinate? a. 65 m b. 91 m c. 54 m d. 78 m e. 86 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.2 Two-Dimensional Motion with Constant Acceleration HAS VARIABLES: False 18. At t = 0, a particle leaves the origin with a velocity of 5.0 m/s in the positive y direction. Its acceleration is given by Copyright Cengage Learning. Powered by Cognero.

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2

= (3.0 − 2.0 ) m/s . At the instant the particle reaches its maximum y coordinate, how far is the particle from the origin? a. 11 m b. 16 m c. 22 m d. 29 m e. 19 m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 4.2 Two-Dimensional Motion with Constant Acceleration HAS VARIABLES: False 19. A particle moves in the xy plane with a constant acceleration given by

. At t = 0, its position and

velocity are 10 m and , respectively. What is the distance from the origin to the particle at t = 2.0 s? a. 6.4 m b. 10 m c. 8.9 m d. 2.0 m e. 6.2 m ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 4.2 Two-Dimensional Motion with Constant Acceleration HAS VARIABLES: False 20. A particle starts from the origin at t = 0 with a velocity of (16 − 12 ) m/s and moves in the xy plane with a constant 2

acceleration of = (3.0 − 6.0 ) m/s . What is the speed of the particle at t = 2.0 s? a. 52 m/s b. 39 m/s c. 46 m/s d. 33 m/s e. 43 m/s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.2 Two-Dimensional Motion with Constant Acceleration HAS VARIABLES: False 21. At t = 0, a particle leaves the origin with a velocity of 12 m/s in the positive x direction and moves in the xy plane with a constant acceleration of

. At the instant the y coordinate of the particle is 18 m, what is the x

coordinate of the particle? a. 30 m b. 21 m Copyright Cengage Learning. Powered by Cognero.

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c. 27 m d. 24 m e. 45 m ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.2 Two-Dimensional Motion with Constant Acceleration HAS VARIABLES: False 22. The initial speed of a cannon ball is 0.20 km/s. If the ball is to strike a target that is at a horizontal distance of 3.0 km from the cannon, what is the minimum time of flight for the ball? a. 16 s b. 21 s c. 24 s d. 14 s e. 19 s ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 23. A ball is thrown horizontally from the top of a building 0.10 km high. The ball strikes the ground at a point 65 m horizontally away from and below the point of release. What is the speed of the ball just before it strikes the ground? a. 43 m/s b. 47 m/s c. 39 m/s d. 36 m/s e. 14 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 24. A baseball is hit at ground level. The ball is observed to reach its maximum height above ground level 3.0 s after being hit. And 2.5 s after reaching this maximum height, the ball is observed to barely clear a fence that is 97.5 m from where it was hit. How high is the fence? a. 8.2 m b. 15.8 m c. 13.5 m d. 11.0 m e. 4.9 m ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 25. A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the horizontal. The rock strikes the ground a horizontal distance of 25 m from the base of the building. Assume that the ground is level and that the side of the building is vertical. How tall is the building? a. 25.3 m b. 29.6 m c. 27.4 m d. 23.6 m e. 18.9 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 26. A projectile is thrown from the top of a building with an initial velocity of 30 m/s in the horizontal direction. If the top of the building is 30 m above the ground, how fast will the projectile be moving just before it strikes the ground? a. 35 m/s b. 39 m/s c. 31 m/s d. 43 m/s e. 54 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 27. A rifle is aimed horizontally at the center of a large target 60 m away. The initial speed of the bullet is 240 m/s. What is the distance from the center of the target to the point where the bullet strikes the target? a. 48 cm b. 17 cm c. 31 cm d. 69 cm e. 52 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 28. A rock is thrown from the edge of the top of a 100-ft tall building at some unknown angle above the horizontal. The rock strikes the ground a horizontal distance of 160 ft from the base of the building 5.0 s after being thrown. Assume that the ground is level and that the side of the building is vertical. Determine the speed with which the rock was thrown. a. 72 ft/s Copyright Cengage Learning. Powered by Cognero.

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b. 77 ft/s c. 68 ft/s d. 82 ft/s e. 87 ft/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 29. An airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m. Assume that the ground is level. At what horizontal distance from a target must the pilot release a care package so as to hit a target? a. 3.0 km b. 2.4 km c. 3.3 km d. 2.7 km e. 1.7 km ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 30. Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant. A glob of dough flies off each beater. Each glob lands on the top of a tin the same horizontal distance away and at its initial height.

However, one lands later than the other. The explanation is that they left the beaters at angles θ1 and θ2 such that: a. θ2 = −θ1. b. c.

θ1 + θ2 =

.

θ1 + θ2 =

.

d. θ1 + θ2 = π. e. θ1 − θ2 = π.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 31. Two balls, projected at different times so they don't collide, have trajectories A and B, as shown below.

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Which statement is correct? a. v0B must be greater than v0A. b. Ball A is in the air for a longer time than ball B. c. Ball B is in the air for a longer time than ball A. d. Ball B has a greater acceleration than ball A. e. Ball A has a greater acceleration than ball B. ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 32. The vector indicates the instantaneous displacement of a projectile from the origin. At the instant when the projectile is at , its velocity and acceleration vectors are and . Which statement is correct? a. is always perpendicular to . b.

is always perpendicular to

.

c.

is always perpendicular to

.

d.

is always perpendicular to

.

e.

is always perpendicular to

.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 33. A projectile starts at the coordinate origin, where the displacement vector also originates. The initial velocity, v0, makes an angle θ0 with the horizontal, where 0 < θ0 < 90°. At the instant when the projectile is at the highest point of its trajectory, the displacement, velocity, and acceleration vectors are , and . Which statement is true? a. is parallel to . b.

is perpendicular to

c.

is parallel to

d.

is perpendicular to

.

. .

e.

is perpendicular to .

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.3 Projectile Motion Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 34. With the x axis horizontal and the y axis vertically upward, the change in the horizontal component of velocity, Δvx, and the change in the vertical component of velocity, Δvy, of a projectile are related to the time since leaving the barrel, Δt, as a. Δvx = 0; Δvy = 0. b. Δvx = gΔt; Δvy = 0. c. Δvx = 0; Δvy = gΔt. d. Δvx = 0; Δvy = −gΔt. e. Δvx = gΔt; Δvy = −gΔt.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 35. Which of the following quantities is directly proportional to the time interval after a projectile has left the barrel that shot it out? The x axis is horizontal; the y axis is vertically upward. a. b. Δay c. Δy d. e. Δvy ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 36. A block is supported on a compressed spring, which projects the block straight up in the air at velocity

. The

spring and ledge it sits on then retract. You can win a prize by hitting the block with a ball. When should you throw the ball and in what direction to be sure the ball hits the block? (Assume the ball can reach the block before the block reaches the ground and that the ball is thrown from a height equal to the release position of the block.) a. At the instant when the block leaves the spring, directed at the block. b. At the instant when the block leaves the spring, directed at the spring. c. At the instant when the block is at the highest point, directed at the block. d. At the instant when the block is at the highest point, directed at the spring. e. When the block is back at the spring's original position, directed at that position.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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37. Given the equations below, which description best fits the physical situation?

a. A projectile's displacement two seconds after being fired upward with a speed of 30.0 m/s. b. A projectile's displacement two seconds after being fired upward with a speed of 40.0 m/s. c. A projectile's displacement two seconds after being fired upward with a speed of 50.0 m/s. d. A projectile's displacement two seconds after being fired upward with a speed of 60.0 m/s. e. A projectile's displacement two seconds after being fired upward with a speed of 80.0 m/s.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 38. Given the equations below, which description best fits the physical situation?

a. A projectile's displacement two seconds after being fired downward with a speed of 30.0 m/s. b. A projectile's displacement two seconds after being fired downward with a speed of 40.0 m/s. c. A projectile's displacement two seconds after being fired downward with a speed of 50.0 m/s. d. A projectile's displacement two seconds after being fired downward with a speed of 60.0 m/s. e. A projectile's displacement two seconds after being fired downward with a speed of 80.0 m/s.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 39. A motorcycle daredevil wants to ride up a 50.0-m ramp set at a 30.0° incline to the ground. It will launch him in the air and he wants to come down so he just misses the last of a number of 1.00-m diameter barrels. If the speed at the instant when he leaves the ramp is 60.0 m/s, how many barrels can be used? a. 79 b. 318 c. 332 d. 355 e. 402 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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40. Wiley Coyote has missed the elusive roadrunner once again. This time, he leaves the edge of the cliff at 50.0 m/s horizontal velocity. If the canyon is 100 m deep, how far from the edge of the cliff does the coyote land?

ANSWER: 226 m POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 41. A track star in the broad jump goes into the jump at 12 m/s and launches himself at 20° above the horizontal. How long is he in the air before returning to Earth?

ANSWER: 0.84 s POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 42. An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. It explodes on a mountainside 42.0 s after firing. If x is horizontal and y vertical, find the (x, y) coordinates where the shell explodes.

ANSWER: 7.22 km, 1.68 km POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 43. A football is thrown upward at a 30.0° angle to the horizontal. To throw a 40.0-m pass, what must be the initial speed of the ball?

ANSWER: 21.3 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 44. A tennis player standing 12.6 m from the net hits the ball at 3.00° above the horizontal. To clear the net, the ball must rise at least 0.330 m. If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racket?

ANSWER: 48.6 m/s POINTS: 3 DIFFICULTY: Challenging REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False 45. A rifle is aimed horizontally toward the center of a target 0.10 km away, but the bullet strikes 10 cm below the center.

Calculate the velocity of the bullet just as it emerges from the rifle.

ANSWER: 700 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 4.3 Projectile Motion HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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46. An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m. What is the magnitude of the instantaneous acceleration of the particle during this time? a. 2.2 m/s2 b. 2.7 m/s2 c. 3.3 m/s2 d. 3.8 m/s2 e. 4.4 m/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 4.4 Analysis Model: Particle in Uniform Circular Motion HAS VARIABLES: False 47. A particle moves at a constant speed in a circular path with a radius of 2.06 cm. If the particle makes four revolutions each second, what is the magnitude of its acceleration? a. 20 m/s2 b. 18 m/s2 c. 13 m/s2 d. 15 m/s2 e. 24 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.4 Analysis Model: Particle in Uniform Circular Motion HAS VARIABLES: False 48. A race car moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s. What is the magnitude of the acceleration of the race car? a. 8.8 m/s2 b. 7.5 m/s2 c. 9.4 m/s2 d. 6.3 m/s2 e. 5.3 m/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 4.4 Analysis Model: Particle in Uniform Circular Motion HAS VARIABLES: False 49. At the lowest point in a vertical dive (radius = 0.58 km), an airplane has a speed of 300 km/h which is not changing.

Determine the magnitude of the acceleration of the pilot at this lowest point. a. 26 m/s2 Copyright Cengage Learning. Powered by Cognero.

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b. 21 m/s2 c. 16 m/s2 d. 12 m/s2 e. 8.8 m/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.4 Analysis Model: Particle in Uniform Circular Motion HAS VARIABLES: False 50. A carnival Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute. What is the acceleration of a passenger at his lowest point during the ride? a. 5.7 m/s2 downward b. 4.1 m/s2 upward c. 14 m/s2 downward d. 4.1 m/s2 downward e. 19 m/s2 downward ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 4.4 Analysis Model: Particle in Uniform Circular Motion HAS VARIABLES: False 51. A space station of diameter 80 m is turning about its axis at a constant rate. If the acceleration of the outer rim of the 2 station is 2.5 m/s , what is the period of revolution of the space station? a. 22 s b. 19 s c. 25 s d. 28 s e. 40 s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.4 Analysis Model: Particle in Uniform Circular Motion HAS VARIABLES: False 52. A car travels counterclockwise around a flat circle of radius 0.25 km at a constant speed of 20 m/s. When the car is at point A as shown in the figure, what is the car's acceleration?

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a. 1.6 m/s2, south b. Zero c. 1.6 m/s2, east d. 1.6 m/s2, north e. 1.6 m/s2, west ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.4 Analysis Model: Particle in Uniform Circular Motion HAS VARIABLES: False 53. Two cars are traveling around identical circular racetracks. Car A travels at a constant speed of 20 m/s. Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s. When car B has the same (tangential) velocity as car A, it is always true that a. it is passing car A. b. it has the same linear (tangential) acceleration as car A. c. it has the same centripetal acceleration as car A. d. it has the same total acceleration as car A. e. it has traveled farther than car A since starting.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.4 Analysis Model: Particle in Uniform Circular Motion HAS VARIABLES: False 2

54. A satellite is in a circular orbit 600 km above the Earth's surface. The acceleration of gravity is 8.21 m/s at this altitude. The radius of the Earth is 6 400 km. Determine the speed of the satellite, and the time to complete one orbit around the Earth.

ANSWER: 7580 m/s, 5 800 s POINTS: 2 DIFFICULTY: Average REFERENCES: 4.4 Analysis Model: Particle in Uniform Circular Motion HAS VARIABLES: False 55. A particle moves along a circular path having a radius of 2.0 m. At an instant when the speed of the particle is equal to 2 3.0 m/s and changing at the rate of 5.0 m/s , what is the magnitude of the total acceleration of the particle? a. 7.5 m/s2 Copyright Cengage Learning. Powered by Cognero.

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b. 6.0 m/s2 c. 5.4 m/s2 d. 6.7 m/s2 e. 4.5 m/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.5 Tangential and Radial Acceleration HAS VARIABLES: False 56. A car travels in a flat circle of radius R. At a certain instant, the velocity of the car is 20 m/s north, and the total 2 acceleration of the car is 2.5 m/s 37° south of west. Which of the following is correct? a. R = 0.40 km, and the car's speed is decreasing. b. R = 0.20 km, and the car's speed is decreasing. c. R = 0.20 km, and the car's speed is increasing. d. R = 0.16 km, and the car's speed is increasing. e. R = 0.16 km, and the car's speed is decreasing.

ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 4.5 Tangential and Radial Acceleration HAS VARIABLES: False 57. A car travels in a flat circle of radius R. At a certain instant, the velocity of the car is 24 m/s west, and the total 2 acceleration of the car is 2.5 m/s 53° north of west. Which of the following is correct? a. R = 0.29 km, and the car's speed is increasing. b. R = 0.23 km, and the car's speed is decreasing. c. R = 0.23 km, and the car's speed is increasing. d. R = 0.29 km, and the car's speed is decreasing. e. R = 0.29 km, and the car's speed is constant.

ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 4.5 Tangential and Radial Acceleration HAS VARIABLES: False 58. A stunt pilot performs a circular dive of radius 800 m. At the bottom of the dive (point B in the figure) the pilot has a 2 speed of 200 m/s, which at that instant is increasing at a rate of 20 m/s . What acceleration does the pilot have at point B?

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a. (50i + 20j) m/s2 b. (20i − 50j) m/s2 c. (20i + 50j) m/s2 d. (−20i + 50j) m/s2 e. (−50i + 20j) m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.5 Tangential and Radial Acceleration HAS VARIABLES: False 2

59. The speed of a particle moving in a circle 2.0 m in radius increases at the constant rate of 4.4 m/s . At an instant when 2 the magnitude of the total acceleration is 6.0 m/s , what is the speed of the particle? a. 3.9 m/s b. 2.9 m/s c. 3.5 m/s d. 3.0 m/s e. 1.4 m/s ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 4.5 Tangential and Radial Acceleration HAS VARIABLES: False 60. A car travels in a flat circle of radius R. At a certain instant, the velocity of the car is 24 m/s west, and the acceleration 2 2 of the car has components of 2.4 m/s east and 1.8 m/s south. What is the radius of the circle? a. 0.24 km b. 0.19 km c. 0.32 km d. 0.14 km e. 0.27 km ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.5 Tangential and Radial Acceleration Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 61. A particle moves in the xy plane in a circle centered on the origin. At a certain instant, the velocity and acceleration of 2

the particle are 6.0 m/s and (3.0 + 4.0 ) m/s . What are the x and y coordinates of the particle at this moment? a. x = 0, y = −9.0 m b. x = 0, y = +7.2 m c. x = 0, y = +9.0 m d. x = 0, y = −7.2 m e. x = 6.0 m, y = −9.0 m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 4.5 Tangential and Radial Acceleration HAS VARIABLES: False 62. A particle moves in the xy plane in a circle centered on the origin. At a certain instant, the velocity and acceleration of 2

the particle are 4.0 m/s and (−3.0 − 2.0 ) m/s . What are the x and y coordinates of the particle at this moment? a. x = −4.4 m, y = 0 b. x = +5.3 m, y = 0 c. x = −5.3 m, y = 0 d. x = +4.4 m, y = 0 e. x = −1.8 m, y = 0 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 4.5 Tangential and Radial Acceleration HAS VARIABLES: False 63. A car travels around an oval racetrack at constant speed. The car is accelerating

a. at all points except B and D. b. at all points except A and C. c. at all points except A, B, C, and D. d. everywhere, including points A, B, C, and D. e. nowhere, because it is traveling at constant speed.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.5 Tangential and Radial Acceleration HAS VARIABLES: False 64. A 0.14-km-wide river flows with a uniform speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river Copyright Cengage Learning. Powered by Cognero.

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to a point directly north of its departure point on the south bank. What is the speed of the boat relative to the water? a. 5.7 m/s b. 8.5 m/s c. 8.1 m/s d. 7.0 m/s e. 6.4 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 65. A 0.20-km-wide river has a uniform flow speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank. In what direction must the boat be pointed in order to accomplish this? a. 23° west of north b. 20° west of north c. 24° west of north d. 22° west of north e. 17° west of north ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 66. A 0.20-km-wide river has a uniform flow speed of 3.0 m/s toward the east. A boat with a speed of 8.0 m/s relative to the water leaves the south bank and heads in such a way that it crosses to a point directly north of its departure point. How long does it take the boat to cross the river? a. 29 s b. 23 s c. 25 s d. 27 s e. 17 s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 67. A river has a steady speed of 0.30 m/s. A student swims downstream a distance of 1.2 km and returns to the starting point. If the student swims with respect to the water at a constant speed and the downstream portion of the swim requires 20 minutes, how much time is required for the entire swim? a. 50 minutes b. 80 minutes c. 90 minutes d. 70 minutes Copyright Cengage Learning. Powered by Cognero.

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e. 60 minutes ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 68. The pilot of an aircraft flies due north relative to the ground in a wind blowing 40 km/h toward the east. If his speed relative to the ground is 80 km/h, what is the speed of his airplane relative to the air? a. 89 km/h b. 85 km/h c. 81 km/h d. 76 km/h e. 72 km/h ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 69. A car travels due north at a speed of 55 km/h. The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal. If the rain is falling vertically with respect to the Earth, what is the speed of the rain with respect to the Earth? a. 48 km/h b. 95 km/h c. 58 km/h d. 32 km/h e. 80 km/h ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 70. A car travels in an oval path as shown below.

= 25 m/s, west, and

of the centripetal acceleration at B to that at A,

, is what?

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= 20 m/s, north. The ratio of the magnitude

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a. 0.512 b. 0.64 c. 0.8 d. 1.25 e. 1.56 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False Exhibit 4-1 While her kid brother is on a wooden horse at the edge of a merry-go-round, Sheila rides her bicycle parallel to its edge.

The wooden horses have a tangential speed of 6 m/s. Sheila rides at 4 m/s. The radius of the merry-go-round is 8 m.

Use this exhibit to answer the following question(s).

71. Refer to Exhibit 4-1. At what time intervals does Sheila encounter her brother, if she rides in the direction of rotation of the merry-go-round? a. 5.03 s b. 8.37 s c. 12.6 s d. 25.1 s e. 50.2 s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 72. Refer to Exhibit 4-1. At what time intervals does Sheila encounter her brother, if she rides opposite to the direction of rotation of the merry-go-round? a. 5.03 s b. 8.37 s c. 12.6 s d. 25.1 s e. 50.2 s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 73. A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity. The speed of the ball as seen by a stationary observer in the street a. is less than that observed inside the bus. b. is the same as that observed inside the bus.

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c. is greater than that observed inside the bus. d. may be either greater or smaller than that observed inside the bus. e. may be either greater, smaller, or equal to that observed inside the bus.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 74. While a balloon-supported gondola is rising at a speed of 2.0 m/s, a passenger in the gondola throws a small ball down at a speed of 5.0 m/s relative to his body. A person who measures the ball's velocity at the instant of release will find that the ball's velocity relative to the ground at that instant is a. 2.0 m/s, up. b. 3.0 m/s, down. c. 3.0 m/s, up. d. 5.0 m/s, down. e. 12.8 m/s, down.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 75. While a balloon-supported gondola is rising at a speed of 2.0 m/s, a passenger in the gondola throws a small ball up at a speed of 2.0 m/s relative to his body. A person who measures the ball's velocity at the instant of release will find that the ball's velocity relative to the ground at that instant is a. 2.0 m/s, up. b. 2.8 m/s, down. c. 3.0 m/s, up. d. 5.0 m/s, up. e. 7.0 m/s, up.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 76. Jane plans to fly from Binghampton, New York, to Springfield, Massachusetts, about 280 km due east of Binghampton. She heads due east at 280 km/h for one hour but finds herself at Keene, which is 294 km from Binghampton in a direction 17.8 degrees north of due east. What was the wind velocity? a. 14 km/h, E b. 14 km/h, W c. 14 km/h, N d. 90 km/h, S e. 90 km/h, N ANSWER: e POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 77. A park ranger wishes to cross a river that is 1.5 km wide and flows with a velocity of 5.0 km/h parallel to its banks.

The park ranger uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time for crossing?

ANSWER: 0.14 h POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 78. Raindrops are falling straight downward. When observed from a car traveling at 55.0 mi/h, the drops streak the side window at an angle of 60.0° with the vertical. Find the speed with which the drops are falling.

ANSWER: 31.8 mi/h POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False 79. A fast duck is flying

mi/h at the same altitude as a slow airplane flying with a velocity of

mi/h. How fast and in what direction is the duck moving relative to the airplane?

ANSWER:

100 mi/h, along POINTS: 2 DIFFICULTY: Average REFERENCES: 4.6 Relative Velocity and Relative Acceleration HAS VARIABLES: False

1. The vector sum of three co-planar forces a. must be zero. b. must be perpendicular to one of the three. c. must be parallel to one of the three. d. must be perpendicular to the plane. e. may have any direction in the plane.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.1 The Concept of Force HAS VARIABLES: False 2. When the vector sum of three co-planar forces, a. must sum to zero.

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,

and

, is parallel to

, we can conclude that

and Page 75

b. must be equal and opposite. c. must have equal and opposite components perpendicular to . d. must have equal and opposite components parallel to . e. must have equal and opposite components parallel and perpendicular to ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.1 The Concept of Force HAS VARIABLES: False

.

3. A catcher arranges to catch a baseball dropped from a height 50 m above his glove. However, his friends substitute a soft 250 g red grapefruit, so that it will smash apart when he catches it. His glove stops the grapefruit in 0.010 s. What force does the glove exert on the grapefruit? a. 0.078 3 N b. 783 N c. 2 450 N d. 24 500 N e. 78 300 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.1 The Concept of Force HAS VARIABLES: False 4. Which of the following is not a fundamental force? a. the gravitational force b. the electromagnetic force c. the strong force d. the force of forward motion also known as the inertial force e. Choose this answer if two of the named forces are not fundamental.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.1 The Concept of Force HAS VARIABLES: False 5. A high-diver of mass 70.0 kg jumps off a board 10.0 m above the water. If, two seconds after entering the water, his downward motion is stopped, what average upward force did the water exert on him?

ANSWER: 1 180 N POINTS: 2 DIFFICULTY: Average REFERENCES: 5.1 The Concept of Force HAS VARIABLES: False 6. A constant force is applied to a body that is already moving. The force is directed at an angle of 60 degrees to the Copyright Cengage Learning. Powered by Cognero.

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direction of the body's velocity. What is most likely to happen is that a. the body will stop moving. b. the body will move in the direction of the force. c. the body's velocity will increase in magnitude but not change direction. d. the body will gradually change direction, toward that of the force, while speeding up. e. the body will first stop moving and then move in the direction of the force.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.2 Newton’s First Law and Inertial Frames HAS VARIABLES: False 7. A bumper car is moving at constant velocity when another bumper car starts to push on it with a constant force at an angle of 60 degrees with respect to the first car's initial velocity. The second bumper car continues pushing in exactly that direction for some time. What is most likely to happen is that a. the first car will stop moving. b. the first car will move in the direction of the force. c. the first car's velocity will increase in magnitude but not change direction. d. the first car's velocity will gradually change direction more and more toward that of the force while increasing in magnitude. e. the first car's velocity will gradually change direction more and more toward that of the force while decreasing in magnitude.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.2 Newton’s First Law and Inertial Frames HAS VARIABLES: False 2

8. Two forces are the only forces acting on a 3.0-kg object which moves with an acceleration of 3.0 m/s in the positive y direction. If one of the forces acts in the positive x direction and has a magnitude of 8.0 N, what is the magnitude of the other force? a. 12 N b. 14 N c. 16 N d. 18 N e. 22 N ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 9. The only two forces acting on a body have magnitudes of 20 N and 35 N and directions that differ by 80°. The resulting 2 acceleration has a magnitude of 20 m/s . What is the mass of the body? a. 2.4 kg b. 2.2 kg c. 2.7 kg Copyright Cengage Learning. Powered by Cognero.

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d. 3.1 kg e. 1.5 kg ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 10. If the only forces acting on a 2.0-kg mass are acceleration of the particle? a. 1.5 m/s2

N and

N, what is the magnitude of the

b. 6.5 m/s2 c. 4.7 m/s2 d. 9.4 m/s2 e. 7.2 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 11. At an instant when a 4.0-kg object has an acceleration equal to object is known to be

2

m/s , one of the two forces acting on the

N. Determine the magnitude of the other force acting on the object.

a. 2.0 N b. 13 N c. 18 N d. 1.7 N e. 20 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 12. A 1.5-kg object has a velocity of 5 m/s at t = 0. It is accelerated at a constant rate for five seconds, after which it has a velocity of (6 + 12 ) m/s. What is the magnitude of the resultant force acting on the object during this time interval? a. 3.8 N b. 3.2 N c. 2.8 N d. 4.3 N e. 4.6 N ANSWER:

c

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POINTS: 2 DIFFICULTY: Average REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 13. A 1.5-kg object has a velocity of 5 m/s at t = 0. It is accelerated at a constant rate for five seconds, after which it has a velocity of (6 + 12 ) m/s. What is the direction of the resultant force acting on the object during this time interval? a. 65° b. 56° c. 61° d. 49° e. 27° ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 14. A 2.0-kg object has a velocity of 4.0 m/s at t = 0. A constant resultant force of (2.0 + 4.0 ) N then acts on the object for 3.0 s. What is the magnitude of the object's velocity at the end of the 3.0-s interval? a. 9.2 m/s b. 6.3 m/s c. 8.2 m/s d. 7.2 m/s e. 7.7 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 2

15. A 1.5-kg mass has an acceleration of (4.0 − 3.0 ) m/s . Only two forces act on the mass. If one of the forces is (2.0 − 1.4 ) N, what is the magnitude of the other force? a. 4.1 N b. 6.1 N c. 5.1 N d. 7.1 N e. 2.4 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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16. Only two forces act on a 3.0-kg mass. One of the forces is 9.0 N east, and the other is 8.0 N in the direction of 62° north of west. What is the magnitude of the acceleration of the mass? a. 2.0 m/s2 b. 2.4 m/s2 c. 3.3 m/s2 d. 2.9 m/s2 e. 5.7 m/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 17. When an acrobat hangs motionless from a pair of rings a. she has no measurable weight. b. her weight depends on the angles the ropes make with the ceiling. c. her weight is reduced by the upward force the rings exert on her. d. her weight is increased by the upward force the rings exert on her. e. she exerts a gravitational force on the Earth that is equal to the sum of the forces the rings exert on her.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 18. Two experiments are performed. In (A), an 18.0-N force pushes horizontally on a 2.00-kg block that then pushes on a 4.00-kg block. In (B), an 18.0-N force pushes on a 4.00-kg block that then pushes on a 2.00-kg block. Which statement is correct? a. The acceleration is 3.00 m/s2 in both (A) and (B). b. The acceleration is 4.50 m/s2 in both (A) and (B). c. The acceleration is 6.00 m/s2 in both (A) and (B). d. The acceleration is 9.00 m/s2 in both (A) and (B). e. The 2.00-kg block has a 9.00 m/s2 acceleration. The 4.00-kg block has a 4.50 m/s2 acceleration.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.4 Newton’s Second Law HAS VARIABLES: False 19. The apparent weight of a fish in an elevator is greatest when the elevator a. moves downward at constant velocity. b. moves upward at constant velocity. c. accelerates downward. d. accelerates upward.

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e. is not moving.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.5 The Gravitational Force and Weight HAS VARIABLES: False 20. A juggler throws two balls up to the same height so that they pass each other halfway up when A is rising and B is descending. Ignore air resistance and buoyant forces. Which statement is true of the two balls at that point? a. There is a residual upward force from the hand on each ball. b. There is a greater residual force from the hand on A than there is on B. c. Only gravity acts on B but there is an additional residual force from the hand on A. d. There is an additional downwards force besides gravity on each ball. e. The only force acting on each ball is the gravitational force.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.5 The Gravitational Force and Weight HAS VARIABLES: False 21. An astronaut who weighs 800 N on the surface of the Earth lifts off from planet Zuton in a space ship. The free-fall 2 2 acceleration on Zuton is 3.0 m/s (down). At the moment of liftoff the acceleration of the spaceship is 0.50 m/s (up).

What is the magnitude of the force of the spaceship on the astronaut? a. 41 N b. 0.29 kN c. 0.24 kN d. 0.20 kN e. 0.37 kN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.5 The Gravitational Force and Weight HAS VARIABLES: False 22. Aline and Charlie are arguing as to whether or not it is possible in principle for an elevator to have an acceleration of magnitude greater than g. In the course of their discussion they come up with the statements below. Which one is correct? a. No, because once reaches g, the elevator is in free fall. b. No, because an acceleration greater than g is not possible. c. Yes, because it can reach an acceleration greater than g when the cable breaks. d. Yes, because it can reach an acceleration greater than g if the motor is strong enough. e. No, because it cannot exceed its terminal acceleration.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.5 The Gravitational Force and Weight HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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23. A book is placed on a chair. Then a videocassette is placed on the book. The floor exerts a normal force a. on all three. b. only on the book. c. only on the chair. d. upwards on the chair and downwards on the book. e. only on the objects that you have defined to be part of the system.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False 24. Two people, each of mass 70 kg, are riding in an elevator. One is standing on the floor. The other is hanging on a rope suspended from the ceiling. Compare the force the floor exerts on the first person to the force the second person. Which statement is correct? a. They are equal and opposite in direction. b. They are equal and have the same direction. c. is greater than , but they have the same direction. d. e.

is greater than is less than

the rope exerts on

, but they have opposite directions. , but they have the same direction.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False 25. Two people, each of mass 70 kg, are riding in an elevator. One is standing on the floor. The other is hanging on a rope suspended from the ceiling. Compare the acceleration of the first person to the acceleration of the second person.

Which statement is correct? a. They are equal and opposite in direction. b. They are equal and have the same direction. c. The acceleration is greater than , but they have the same direction. d. The acceleration

is greater than

e. The acceleration

is less than

, but they have opposite directions. , but they have the same direction.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False 26. A chair is placed on a rug. Then a book is placed on the chair. The floor exerts a normal force Copyright Cengage Learning. Powered by Cognero.

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a. on all three. b. only on the book. c. only on the rug. d. upwards on the rug and downwards on the chair. e. only on the objects you have defined to be part of the system.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False 27. A book is placed on a chair. Then a videocassette is placed on the book. The floor exerts a normal force a. on all three. b. only on the book. c. only on the chair. d. upwards on the chair and downwards on the book. e. only on the objects that you have defined to be part of the system.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False 28. Two bodies, A and B, collide as shown in Figures I and II below.

Which statement is true? a. They exert equal and opposite forces on each other in I but not in II. b. They exert equal and opposite forces on each other in II but not in I. c. They exert equal and opposite forces on each other in both I and II. d. The forces are equal and opposite to each other in I, but only the components of the forces parallel to the velocities are equal in II. e. The forces are equal and opposite in I, but only the components of the forces perpendicular to the velocities are equal in II ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False 29. You throw a ball up in the air and hold your hand under it to catch it when it comes down. The reason why the ball stops is because a. your hand is there: your hand exerts no force on the ball.

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b. your hand exerts a force on the ball perpendicular to its velocity. c. your hand exerts a force on the ball in the direction of its velocity. d. your hand exerts a force on the ball in the direction opposite to its velocity. e. your hand and the ball exert forces in the same direction on each other.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False 30. You hold a tennis racket in your hand. On top of the racket you have balanced a ball. Which statement is true? a. The force of your hand on the racket and the force of the ball on the racket are equal and opposite. b. The force of the racket on your hand and the force of the ball on the racket are equal and opposite. c. The force of your hand on the racket and the force of the racket on the ball are equal and opposite. d. The force of the racket on your hand and the force of the racket on the ball are equal and opposite. e. The force of your hand on the racket and the force of the racket on your hand are equal and opposite.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False 31. In order to jump off the floor, the floor must exert a force on you a. in the direction of and equal to your weight. b. opposite to and equal to your weight. c. in the direction of and less than your weight. d. opposite to and less than your weight. e. opposite to and greater than your weight.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False 32. Which type of force would be the equal and opposite force to a gravitational force? a. gravitational b. electromagnetic c. strong d. weak e. It could be any one of the above or some combination of them.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.6 Newton’s Third Law HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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33. In the figure, if the tension in string 1 is 34 N and the tension in string 2 is 24 N, what is the mass of the object shown?

a. 7.3 kg b. 5.5 kg c. 1.8 kg d. 3.7 kg e. 4.5 kg ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 34. If M = 2.0 kg, what is the tension in string 1?

a. 1.2 N b. 11 N c. 34 N d. 3.5 N e. 40 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 35. If M = 6.0 kg, what is the tension in string 1?

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a. 39 N b. 34 N c. 29 N d. 44 N e. 51 N ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 36. If M = 1.1 kg, what is the tension in string 1?

a. 54 N b. 47 N c. 40 N d. 62 N e. 57 N ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 37. An object of unknown weight is suspended as shown. The tension in rope 1 is 25 lb, and the tension in rope 2 is 31 lb.

What is the weight of the suspended object?

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a. 36 lb b. 33 lb c. 41 lb d. 39 lb e. 56 lb ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 38. If α = 40°, β = 60°, and M = 4.0 kg, determine the tension in string 1.

a. 15 N b. 22 N c. 17 N d. 20 N e. 36 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 39. If α = 40° and the tension in string 2 is 30 N, determine M.

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a. 3.4 kg b. 3.6 kg c. 2.6 kg d. 4.9 kg e. 7.5 kg ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 40. The horizontal surface on which the block slides is frictionless. If F = 20 N and M = 5.0 kg, what is the magnitude of the resulting acceleration of the block?

a. 5.3 m/s2 b. 6.2 m/s2 c. 7.5 m/s2 d. 4.7 m/s2 e. 3.2 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 41. If F = 4.0 N and m = 2.0 kg, what is the magnitude a of the acceleration for the block shown below? The surface is frictionless.

a. 5.3 m/s2 Copyright Cengage Learning. Powered by Cognero.

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b. 4.4 m/s2 c. 3.5 m/s2 d. 6.2 m/s2 e. 8.4 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 42. A block is pushed up a frictionless 30° incline by an applied force as shown. If F = 25 N and M = 3.0 kg, what is the magnitude of the resulting acceleration of the block?

a. 2.3 m/s2 b. 4.6 m/s2 c. 3.5 m/s2 d. 2.9 m/s2 e. 5.1 m/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 43. A 5.0-kg object is suspended by a string from the ceiling of an elevator that is accelerating downward at a rate of 2.6 2 m/s . What is the tension in the string? a. 49 N b. 36 N c. 62 N d. 13 N e. 52 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 44. The tension in a string from which a 4.0-kg object is suspended in an elevator is equal to 44 N. What is the acceleration of the elevator?

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a. 11 m/s2 upward b. 1.2 m/s2 upward c. 1.2 m/s2 downward d. 10 m/s2 upward e. 2.4 m/s2 downward ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 45. A 5.0-kg mass is attached to the ceiling of an elevator by a rope whose mass is negligible. What force does the mass 2 exert on the rope when the elevator has an acceleration of 4.0 m/s upward? a. 69 N downward b. 29 N downward c. 49 N downward d. 20 N downward e. 19 N downward ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 46. A 5.0-kg mass is suspended by a string from the ceiling of an elevator that is moving upward with a speed which is decreasing at a constant rate of 2.0 m/s in each second. What is the tension in the string supporting the mass? a. 49 N b. 39 N c. 59 N d. 10 N e. 42 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 2

47. A person weighing 0.70 kN rides in an elevator that has an upward acceleration of 1.5 m/s . What is the magnitude of the force of the elevator floor on the person? a. 0.11 kN b. 0.81 kN c. 0.70 kN d. 0.59 kN e. 0.64 kN Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 48. A 3.0-kg block slides on a frictionless 20° inclined plane. A force of 16 N acting parallel to the incline and up the incline is applied to the block. What is the acceleration of the block? a. 2.0 m/s2 down the incline b. 5.3 m/s2 up the incline c. 2.0 m/s2 up the incline d. 3.9 m/s2 down the incline e. 3.9 m/s2 up the incline ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 49. A 2.0-kg block slides on a frictionless, 25° inclined plane. A force of 4.6 N acting parallel to the incline and up the incline is applied to the block. What is the acceleration of the block? a. 1.8 m/s2 up the incline b. 2.3 m/s2 up the incline c. 6.6 m/s2 down the incline d. 1.8 m/s2 down the incline e. 2.3 m/s2 down the incline ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 50. A 2.0-kg block slides on a frictionless, 15° inclined plane. A force acting parallel to the incline is applied to the block.

2 The acceleration of the block is 1.5 m/s down the incline. What is the applied force? a. 8.1 N down the incline b. 3.0 N down the incline c. 2.1 N up the incline d. 3.0 N up the incline e. 8.1 N up the incline ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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51. You have a machine which can accelerate pucks on frictionless ice. Starting from rest, the puck travels a distance x in time t when force F is applied. If force 3F is applied, the distance the puck travels in time t is a. x. b. (3/2)x. c. 3x. d. (9/2)x. e. 9x.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 52. A constant force F is applied to a body of mass m that initially is headed east at velocity v0 until its velocity becomes −v0. The total time of travel is 2t. The total distance the body travels in that time is a. . b. . c. . d. . e. .

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 53. The first of two identical boxes of mass m is sitting on level ground. The second box is sitting on a ramp that makes a 20° angle with the ground. The normal force of the level ground on the first box is NL; the normal force of the ramp on the second box is NR. Which statement is correct? a. NR = NL = mg b. NL = mg; NR = mg sin 20° c. NL = mg; NR = mg cos 20° d. NL = mg; NR = −mg cos 20° e. NR = −NL = −mg ANSWER: POINTS: DIFFICULTY:

c 1 Easy

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REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 54. A heavy weight is supported by two cables that exert tensions of magnitude T1 and T2. Which statement is correct?

a. T1 = T2. b. T1y = T2y. c. T1 > T2. d. T1 < T2. e. We need the mass of the box in order to determine the correct answer.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 55. The horizontal surface on which the objects slide is frictionless. If M = 2.0 kg, the tension in string 1 is 12 N. Determine F.

a. 25 N b. 20 N c. 30 N d. 35 N e. 40 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 56. The horizontal surface on which the objects slide is frictionless. If F = 12 N, what is the tension in string 1?

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a. 35 N b. 30 N c. 40 N d. 45 N e. 25 N ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 57. The surface of the inclined plane shown is frictionless. If F = 30 N, what is the magnitude of the force exerted on the 3.0-kg block by the 2.0-kg block?

a. 18 N b. 27 N c. 24 N d. 21 N e. 15 N ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 58. If P = 6.0 N, what is the magnitude of the force exerted on block 1 by block 2?

a. 6.4 N b. 5.6 N c. 4.8 N d. 7.2 N e. 8.4 N ANSWER:

c

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POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 59. If F = 5.0 N, what is the magnitude of the force exerted by block 2 on block 1?

a. 17 N b. 19 N c. 21 N d. 23 N e. 5.0 N ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 60. The horizontal surface on which the objects slide is frictionless. If M = 1.0 kg and the magnitude of the force of the small block on the large block is 5.2 N, determine F.

a. 6.0 N b. 9.0 N c. 7.8 N d. 4.8 N e. 4.1 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 61. The horizontal surface on which the objects slide is frictionless. If F = 6.0 N and M = 1.0 kg, what is the magnitude of the force exerted on the large block by the small block?

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a. 7.7 N b. 9.8 N c. 9.1 N d. 8.4 N e. 6.5 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 62. A 6.0-kg object is suspended by a vertical string from the ceiling of an elevator which is accelerating upward at a rate 2 of 1.8 m/s . Determine the tension in the string. a. 11 N b. 70 N c. 48 N d. 59 N e. 62 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 2

63. An 8.0-kg object rests on the floor of an elevator which is accelerating downward at a rate of 1.3 m/s . What is the magnitude of the force the object exerts on the floor of the elevator? a. 59 N b. 10 N c. 89 N d. 68 N e. 78 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 64. A 70-kg stunt artist rides in a rocket sled which slides along a flat, inclined surface. At an instant when the sled's 2 2 acceleration has a horizontal component of 6.0 m/s and a downward component of 2.8 m/s , what is the magnitude of the force on the rider by the sled? a. 0.83 kN b. 0.98 kN Copyright Cengage Learning. Powered by Cognero.

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c. 0.65 kN d. 0.68 kN e. 0.72 kN ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 65. If F = 40 N and M = 1.5 kg, what is the tension in the string connecting M and 2M? Assume that all surfaces are frictionless.

a. 13 N b. 23 N c. 36 N d. 15 N e. 28 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 66. The system shown is released from rest and moves 50 cm in 1.0 s. What is the value of M? All surfaces are frictionless.

a. 0.42 kg b. 0.34 kg c. 0.50 kg d. 0.59 kg e. 0.68 kg ANSWER:

b

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POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 67. If F = 40 N and M = 2.0 kg, what is the magnitude of the acceleration of the suspended object? All surfaces are frictionless.

a. 1.2 m/s2 b. 2.0 m/s2 c. 1.5 m/s2 d. 2.5 m/s2 e. 5.6 m/s2 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 68. If M = 2.2 kg, what is the tension in the connecting string? The pulley and all surfaces are frictionless.

a. 6.4 N b. 5.9 N c. 5.4 N d. 6.9 N e. 8.3 N ANSWER: POINTS: DIFFICULTY:

c 3 Challenging

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REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 2

69. A 5.0-kg mass sits on the floor of an elevator that has a downward acceleration of 1.0 m/s . On top of the 5.0-kg mass is an object of unknown mass. The force of the elevator on the 5.0-kg mass is 80 N up. Determine the unknown mass. a. 3.3 kg b. 2.4 kg c. 1.6 kg d. 4.1 kg e. 5.0 kg ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 2

70. If the tension, T, is 15 N and the magnitude of the acceleration, a, is 3.0 m/s , what is the mass, m, of the suspended object? Assume that all surfaces and the pulley are frictionless.

a. 3.1 kg b. 2.5 kg c. 2.8 kg d. 2.2 kg e. 3.7 kg ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 71. If F = 8.0 N and M = 1.0 kg, what is the tension in the connecting string? The pulley and all surfaces are frictionless.

a. 4.1 N b. 3.5 N Copyright Cengage Learning. Powered by Cognero.

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c. 3.8 N d. 3.1 N e. 4.8 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 72. In the figure, if F = 2.0 N and M = 1.0 kg, what is the tension in the connecting string? The pulley and all surfaces are frictionless.

a. 2.6 N b. 1.1 N c. 2.1 N d. 1.6 N e. 3.7 N ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 73. Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below. What is the tension in spring A?

a. 1.45 N b. 2.50 N c. 2.89 N d. 3.75 N e. 5.00 N ANSWER: POINTS:

c 2

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DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 74. Three boxes slide on a frictionless, horizontal surface when pulled by a force of magnitude F. When we compare the tensions T1 and T2 with the force F, we find that

a. T1 = T2 = F. b. T1 = F > T2. c. F > T1 = T2. d. F > T1 > T2. e. F − T1 < T1 − T2.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 75. Three boxes are pushed across a frictionless, horizontal surface as shown. When we compare the normal force N2,5 that mass 2m exerts on mass 5m with the normal force N5,10 that mass 5m exerts on mass 10m, we find that

a. N2,5 = N5,10 = F. b. N2,5 = F > N5,10. c. F > N2,5 = N5,10. d. F > N2,5 > N5,10. e. F > N5,10 > N2,5.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False

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76. Given the equation

, which answer or answers provide(s) the best

description of a possible physical situation? a. A 20.00 N tension pulls a 2.00 kg mass. The 2.00 kg mass pulls another 2.00 kg mass. b. A 20.00 N force pushes a 2.00 kg mass. The 2.00 kg mass pushes another 2.00 kg mass. c. A 2.00 kg mass on a flat surface is acted on by gravity while another 2.00 kg mass sits on top of it. d. All of the situations above are possible. e. Only (a) and (b) above are possible.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False

77. Given the equation

, which answer

provides the best description of a possible physical situation? a. A 3.00-kg mass is suspended from the ceiling. b. A 2.00-kg mass hanging over a pulley drags a 3.00-kg mass along a frictionless, horizontal surface. c. A 3.00-kg mass hanging over a pulley drags a 2.00-kg mass along a frictionless, horizontal surface. d. A 3.00-kg mass hanging over a pulley drags a 5.00-kg mass along a frictionless, horizontal surface. e. A 5.00-kg mass hanging over a pulley drags a 3.00-kg mass along a frictionless, horizontal surface.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False Exhibit 5-1 A 2.30-kg mass is suspended from the ceiling and a 1.70-kg mass is suspended from the 2.30-kg mass, as shown. The tensions in the strings are labeled

and

.

Use this exhibit to answer the following question(s).

78. Refer to Exhibit 5-1. A hand exerts an upward force of 6.70 N on the 1.70-kg mass. The magnitudes of the tensions are a. T1 = 15.8 N; T2 = 10.0 N. b. T1 = 15.8 N; T2 = 16.7 N. c. T1 = 22.5 N; T2 = 10.0 N. Copyright Cengage Learning. Powered by Cognero.

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d. T1 = 22.5 N; T2 = 16.7 N. e. T1 = 32.5 N; T2 = 10.0 N. ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 79. Refer to Exhibit 5-1. The string supporting the 1.70-kg mass is cut. The magnitudes of the tension in string 1 before and after string 2 is cut are a. T1,i = 22.5 N; T1,f = 5.80 N. b. T1,i = 39.2 N; T1,f = 5.80 N. c. T1,i = 22.5 N; T1,f = 22.5 N. d. T1,i = 39.2 N; T1,f = 22.5 N. e. T1,i = 39.2 N; T1,f = 39.2 N. ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 80. A 6.00-kg block is placed on a 30.0° incline and connected to another block on a 36.87° incline. Although the surfaces are frictionless, the blocks do not move. What is the mass in kilograms of the block on the 36.87° incline?

a. 1.80 b. 3.00 c. 4.00 d. 5.00 e. 6.00 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False Exhibit 5-2 A 4.00-kg block is suspended from the roof of an elevator. A 2.00-kg block is suspended from the 4.00-kg block. The tensions in strings 1 and 2 are labeled

and

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.

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Use this exhibit to answer the following question(s).

2

81. Refer to Exhibit 5-2. When the elevator accelerates upwards with an acceleration of 2.20 m/s , the magnitudes of and

are

a. 30.4 N; 15.2 N. b. 39.2 N; 19.6 N. c. 45.6 N; 15.2 N. d. 48.0 N; 24.0 N. e. 72.0 N; 24.0 N. ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 2

82. Refer to Exhibit 5-2. When the elevator accelerates downwards with an acceleration of 2.20 m/s , the magnitudes of and

are

a. 30.4 N; 15.2 N. b. 39.2 N; 19.6 N. c. 45.6 N; 15.2 N. d. 48.0 N; 24.0 N. e. 72.0 N; 24.0 N. ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 83. A book is resting on a table. How many forces would be in the free-body diagram of the book? a. one b. two of the same type c. two of different types d. three or more of the same type e. three or more of at least two different types ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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84. A 2 000-kg sailboat experiences an eastward force of 3 000 N by the ocean tide and a wind force against its sails of magnitude 6 000 N directed toward the northwest (45° N of W). What is the magnitude and direction of the resultant acceleration?

2 ANSWER: 2.2 m/s at 74° N of W POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 85. The same force F is applied horizontally to bodies 1, 2, 3, and 4, of masses m, 2m, 3m, and 4m, initially at rest and on a frictionless surface, until each body has traveled distance d. The correct listing of the magnitudes of the velocities of the bodies, v1, v2, v3, and v4 is a. . b. v4 = v2 > v3 = v1. c.

.

d. v1 = 2v2 = 3v3 = 4v4. e. .

ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.7 Analysis Models Using Newton’s Second Law HAS VARIABLES: False 86. The first of two identical boxes of mass m is sitting on level ground. The second box is sitting on a ramp that makes an angle with the ground. When a force of magnitude F is applied to each box in a direction parallel to the surface it is on, upwards on the box on the ramp, neither box moves. Which statement comparing the friction force on the box on the level, fL, to the friction force on the box on the ramp, fR, is correct? a. fR = fL. b. fR > fL. c. fR < fL. d. The coefficient of static friction is needed to determine the correct answer. e. Depending on the values of the coefficient of static friction, the angle of elevation of the ramp, the mass of the boxes, and the applied force, answers (a), (b), and (c) are each a possible correct answer.

ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 87. The total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction μk is least when the force is applied at an angle θ such that a. sinθ = μk.

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b. cosθ = μk. c. tanθ = μk. d. cotθ = μk. e. secθ = μk.

ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 88. A 4.0-kg block slides down a 35° incline at a constant speed when a 16-N force is applied acting up and parallel to the incline. What is the coefficient of kinetic friction between the block and the surface of the incline? a. 0.20 b. 0.23 c. 0.26 d. 0.33 e. 0.41 ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 89. A block is pushed across a horizontal surface by the force shown. If the coefficient of kinetic friction between the block and the surface is 0.30, F = 20 N, θ = 30°, and M = 3.0 kg, what is the magnitude of the acceleration of the block?

a. 2.8 m/s2 b. 2.3 m/s2 c. 1.8 m/s2 d. 3.3 m/s2 e. 5.4 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 90. A 3.0-kg block moves up a 40° incline with constant speed under the action of a 26-N force acting up and parallel to the incline. What magnitude force must act up and parallel to the incline for the block to move down the incline at constant velocity?

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a. 14 N b. 12 N c. 16 N d. 18 N e. 25 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 91. The block shown is pulled across the horizontal surface at a constant speed by the force shown. If M = 5.0 kg, F = 14 N and θ = 35°, what is the coefficient of kinetic friction between the block and the horizontal surface?

a. 0.44 b. 0.33 c. 0.38 d. 0.28 e. 0.17 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 92. A box rests on the (horizontal) back of a truck. The coefficient of static friction between the box and the surface on which it rests is 0.24. What maximum distance can the truck travel (starting from rest and moving horizontally with constant acceleration) in 3.0 s without having the box slide? a. 14 m b. 11 m c. 19 m d. 24 m e. 29 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 93. In a game of shuffleboard (played on a horizontal surface), a puck is given an initial speed of 6.0 m/s. It slides a distance of 9.0 m before coming to rest. What is the coefficient of kinetic friction between the puck and the surface?

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a. 0.20 b. 0.18 c. 0.15 d. 0.13 e. 0.27 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 94. A 2.0-kg block slides on a rough, horizontal surface. A force (magnitude P = 4.0 N) acting parallel to the surface is 2 applied to the block. The magnitude of the block's acceleration is 1.2 m/s . If P is increased to 5.0 N, determine the magnitude of the block's acceleration. a. 2.1 m/s2 b. 2.3 m/s2 c. 1.9 m/s2 d. 1.7 m/s2 e. 3.2 m/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 95. A 4.0-kg block is pushed up a 36° incline by a force of magnitude P applied parallel to the incline. When P is 31 N, it is observed that the block moves up the incline with a constant speed. What value of P would be required to lower the block down the incline at a constant speed? a. 27 N b. 15 N c. 13 N d. 17 N e. 19 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 96. A 1.8-kg block is released from rest at the top of a rough, 30° inclined plane. As the block slides down the incline, its 2 acceleration is 3.0 m/s down the incline. Determine the magnitude of the force of friction acting on the block. a. 4.2 N b. 3.0 N c. 3.4 N d. 3.8 N Copyright Cengage Learning. Powered by Cognero.

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e. 2.3 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 97. A 1.8-kg block is projected up a rough, 10° inclined plane. As the block slides up the incline, its acceleration is 3.8 2 m/s down the incline. What is the magnitude of the force of friction acting on the block? a. 5.0 N b. 3.8 N c. 4.2 N d. 4.6 N e. 6.5 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 98. A 2.0-kg block slides on a rough, horizontal surface. A force (P = 6.0 N) is applied to the block as shown. The 2 magnitude of the block's acceleration is 1.2 m/s . What is the magnitude of the force of friction acting on the block?

a. 2.0 N b. 1.4 N c. 1.6 N d. 2.8 N e. 3.4 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 99. A 3.0-kg block slides on a rough horizontal surface. A force of 8.0 N acting parallel to the surface is applied to the block. The coefficient of kinetic friction between the block and the surface is 0.15. What is the magnitude of the block's acceleration? a. 1.9 m/s2 b. 1.2 m/s2 c. 2.3 m/s2 d. 1.5 m/s2 Copyright Cengage Learning. Powered by Cognero.

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e. 2.9 m/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 100. A 1.0-kg block is pushed up a rough, 22° inclined plane by a force of 7.0 N acting parallel to the incline. The 2 acceleration of the block is 1.4 m/s up the incline. Determine the magnitude of the force of friction acting on the block. a. 1.9 N b. 2.2 N c. 1.3 N d. 1.6 N e. 3.3 N ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 101. In the figure shown, the coefficient of kinetic friction between the block and the incline is 0.29. What is the magnitude of the acceleration of the suspended block as it falls? Disregard any pulley mass or friction in the pulley.

a. 5.4 m/s2 b. 5.2 m/s2 c. 4.9 m/s2 d. 5.6 m/s2 e. 7.9 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 102. In the figure shown, the coefficient of kinetic friction between the block and the incline is 0.40. What is the magnitude of the acceleration of the suspended block as it falls? Disregard any pulley mass or friction in the pulley.

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a. 3.4 m/s2 b. 3.7 m/s2 c. 4.2 m/s2 d. 3.9 m/s2 e. 5.4 m/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 103. The three blocks shown are released from rest and are observed to move with accelerations that have a magnitude of 2 1.5 m/s . What is the magnitude of the friction force on the block that slides horizontally? Disregard any pulley mass or friction in the pulley and let M = 2.0 kg.

a. 6.0 N b. 5.1 N c. 5.5 N d. 4.6 N e. 3.7 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 104. Two blocks in contact with each other are pushed to the right across a rough, horizontal surface by the two forces shown. If the coefficient of kinetic friction between each of the blocks and the surface is 0.30, determine the magnitude of the force exerted on the 2.0-kg block by the 3.0-kg block.

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a. 15 N b. 25 N c. 11 N d. 22 N e. 33 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 105. Two blocks are accelerated across a horizontal, frictionless surface as shown. Frictional forces keep the two blocks from sliding relative to each other, and the two move with the same acceleration. If F = 1.2 N and M = 1.0 kg, what is the horizontal component (frictional force) of the force of the large block on the small block?

a. 0.40 N to the left b. 0.80 N to the right c. 0.40 N to the right d. 0.80 N to the left e. 1.20 N to the left ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 106. The coefficient of kinetic friction between the surface and the larger block is 0.25, and the coefficient of kinetic friction between the surface and the smaller block is 0.40. If F = 22N and M = 1.0 kg in the figure, what is the magnitude of the acceleration of either block?

a. 1.8 m/s2 b. 2.6 m/s2 Copyright Cengage Learning. Powered by Cognero.

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c. 1.4 m/s2 d. 2.2 m/s2 e. 3.7 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 107. In the figure, the coefficient of kinetic friction between the surface and the larger block is 0.20, and the coefficient of kinetic friction between the surface and the smaller block is 0.30. If F = 14 N and M = 1.0 kg, what is the magnitude of the acceleration of either block?

a. 2.0 m/s2 b. 1.3 m/s2 c. 1.5 m/s2 d. 1.8 m/s2 e. 3.5 m/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 108. Two blocks are accelerated across a horizontal, frictionless surface as shown. Frictional forces keep the two blocks from sliding relative to each other, and the two move with the same acceleration. If F = 1.2 N and M = 1.0 kg, what is the horizontal component (frictional force) of the force of the small block on the large block?

a. 0.48 N to the right b. 0.72 N to the right c. 0.72 N to the left d. 0.48 N to the left e. 0.65 N to the left Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 109. Two blocks connected by a string are pulled across a horizontal surface by a force applied to one of the blocks, as shown. The coefficient of kinetic friction between the blocks and the surface is 0.25. If each block has an acceleration of 2 2.0 m/s to the right, what is the magnitude F of the applied force?

a. 25 N b. 18 N c. 11 N d. 14 N e. 7.0 N ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 110. In the figure, the coefficient of kinetic friction between the surface and the larger block is 0.20, and the coefficient of kinetic friction between the surface and the smaller block is 0.30. If F = 10 N and M = 1.0 kg, what is the tension in the connecting string?

a. 8.0 N b. 6.0 N c. 6.7 N d. 8.7 N e. 3.0 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 111. The frictional force of the floor on a large suitcase is least when the suitcase is Copyright Cengage Learning. Powered by Cognero.

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a. pushed by a force parallel to the floor. b. dragged by a force parallel to the floor. c. pulled by a force directed at an angle θ above the floor. d. pushed by a force directed at an angle θ into the floor. e. turned on its side and pushed by a force parallel to the floor.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 112. A 60-kg person rides down an icy hill of 20° slope while standing on a 3.0-kg flat-bottomed bathroom scale. Assume there is no frictional force between the bottom of the scale and the hill. The static friction force the scale exerts on the person is a. 0 N. b. 201 N. c. 211 N. d. 553 N. e. 580 N. ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 113. When you drag a toy teddy bear along the floor by a force that is parallel to the floor, the magnitude of the force of friction a. is independent of velocity or acceleration. b. increases when the velocity increases. c. is proportional to the acceleration. d. decreases when the force parallel to the floor increases. e. increases when the force parallel to the floor increases.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 114. An object on the flat bed of a truck that is accelerating along a straight, horizontal road. The coefficient of static friction is 0.300 in this case. Of the following choices, which is the lowest value of acceleration that would result in the object sliding on the bed of the truck? a. 0.280 m/s2 b. 0.310 m/s2 c. 2.93 m/s2 d. 2.99 m/s2 Copyright Cengage Learning. Powered by Cognero.

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e. 3.02 m/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False 115. A box is dropped onto a conveyor belt moving at 2 m/s. If the coefficient of friction between the box and the belt is 0.3, how long before the box moves without slipping?

ANSWER: 0.7 s POINTS: 2 DIFFICULTY: Average REFERENCES: 5.8 Forces of Friction HAS VARIABLES: False

1. A race car travels 40 m/s around a banked (45° with the horizontal), circular (radius = 0.20 km) track. What is the magnitude of the resultant force on the 80-kg driver of this car? a. 0.68 kN b. 0.64 kN c. 0.72 kN d. 0.76 kN e. 0.52 kN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 2. An airplane travels 80 m/s as it makes a horizontal, circular turn which has a 0.80-km radius. What is the magnitude of the resultant force on the 75-kg pilot of this airplane? a. 0.69 kN b. 0.63 kN c. 0.66 kN d. 0.60 kN e. 0.57 kN ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 3. An airplane moves 140 m/s as it travels around a vertical circular loop which has a 1.0-km radius. What is the magnitude of the resultant force on the 70-kg pilot of this plane at the bottom of this loop? a. 2.1 kN b. 1.4 kN c. 0.69 kN Copyright Cengage Learning. Powered by Cognero.

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d. 1.5 kN e. 1.3 kN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 4. A car travels along the perimeter of a vertical circle (radius = 0.25 km) at a constant speed of 30 m/s. What is the magnitude of the resultant force on the 60-kg driver of the car at the lowest point on this circular path? a. 0.37 kN b. 0.80 kN c. 0.22 kN d. 0.59 kN e. 0.45 kN ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 5. A 30-kg child rides on a circus Ferris wheel that takes her around a vertical circular path with a radius of 20 m every 22 s. What is the magnitude of the resultant force on the child at the highest point on this trajectory? a. 49 N b. 0.29 kN c. 0.34 kN d. 0.25 kN e. 0.76 kN ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 6. An amusement ride consists of a car moving in a vertical circle on the end of a rigid boom. The radius of the circle is 10 m. The combined weight of the car and riders is 5.0 kN. At the top of the circle, the car has a speed of 5.0 m/s, which is not changing at that instant. What is the force of the boom on the car at the top of the circle? a. 3.7 kN down b. 1.3 kN down c. 6.3 kN up d. 3.7 kN up e. 5.2 kN down ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 7. A highway curve has a radius of 0.14 km and is unbanked. A car weighing 12 kN goes around the curve at a speed of 24 m/s without slipping. What is the magnitude of the horizontal force of the road on the car? a. 12 kN b. 17 kN c. 13 kN d. 5.0 kN e. 49 kN ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 8. A 4.0-kg mass on the end of a string rotates in a circular motion on a horizontal, frictionless table. The mass has a constant speed of 2.0 m/s and the radius of the circle is 0.80 m. What is the magnitude of the resultant force acting on the mass? a. 39 N b. 20 N c. 44 N d. 0 N e. 30 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 9. A stunt pilot weighing 0.70 kN performs a vertical circular dive of radius 0.80 km. At the bottom of the dive, the pilot has a speed of 0.20 km/s, which at that instant is not changing. What force does the plane exert on the pilot? a. 3.6 kN up b. 4.3 kN up c. 2.9 kN down d. 2.9 kN up e. 5.8 kN down ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 10. A car travels around an unbanked highway curve (radius 0.15 km) at a constant speed of 25 m/s. What is the magnitude of the resultant force acting on the driver, who weighs 0.80 kN? a. 0.87 kN b. 0.34 kN c. 0.80 kN Copyright Cengage Learning. Powered by Cognero.

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d. 0.00 kN e. 0.67 kN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 11. A 0.50-kg mass attached to the end of a string swings in a vertical circle (radius = 2.0 m). When the mass is at the lowest point on the circle, the speed of the mass is 12 m/s. What is the magnitude of the force of the string on the mass at this position? a. 31 N b. 36 N c. 41 N d. 46 N e. 23 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 12. A roller-coaster car has a mass of 500 kg when fully loaded with passengers. The car passes over a hill of radius 15 m, as shown. At the top of the hill, the car has a speed of 8.0 m/s. What is the force of the track on the car at the top of the hill?

a. 7.0 kN up b. 7.0 kN down c. 2.8 kN down d. 2.8 kN up e. 5.6 kN down ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 13. A 0.20-kg object attached to the end of a string swings in a vertical circle (radius = 80 cm). At the top of the circle, the speed of the object is 4.5 m/s. What is the magnitude of the tension in the string at this position?

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a. 7.0 N b. 2.0 N c. 3.1 N d. 5.1 N e. 6.6 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 14. A roller-coaster car has a mass of 500 kg when fully loaded with passengers. At the bottom of a circular dip of radius 40 m (as shown in the figure) the car has a speed of 16 m/s. What is the magnitude of the force of the track on the car at the bottom of the dip?

a. 3.2 kN b. 8.1 kN c. 4.9 kN d. 1.7 kN e. 5.3 kN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 15. A 0.50-kg mass attached to the end of a string swings in a vertical circle (radius = 2.0 m). When the mass is at the highest point of the circle, the speed of the mass is 8.0 m/s. What is the magnitude of the force of the string on the mass at this position? a. 21 N b. 11 N c. 16 N d. 26 N e. 36 N ANSWER: b POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 16. A 50-kg child riding a Ferris wheel (radius = 10 m) travels in a vertical circle. The wheel completes one revolution every 10 s. What is the magnitude of the force on the child by the seat at the highest point on the circular path? a. 0.29 kN b. 0.49 kN c. 0.69 kN d. 0.20 kN e. 0.40 kN ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 17. A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m), as shown. At an instant when θ = 50°, the tension in the string is 8.0 N. What is the magnitude of the resultant force on the mass at this instant?

a. 5.6 N b. 6.0 N c. 6.5 N d. 5.1 N e. 2.2 N ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 18. An object attached to the end of a string swings in a vertical circle (R = 1.2 m), as shown. At an instant when θ = 30°, the speed of the object is 5.1 m/s and the tension in the string has a magnitude of 20 N. What is the mass of the object?

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a. 2.0 kg b. 1.5 kg c. 1.8 kg d. 1.2 kg e. 0.80 kg ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 19. A 0.40-kg mass attached to the end of a string swings in a vertical circle having a radius of 1.8 m. At an instant when the string makes an angle of 40 degrees below the horizontal, the speed of the mass is 5.0 m/s. What is the magnitude of the tension in the string at this instant? a. 9.5 N b. 3.0 N c. 8.1 N d. 5.6 N e. 4.7 N ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 20. A 0.50-kg mass attached to the end of a string swings in a vertical circle (radius = 2.0 m). When the string is horizontal, the speed of the mass is 8.0 m/s. What is the magnitude of the force of the string on the mass at this position? a. 16 N b. 17 N c. 21 N d. 11 N e. 25 N ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 21. A 4.0-kg mass attached to the end of a string swings in a vertical circle of radius 2.0 m. When the string makes an Copyright Cengage Learning. Powered by Cognero.

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angle of 35° with the vertical as shown, the speed of the mass is 5.0 m/s. At this instant, what is the magnitude of the force the string exerts on the mass?

a. 50 N b. 82 N c. 89 N d. 11 N e. 61 N ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 22. A split highway has a number of lanes for traffic. For traffic going in one direction, the radius for the inside of the curve is half the radius for the outside. One car, car A, travels on the inside while another car of equal mass, car B, travels at equal speed on the outside of the curve. Which statement about resultant forces on the cars is correct? a. The force on A is half the force on B. b. The force on B is half the force on A. c. The force on A is four times the force on B. d. The force on B is four times the force on A. e. There is no net resultant force on either as long as they stay on the road while turning.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 23. A race car traveling at 100 m/s enters an unbanked turn of 400-m radius. The coefficient of (static) friction between the tires and the track is 1.1. The track has both an inner and an outer wall. Which statement is correct? a. The race car will crash into the outer wall. b. The race car will crash into the inner wall. c. The car will stay in the center of the track. d. The car will stay in the center of the track if the driver speeds up. e. The car would stay in the center of the track if the radius were reduced to 200 m.

ANSWER: a POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 24. A student is sitting on the right side of a school bus when it makes a right turn. We know that the force of gravity acts downwards and a normal force from the seat acts upwards. If the student stays in place when the bus turns, we also know that there must be a. no other force on the student. b. a force parallel to the seat directed forward on the student. c. a force parallel to the seat directed to the left on the student. d. a force parallel to the seat directed to the right on the student. e. a force parallel to the seat in a direction between forward and left on the student.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 25. For a plane to be able to fly clockwise in a horizontal circle as seen from above, in addition to exerting a force downwards on the air, a. it must be increasing its speed. b. it must exert a force on the air that is directed to the plane's left side. c. it must exert a force on the air that is directed to the plane's right side. d. it does not need to exert a force: it must only move the wing flaps out. e. it only needs to deflect the air without exerting any additional force on the air.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 26. When a car goes around a circular curve on a level road without slipping, a. no frictional force is needed because the car simply follows the road. b. the frictional force of the road on the car increases when the car's speed decreases. c. the frictional force of the road on the car increases when the car's speed increases. d. the frictional force of the road on the car increases when the car moves to the outside of the curve. e. there is no net frictional force because the road and the car exert equal and opposite forces on each other.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 27. An iceboat is traveling in a circle on the ice. Halfway around the circle, the sail and the steering mechanism fall off the boat. Which statement is correct? a. The boat will continue traveling in the circle because there is no friction. b. The boat will continue to travel in the circle because its velocity exerts a force on it. c. The boat will move off on a line tangent to the circle because there is no force on it.

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d. The boat will move off tangent to the circle because there is a force on it perpendicular to the boat directed to the outside of the circle. e. The boat will move off to the outside perpendicular to the tangent line since a force directed to the outside of the circle always acts on the boat.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 28. A rock attached to a string swings in a vertical circle. Which free-body diagram could correctly describe the force(s) on the rock when it is at the highest point? a. b. c. d.

e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 29. A rock attached to a string swings in a vertical circle. Which free-body diagram could correctly describe the force(s) on the rock when the string is in one possible horizontal position? a. b. c.

d.

e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 30. A rock attached to a string swings in a vertical circle. Which free-body diagram could correctly describe the force(s) on the rock when it is at the lowest point?

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a.

b.

c.

d.

e.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 31. Two small, cylindrical plastic containers with flat bottoms are placed on a turntable that has a smooth, flat surface.

Canister A is empty; canister B contains lead shot. Each canister is the same distance r from the center. The coefficient of static friction between the canisters and the turntable is μs. When the speed of the turntable is gradually increased, a. only the lighter container slides outward off the turntable; the heavier one stays on. b. only the heavier container slides outward off the turntable; the lighter one stays on. c. both containers slide off the turntable at the same turntable speed. d. the lighter container slides inward. e. the heavier container slides inward.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 32. A hornet circles around a pop can at constant speed, once per second, in a path with a 12-cm diameter. We can conclude that the hornet's wings must push on the air with force components that are a. straight down. b. down and inwards. c. down and outwards. d. down and backwards. e. down, inwards and backwards.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 33. A hornet circles around a pop can at increasing speed while flying in a path with a 12-cm diameter. We can conclude that the hornet's wings must push on the air with force components that are a. straight down. b. down and inwards. c. down and outwards. d. down and backwards. e. down, backwards, and outwards.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 34. Frank says that if you release the string when swinging a ball in a horizontal circle, the ball flies out in the radial direction defined by the string at the instant you release the ball. John says that it flies out along a tangent line perpendicular to the string, and that it then drops straight down to the ground. Which one, if either, is correct? a. Frank, because the centrifugal force is no longer counteracted by the string. b. Frank, because balls naturally fly straight out. c. John, because there is no centrifugal force. d. John, because balls fall straight down when released. e. Neither, because although there is no centrifugal force, and the ball's velocity is tangent to the circle at the instant of release, the ball then follows a parabolic trajectory.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 35. The equation below is the solution to a problem.

.

The best physical representation of this equation is a. a sphere of 2.00-kg mass under a 6.00-N tension when at the bottom of a vertical circle. b. a sphere of 2.00-kg mass under a 6.00-N tension when at the side of a vertical circle. c. a sphere of 2.00-kg mass under a 6.00-N tension when at the top of a vertical circle. d. a sphere of 2.00-kg mass at any point on a horizontal circle. e. a 2.00-kg gecko running on the ceiling with a speed of 8.00 m/s.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 36. The equation below is the solution to a problem.

.

The best physical representation of this equation is a. a sphere of 2.00-kg mass under a 45.2-N tension when at the bottom of a vertical circle. b. a sphere of 2.00-kg mass under a 45.2-N tension when at the side of a vertical circle. c. a sphere of 2.00-kg mass under a 45.2-N tension when at the top of a vertical circle. d. a sphere of 2.00-kg mass at any point on a horizontal circle. e. a 2.00-kg gecko running on the ceiling with a speed of 8.00 m/s.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 37. The equation below is the solution to a problem.

.

The best physical representation of this equation is a. a sphere of 2.00-kg mass under a 25.6-N tension when at the bottom of a vertical circle. b. a sphere of 2.00-kg mass under a 25.6-N tension when at the side of a vertical circle. c. a sphere of 2.00-kg mass under a 25.6-N tension when at the top of a vertical circle. d. a sphere of 2.00-kg mass at any point on a horizontal circle. e. a 2.00-kg gecko running on the ceiling with a speed of 8.00 m/s.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 38. The coefficient of static friction for the tires of a race car is 0.950 and the coefficient of kinetic friction is 0.800. The car is on a level, circular track of 50.0-m radius on a planet where

compared to Earth's

. The

maximum safe speed on the track on the planet is ____ times as large as the maximum safe speed on Earth. a. 0.250 b. 0.500 c. 1.00 Copyright Cengage Learning. Powered by Cognero.

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d. 2.00 e. 4.00 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 39. The coefficient of static friction for the tires of a race car is 0.950 and the coefficient of kinetic friction is 0.800. The car is on a level, circular track of 50.0-m radius on a planet where

compared to Earth's

. If

the car is to be able to travel at the same speed on the planet as on Earth, the radius of the track on the planet must be ____ times as large as the radius of the track on Earth. a. 0.250 b. 0.500 c. 1.00 d. 2.00 e. 4.00 ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 40. The following equation was obtained by solving a physics problem:

The best physical representation of the situation is a. a car traveling at 16.0 m/s is 19.2° into a turn of a quarter circle on a level road. b. a mass on a string that is originally horizontal has fallen to where the angle between the string and the vertical direction is 19.2°. c. a mass on a string originally horizontal has fallen 19.2° from the horizontal direction. d. a car traveling at 16.0 m/s is on a circular curve banked at 19.2°. e. a car traveling at 16.0 m/s and going over a semicircular mountain-top road is 19.2° down from the top.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 41. An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 500Copyright Cengage Learning. Powered by Cognero.

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m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change? a. 0.25 b. 0.50 c. 1.00 d. 2.00 e. 4.00 ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 42. An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the radius were changed to 1000 m, but the speed remained the same, by what factor would its centripetal acceleration change? a. 0.25 b. 0.50 c. 1.00 d. 2.00 e. 4.00 ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 43. An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 1000m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change? a. 0.25 b. 0.50 c. 1.00 d. 2.00 e. 4.00 ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 44. A car enters a level, unbanked, semicircular hairpin turn of 100-m radius at a speed of 28 m/s. The coefficient of friction between the tires and the road is μ = 0.800. If the car maintains a constant speed of 28 m/s, it will a. attempt to dig into the road surface. b. tend to veer toward the center of the semicircle. c. arrive safely at the end of the semicircle. d. tend to veer toward the outside of the circle. e. veer toward the center for the first quarter circle, then veer toward the outside for the second quarter circle.

ANSWER: c Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 45. A car enters a level, unbanked semi-circular hairpin turn of 300 m radius at a speed of 40 m/s. The coefficient of friction between the tires and the road is μ = 0.25. If the car maintains a constant speed of 40 m/s, it will a. attempt to dig into the road surface. b. tend to veer toward the center of the semicircle. c. arrive safely at the end of the semicircle. d. tend to veer toward the outside of the circle. e. veer toward the center for the first quarter-circle, then veer toward the outside for the second quarter-circle.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 46. A space station in the form of a large wheel, 120 m in diameter, rotates to provide an "artificial gravity" of 3.00 m/s for persons located at the outer rim. Find the rotational frequency of the wheel (in revolutions per minute) that will produce this effect.

ANSWER: 2.14 rpm POINTS: 3 DIFFICULTY: Challenging REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False

2

47. An airplane pilot experiences weightlessness as she passes over the top of a loop-the-loop maneuver. If her speed is 200 m/s at the time, find the radius of the loop.

ANSWER: 4080 m POINTS: 2 DIFFICULTY: Average REFERENCES: 6.1 Extending the Particle in Uniform Circular Motion HAS VARIABLES: False 2

48. A race car starts from rest on a circular track of radius 400 m. Its speed increases at the constant rate of 0.500 m/s . At the point where the magnitudes of the radial and tangential accelerations are equal, determine (a) the speed of the race car, and (b) the elapsed time.

ANSWER: 14.1 m/s, 28.3 s POINTS: 2 DIFFICULTY: Average REFERENCES: 6.2 Nonuniform Circular Motion HAS VARIABLES: False 49. A small, dense object is suspended from the rear view mirror in a car by a lightweight fiber. As the car is accelerating 2 at 1.90 m/s , what angle does the string make with the vertical?

ANSWER: 11.0 degrees Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 6.2 Nonuniform Circular Motion HAS VARIABLES: False 50. A boy on board a cruise ship drops a 30.0-g marble into the ocean. If the resistive force proportionality constant is 0.500 kg/s, what is the terminal speed of the marble in m/s? a. 0.147 b. 0.294 c. 0.588 d. 1.18 e. 2.35 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 6.4 Motion in the Presence of Resistive Forces HAS VARIABLES: False 51. A skydiver of 75 kg mass has a terminal velocity of 60 m/s. At what speed is the resistive force on the skydiver half that when at terminal speed? a. 15 m/s b. 49 m/s c. 30 m/s d. 42 m/s e. 36 m/s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 6.4 Motion in the Presence of Resistive Forces HAS VARIABLES: False 52. If a 20-kg object dropped in air has a terminal speed of 60 m/s, what was its acceleration at 30 m/s? a. 9.80 m/s2 b. 7.35 m/s2 c. 4.90 m/s2 d. 2.45 m/s2 e. More information is needed to answer this question.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 6.4 Motion in the Presence of Resistive Forces HAS VARIABLES: False 53. If a dense, 20.0-kg object is falling in air at half its terminal velocity, what is the drag force on the object at this moment?

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a. 24.5 N b. 49.0 N c. 69.3 N d. 98.0 N e. 139 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 6.4 Motion in the Presence of Resistive Forces HAS VARIABLES: False 54. What is the net force on a 10-kg solid steel sphere falling in air at terminal speed? a. 980 N b. 200 N c. 98 N d. 49 N e. Some value other than those given above.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.4 Motion in the Presence of Resistive Forces HAS VARIABLES: False −16

55. A sample of blood is placed into a centrifuge of radius 15.0 cm. The mass of a red corpuscle is 3.0 × 10 kg, and the −11 centripetal force required to make it settle out of the plasma is 4.0 × 10 N. At how many revolutions per second should the centrifuge be operated?

ANSWER: 150 rev/s (9000 rpm) POINTS: 3 DIFFICULTY: Challenging REFERENCES: 6.4 Motion in the Presence of Resistive Forces HAS VARIABLES: False 56. The force of static friction exerted on an automobile's tires by the ground a. provides the accelerating force that makes the car move forward. b. does positive work on the car while it is accelerating. c. does negative work on the car while it is decelerating. d. does everything listed in (a), (b) and (c). e. only does positive or negative work as in (b) or (c).

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 6.4 Motion in the Presence of Resistive Forces HAS VARIABLES: False

1. A 5.0-kg object is pulled along a horizontal surface at a constant speed by a 15-N force acting 20° above the horizontal.

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How much work is done by this force as the object moves 6.0 m? a. 78 J b. 82 J c. 85 J d. 74 J e. 43 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 7.2 Work Done by a Constant Force HAS VARIABLES: False 2. The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal, frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is WA; that on B is WB. Which statement is correct? a. WA = WB. b.

WA =

WB.

c. WA = 2 WB. d. WA = 4 WB. e. WB = 2 WA. ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.2 Work Done by a Constant Force HAS VARIABLES: False 3. Carts A and B have equal masses and travel equal distances on straight, frictionless tracks, while a constant force F is applied to A, and a constant force 2F is applied to B. The relative amounts of work done by the two forces are related by a. WA = 4 WB. b. WA = 2 WB. c. WA = WB. d. WB = 2 WA. e. WB = 4 WA. ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.2 Work Done by a Constant Force HAS VARIABLES: False 4. Carts A and B have equal masses and travel equal distances D on side-by-side straight, frictionless tracks, while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities A and B of the bodies at the end of distance D are related by a. B = A .

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b.

B=

A.

c.

B=2

A.

d.

B=4

A.

e.

A=2

B.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.2 Work Done by a Constant Force HAS VARIABLES: False 5. Jane and Jake are looking at what happens to body 1 of mass m and body 2 of mass 2m, initially at rest, when equal forces are applied separately to the two bodies. Jake says that equal forces applied for equal times do equal amounts of work on the two bodies. Jane says that the two forces do equal amounts of work only if the two bodies move equal distances in the direction of the forces. Which one, if either, is correct? a. Jake, because the speed of body 1 is half the speed of body 2, but m1v1 = m2v2. b. Jane, because work does not depend on mass, only on force times distance. c. Jake, because all bodies travel equal distances when equal forces are applied for equal times. d. Jane, because it takes the same time for all bodies to travel equal distances when equal forces are involved. e. Neither, because we can't compare the amounts of work done on bodies of different mass.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.2 Work Done by a Constant Force HAS VARIABLES: False 6. A constant force of 12 N in the positive x direction acts on a 4.0-kg object as it moves from the origin to the point m. How much work is done by the given force during this displacement? a. +60 J b. +84 J c. +72 J d. +48 J e. +57 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 7.2 Work Done by a Constant Force HAS VARIABLES: False 7. A constant force of 15 N in the negative y direction acts on a particle as it moves from the origin to the point m. How much work is done by the given force during this displacement? a. +45 J b. −45 J c. +30 J Copyright Cengage Learning. Powered by Cognero.

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d. −30 J e. +75 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.2 Work Done by a Constant Force HAS VARIABLES: False 8. An object moving along the x axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m?

a. −10 J b. +10 J c. +30 J d. −30 J e. +40 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 9. A body moving along the x axis is acted upon by a force Fx that varies with x as shown. How much work is done by this force as the object moves from x = 1 m to x = 8 m?

a. −2 J b. −18 J Copyright Cengage Learning. Powered by Cognero.

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c. −10 J d. −26 J e. +18 J ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 2

10. A force acting on an object moving along the x axis is given by Fx = (14x − 3.0x ) N, where x is in m. How much work is done by this force as the object moves from x = −1 m to x = +2 m? a. +12 J b. +28 J c. +40 J d. +42 J e. −28 J ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 11. The force an ideal spring exerts on an object is given by Fx = −kx, where x measures the displacement of the object from its equilibrium (x = 0) position. If k = 60 N/m, how much work is done by this force as the object moves from x = −0.20 m to x = 0? a. −1.2 J b. +1.2 J c. +2.4 J d. −2.4 J e. +3.6 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 12. Planets go around the Sun in elliptical orbits. The highly exaggerated diagram below shows a portion of such an orbit and the force on the planet at one position along that orbit. The planet is moving to the right. F|| and are the components of the force parallel (tangential) and perpendicular (normal) to the orbit. The work they do is W|| and the position shown,

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a. W|| slows the planet down;

speeds it up.

b. W|| slows the planet down;

does no work on it.

c. W|| speeds the planet up;

does no work on it.

d. W|| speeds the planet up;

slows it down.

e. W|| does no work on it;

speeds the planet up.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 13. A mass attached to the end of a spring is pulled out and released on a surface with friction. The work

done

on the mass by the force exerted by the spring a. never has the same sign as the change in energy owing to friction. b. always has the same sign as the change in energy owing to friction. c. has the same sign as the change in energy owing to friction during one-half of each cycle. d. never has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force. e. always has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 14. The work

done by the force exerted by the spring on a mass attached to the end of the spring when the mass

has displacement d is a. always negative. b. always positive. c. negative half the time, positive the other half of the time. d. positive more than it is negative. e. negative more than it is positive.

ANSWER: c POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 15. A 30-kg child sitting 5.0 m from the center of a merry-go-round has a constant speed of 5.0 m/s. While she remains seated in the same spot and travels in a circle, the work the seat performs on her in one complete rotation is a. 0 J. b. 150 J. c. 1 500 J. d. 4 700 J. e. 46 000 J. ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 16. Sally, who weighs 450 N, stands on a skateboard while Roger pushes it forward 13.0 m at constant velocity on a level, straight street. He applies a constant 100-N force. a. The work Roger does on the skateboard is 0 J. b. The work Roger does on the skateboard is 1 300 J. c. The work Sally does on the skateboard is 1 300 J. d. The work Sally does on the skateboard is 5 850 J. e. The work Roger does on the skateboard is 5 850 J. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 17. Negative work can be done a. by friction on the tires while a car is accelerating without skidding. b. by a spring at the bottom of an elevator shaft when it stops a falling elevator. c. by a hand catching a ball. d. by all of the above. e. only by (b) and (c) above.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 18. Positive work can be done a. by friction on the tires when a car is accelerating without skidding. b. by a spring when it launches a clown in the air. c. by a hand throwing a ball. d. by all of the above.

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e. only by (b) and (c) above.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.3 Work Done by a Varying Force HAS VARIABLES: False 19. A 2.0-kg particle has an initial velocity of

m/s. Some time later, its velocity is

m/s. How much

work was done by the resultant force during this time interval, assuming no energy is lost in the process? a. 17 J b. 49 J c. 19 J d. 53 J e. 27 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 20. A block is pushed across a rough, horizontal surface from point A to point B by a force (magnitude P = 5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N, and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B?

a. 2.7 J b. 1.0 J c. 2.2 J d. 1.6 J e. 3.2 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 21. A 4.0-kg block is lowered down a 37° incline a distance of 5.0 m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B it is 20 J. How much work is done on the block by the force of friction between A and B?

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a. −58 J b. −53 J c. −68 J d. −63 J e. −47 J ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 22. If the resultant force acting on a 2.0-kg object is equal to object moves from

m to

N, what is the change in kinetic energy as the

m?

a. +36 J b. +28 J c. +32 J d. +24 J e. +60 J ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 23. As a 2.0-kg object moves from

m to

m, the constant resultant force acting on it is equal to

N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position? a. 62 J b. 53 J c. 73 J d. 86 J e. 24 J ANSWER: POINTS: DIFFICULTY:

b 3 Challenging

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REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 24. A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

a. 27 J b. 20 J c. 24 J d. 17 J e. 37 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 25. A 10-kg block on a horizontal, frictionless surface is attached to a light spring (force constant = 0.80 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown. What is the speed of the block when it is 13 cm from its equilibrium position?

a. 0.85 m/s b. 0.89 m/s c. 0.77 m/s d. 0.64 m/s e. 0.52 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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26. A 10-kg block on a horizontal, frictionless surface is attached to a light spring (force constant = 1.2 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P) acting parallel to the surface is applied to the block, as shown. When the block is 8.0 cm from the equilibrium position, it has a speed of 0.80 m/s. How much work is done on the block by the force P as the block moves the 8.0 cm?

a. 8.3 J b. 6.4 J c. 7.0 J d. 7.7 J e. 3.9 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 27. The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm? k = 2.0 kN/m

a. 3.7 m/s b. 4.4 m/s c. 4.9 m/s d. 5.4 m/s e. 14 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 28. A 2.0-kg block situated on a frictionless incline is connected to a light spring (k = 100 N/m), as shown. The block is released from rest when the spring is unstretched. The pulley is frictionless and has negligible mass. What is the speed of the block when it has moved 0.20 m down the plane?

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a. 76 cm/s b. 68 cm/s c. 60 cm/s d. 82 cm/s e. 57 cm/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 29. A 2.0-kg block sliding on a frictionless, horizontal surface is attached to one end of a horizontal spring (k = 600 N/m) which has its other end fixed. The speed of the block when the spring is extended 20 cm is equal to 3.0 m/s. What is the maximum speed of this block as it oscillates? a. 4.6 m/s b. 5.3 m/s c. 5.7 m/s d. 4.9 m/s e. 3.5 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 30. A 2.0-kg body moving along the x axis has a velocity vx = 5.0 m/s at x = 0. The only force acting on the object is given

by Fx = (−4.0x) N, where x is in m. For what value of x will this object first come (momentarily) to rest? a. 4.2 m b. 3.5 m c. 5.3 m d. 6.4 m e. 5.0 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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31. A 1.5-kg object moving along the x axis has a velocity of +4.0 m/s at x = 0. If the only force acting on this object is shown in the figure, what is the kinetic energy of the object at x = +3.0 m?

a. 18 J b. 21 J c. 23 J d. 26 J e. 8 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 32. The only force acting on a 1.6-kg body as it moves along the x axis is given in the figure. If the velocity of the body at x = 2.0 m is 5.0 m/s, what is its kinetic energy at x = 5.0 m?

a. 52 J b. 44 J c. 36 J d. 60 J e. 25 J ANSWER: POINTS:

c 2

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DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 33. The only force acting on a 2.0-kg body moving along the x axis is given by Fx = (2.0x) N, where x is in m. If the velocity of the object at x = 0 is +3.0 m/s, how fast is it moving at x = 2.0 m? a. 4.2 m/s b. 3.6 m/s c. 5.0 m/s d. 5.8 m/s e. 2.8 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 34. The only force acting on a 2.0-kg body as it moves along the x axis is given by Fx = (12 − 2.0x) N, where x is in m.

The velocity of the body at x = 2.0 m is 5.5 m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction? a. 36 J b. 39 J c. 43 J d. 46 J e. 30 J ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 35. The only force acting on a 1.8-kg body as it moves along the x axis is given by Fx = −(3.0x) N, where x is in m. If the velocity of the body at x = 0 is vx = +8.0 m/s, at what value of x will the body have a velocity of +4.0 m/s? a. 5.7 m b. 5.4 m c. 4.8 m d. 4.1 m e. 6.6 m ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 36. Equal amounts of work are performed on two bodies, A and B, initially at rest, and of masses M and 2M, respectively.

The relation between their speeds immediately after the work has been done on them is Copyright Cengage Learning. Powered by Cognero.

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a.

vA =

vB.

b. vA = 2vB. c. vA = vB. d.

vB =

vA.

e. vB = 2vA. ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 37. Two cannonballs are dropped from a second-floor physics lab at height h above the ground. Ball B has four times the mass of ball A. When the balls pass the bottom of a first-floor window at height

above the ground, the relation between

their kinetic energies, KA and KB, is a. KA = 4KB. b. KA = 2KB. c. KA = KB. d. KB = 2KA. e. KB = 4KA. ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 38. Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B a 60-kg mass. The relation between their kinetic energies at the instant of launch is a. . b. . c. KA = KB. d. . e. .

ANSWER: POINTS: DIFFICULTY:

c 1 Easy

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REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 39. Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B a 60-kg mass. The relation between their speeds at the instant of launch is a. . b. . c. vA = vB. d. . e. .

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 40. In a contest, two tractors pull two identical blocks of stone the same distance over identical surfaces. However, block A is moving twice as fast as block B when it crosses the finish line. Which statement is correct? a. Block A has twice as much kinetic energy as block B. b. Block B has lost twice as much kinetic energy to friction as block A. c. Block B has lost twice as much kinetic energy as block A. d. Both blocks have had equal losses of energy to friction. e. No energy is lost to friction because the ground has no displacement.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 41. Two eggs of equal mass are thrown at a blanket with equal velocity. Egg B hits the blanket but egg A hits the wall instead. Compare the work done on the eggs in reducing their velocities to zero. a. More work was done on A than on B. b. More work was done on B than on A. c. The amount of work is the same for both. d. It is meaningless to compare the amount of work because the forces were so different. e. Work was done on B, but no work was done on A because the wall did not move.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 42. The graph below shows how the force on a 0.500-kg particle varies with position. If the particle has speed at x = 0.00 m, what is its speed in m/s when x = 8.00 m?

a. 2.00 b. 10.7 c. 14.8 d. 15.0 e. 21.1 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 43. The equation below is the solution to a physics problem:

.

The most likely physical situation it describes is a. a 2.30-kg cart rolling up a 30° incline. b. a 2.30-kg cart rolling down a 30° incline. c. a 2.30-kg cart rolling up a 60° incline. d. a 2.30-kg cart rolling down a 60° incline. e. a 2.30-kg cart rolling down a 90° incline.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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44. A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30°. What is the kinetic energy of the baseball at the highest point of the trajectory?

ANSWER: 90 J POINTS: 2 DIFFICULTY: Average REFERENCES: 7.4 Kinetic Energy and the Work-Kinetic Energy Theorem HAS VARIABLES: False 45. A 2.0-kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position. How much work is done by the gravitational force on the projectile? a. +0.29 kJ b. −0.29 kJ c. +30 J d. −30 J e. −50 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.5 Potential Energy of a System HAS VARIABLES: False 46. How much work is done by a person lifting a 2.0-kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s? a. 0.22 kJ b. 0.20 kJ c. 0.24 kJ d. 0.27 kJ e. 0.31 kJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.5 Potential Energy of a System HAS VARIABLES: False 47. A 2.5-kg object falls vertically downward in a viscous medium at a constant speed of 2.5 m/s. How much work is done by the force the viscous medium exerts on the object as it falls 80 cm? a. +2.0 J b. +20 J c. −2.0 J d. −20 J e. +40 J ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 7.5 Potential Energy of a System HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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48. When a ball rises vertically to a height h and returns to its original point of projection, the work done by the gravitational force is a. 0. b. −mgh. c. +mgh. d. −2mgh. e. +2mgh.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.5 Potential Energy of a System HAS VARIABLES: False 49. Two balls, A and B, of mass m and 2m, respectively, are carried to height h at constant velocity, but B rises twice as fast as A. The work the gravitational force does on B is a. one-quarter the work done on A. b. one-half the work done on A. c. the same as the work done on A. d. twice the work done on A. e. four times the work done on A. ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.5 Potential Energy of a System HAS VARIABLES: False 50. After a skydiver reaches terminal velocity, a. the force of gravity no longer performs work on the skydiver. b. work performed by the force of gravity is converted into gravitational potential energy. c. gravitational potential energy is no longer available to the system of the skydiver plus the Earth. d. gravitational potential energy is converted into thermal energy. e. thermal energy is converted into gravitational potential energy.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.5 Potential Energy of a System HAS VARIABLES: False 51. Two identical springs with spring constant 50 N/m support a 5.0-N weight as in the picture below. What is the change in length of each spring when the weight is hung on the springs?

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a. 2.9 cm b. 5.0 cm c. 5.8 cm d. 7.5 cm e. 10.0 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 7.5 Potential Energy of a System HAS VARIABLES: False 52. A baseball is thrown and lands 120 m away. While the ball is in flight, assuming the effect of air friction is negligible, which of the following is true? a. At maximum height the ball has its greatest kinetic energy. b. The horizontal component of the baseball’s kinetic energy is constant. c. The vertical component of the baseball’s kinetic energy is constant. d. The mechanical energy of the baseball is greater when nearer to the ground. e. No answer above is correct.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.5 Potential Energy of a System HAS VARIABLES: False 53. A block slides on a rough, horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B, as shown. Points A and B are 1.5 m apart. If the kinetic energies of the block at A and B are 5.0 J and 4.0 J, respectively, how much work is done on the block by the force of friction as the block moves from A to B?

a. −3.3 J b. +1.3 J c. +3.3 J d. −1.3 J e. +4.6 J ANSWER: POINTS:

a 2

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DIFFICULTY: Average REFERENCES: 7.6 Conservative and Nonconservative Forces HAS VARIABLES: False 54. A 3.0-kg block is dragged over a rough, horizontal surface by a constant force of 16 N acting at an angle of 37° above the horizontal as shown. The speed of the block increases from 4.0 m/s to 6.0 m/s in a displacement of 5.0 m. What work was done by the friction force during this displacement?

a. −34 J b. −64 J c. −30 J d. −94 J e. +64 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 7.6 Conservative and Nonconservative Forces HAS VARIABLES: False 55. A 20-kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 2.0 cm toward its equilibrium position, its kinetic energy is 13 J. How much work is done by the frictional force on the block as it moves the 2.0 cm? a. −2.5 J b. −1.4 J c. −3.0 J d. −1.9 J e. −14 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.6 Conservative and Nonconservative Forces HAS VARIABLES: False 56. A 10-kg block on a rough, horizontal surface is attached to a light spring (force constant = 1.4 kN/m). The block is pulled 8.0 cm to the right from its equilibrium position and released from rest. The frictional force between the block and surface has a magnitude of 30 N. What is the kinetic energy of the block as it passes through its equilibrium position? a. 4.5 J b. 2.1 J c. 6.9 J d. 6.6 J Copyright Cengage Learning. Powered by Cognero.

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e. 4.9 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 7.6 Conservative and Nonconservative Forces HAS VARIABLES: False 57. When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction μk, then dragged back along the same path to its original position, the work done by friction is a. 0. b. −μkmgd. c. +μkmgd. d. −2μkmgd. e. +2μkmgd.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.6 Conservative and Nonconservative Forces HAS VARIABLES: False 58. A moving particle is subject to conservative forces only. When its kinetic energy decreases by 10 J, what happens to its mechanical energy? a. It increases by 10 J. b. It decreases by 10 J. c. It increases, but not necessarily by 10 J. d. It decreases, but not necessarily by 10 J. e. It remains the same.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.6 Conservative and Nonconservative Forces HAS VARIABLES: False 59. The force a spring exerts on a body is a conservative force because a. a spring always exerts a force opposite to the displacement of the body. b. a spring always exerts a force parallel to the displacement of the body. c. the work a spring does on a body is equal for compressions and extensions of equal magnitude. d. the work a spring does on a body is equal and opposite for compressions and extensions of equal magnitude. e. the net work a spring does on a body is zero when the body returns to its initial position.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.6 Conservative and Nonconservative Forces HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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60. For a force to be a conservative force, when applied to a single test body, a. it must have the same value at all points in space. b. it must have the same direction at all points in space. c. it must be parallel to a displacement in any direction. d. equal work must be done in equal displacements. e. no net work must be done for motion in closed paths.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.6 Conservative and Nonconservative Forces HAS VARIABLES: False 61. Which of the following is a conservative force? (All refer to a car on a slope.) a. The force you exert on the car pushing it uphill. b. The force exerted by rain drops falling on the car. c. The frictional force of the road on the car. d. The gravitational force acting on the car. e. The force you exert on the car (pushing it uphill) after it starts to slide downhill.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 7.6 Conservative and Nonconservative Forces HAS VARIABLES: False 62. A conservative force on a particle moving along the x axis is given by potential that is associated with this force? a.

. Which of the following is a

b. c. d. e. No answer given above is correct.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 7.7 Relationship Between Conservative Forces and Potential Energy HAS VARIABLES: False 63. A particle is subject to the potential particle at the point (x, y) = (2.0, 3.0)? a. 24 b. −24 c. 14 d. −14 Copyright Cengage Learning. Powered by Cognero.

. What is the value of the y component of the force on the

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e. 28 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 7.7 Relationship Between Conservative Forces and Potential Energy HAS VARIABLES: False 64. For the potential ANSWER:

, find the stable equilibrium point, if any.

POINTS: 3 DIFFICULTY: Challenging REFERENCES: 7.8 Energy Diagrams and Equilibrium of a System HAS VARIABLES: False

1. A single conservative force Fx = (6.0x − 12) N (x is in m) acts on a particle moving along the x axis. The potential energy associated with this force is assigned a value of +20 J at x = 0. What is the potential energy at x = 3.0 m? a. +11 J b. +29 J c. +9.0 J d. −9.0 J e. +20 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.1 Analysis Model: Nonisolated System (Energy) HAS VARIABLES: False 2. As a particle moves along the x axis it is acted upon by a single conservative force given by Fx = (20 − 4.0x) N, where x is in m. The potential energy associated with this force has the value +30 J at the origin (x = 0). What is the value of the potential energy at x = 4.0 m? a. −48 J b. +78 J c. −18 J d. +48 J e. +80 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.1 Analysis Model: Nonisolated System (Energy) HAS VARIABLES: False 3. A 0.40-kg particle moves under the influence of a single conservative force. At point A, where the particle has a speed of 10 m/s, the potential energy associated with the conservative force is +40 J. As the particle moves from A to B, the force does +25 J of work on the particle. What is the value of the potential energy at point B? a. +65 J Copyright Cengage Learning. Powered by Cognero.

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b. +15 J c. +35 J d. +45 J e. −40 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.1 Analysis Model: Nonisolated System (Energy) HAS VARIABLES: False 4. As a 1.0-kg object moves from point A to point B, it is acted upon by a single conservative force which does −40 J of work during this motion. At point A, the speed of the particle is 6.0 m/s and the potential energy associated with the force is +50 J. What is the potential energy at point B? a. +72 J b. +10 J c. +90 J d. +28 J e. +68 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.1 Analysis Model: Nonisolated System (Energy) HAS VARIABLES: False 5. A 12-kg block on a horizontal, frictionless surface is attached to a light spring (force constant = 0.80 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown. What is the speed of the block when it is 13 cm from its equilibrium position?

a. 0.78 m/s b. 0.81 m/s c. 0.71 m/s d. 0.58 m/s e. 0.64 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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6. A 7.0-kg block on a horizontal, frictionless surface is attached to a light spring (force constant = 1.2 kN/m). The block is initially at rest at its equilibrium position when a force of magnitude P acting parallel to the surface is applied to the block, as shown. When the block is 8.0 cm from the equilibrium position, it has a speed of 0.80 m/s. How much work is done on the block by the force P as the block moves the 8.0 cm?

a. 7.4 J b. 5.4 J c. 6.1 J d. 6.7 J e. 4.9 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 7. A 0.60-kg object is suspended from the ceiling at the end of a 2.0-m string. When pulled to the side and released, it has a speed of 4.0 m/s at the lowest point of its path. What maximum angle does the string make with the vertical as the object swings up? a. 61° b. 54° c. 69° d. 77° e. 47° ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 8. A pendulum is made by letting a 2.0-kg object swing at the end of a string that has a length of 1.5 m. The maximum angle the string makes with the vertical as the pendulum swings is 30°. What is the speed of the object at the lowest point in its trajectory? a. 2.0 m/s b. 2.2 m/s c. 2.5 m/s d. 2.7 m/s e. 3.1 m/s Copyright Cengage Learning. Powered by Cognero.

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ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 9. A 2.0-kg mass swings at the end of a light string (length = 3.0 m). Its speed at the lowest point on its circular path is 6.0 m/s. What is its kinetic energy at an instant when the string makes an angle of 50° with the vertical? a. 21 J b. 15 J c. 28 J d. 36 J e. 23 J ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 10. A 2.5-kg object suspended from the ceiling by a string that has a length of 2.5 m is released from rest with the string 40° below the horizontal position. What is the tension in the string at the instant when the object passes through its lowest position? a. 11 N b. 25 N c. 42 N d. 18 N e. 32 N ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 11. A certain pendulum consists of a 1.5-kg mass swinging at the end of a string (length = 2.0 m). At the lowest point in the swing, the tension in the string is equal to 20 N. To what maximum height above this lowest point will the mass rise during its oscillation? a. 77 cm b. 50 cm c. 63 cm d. 36 cm e. 95 cm ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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12. A 0.80-kg object tied to the end of a 2.0-m string swings as a pendulum. At the lowest point of its swing, the object has a kinetic energy of 10 J. Determine the speed of the object at the instant when the string makes an angle of 50° with the vertical. a. 5.6 m/s b. 4.4 m/s c. 3.3 m/s d. 5.0 m/s e. 6.1 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 13. A 0.04-kg ball is thrown from the top of a 30-m tall building (point A) at an unknown angle above the horizontal. As shown in the figure, the ball attains a maximum height of 10 m above the top of the building before striking the ground at point B. If air resistance is negligible, what is the value of the kinetic energy of the ball at B minus the kinetic energy of the ball at A (KB − KA)?

a. 12 J b. −12 J c. 20 J d. −20 J e. 32 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 14. A 1.2-kg mass is projected from ground level with a velocity of 30 m/s at some unknown angle above the horizontal.

A short time after being projected, the mass barely clears a 16-m tall fence. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass as it clears the fence? a. 0.35 kJ b. 0.73 kJ c. 0.40 kJ d. 0.68 kJ Copyright Cengage Learning. Powered by Cognero.

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e. 0.19 kJ ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 15. A 2.0-kg mass is projected from the edge of the top of a 20-m tall building with a velocity of 24 m/s at some unknown angle above the horizontal. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass just before it strikes the ground? a. 0.18 kJ b. 0.97 kJ c. 0.89 kJ d. 0.26 kJ e. 0.40 kJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 16. A skier weighing 0.70 kN goes over a frictionless, circular hill as shown. If the skier's speed at point A is 9.2 m/s, what is his speed at the top of the hill (point B)?

a. 3.1 m/s b. 6.2 m/s c. 5.2 m/s d. 4.1 m/s e. 6.5 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 17. A skier weighing 0.80 kN comes down a frictionless ski run that is circular (R = 30 m) at the bottom, as shown. If her speed is 12 m/s at point A, what is her speed at the bottom of the hill (point B)?

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a. 17 m/s b. 19 m/s c. 18 m/s d. 20 m/s e. 12 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 18. A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. The upper end is depressed 20 cm, and a 4.0-kg block is placed on top of the depressed spring. The system is then released from rest.

How far above the point of release will the block rise? a. 46 cm b. 36 cm c. 41 cm d. 31 cm e. 20 cm ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 19. A spring (k = 200 N/m) is suspended with its upper end supported from a ceiling. With the spring hanging in its equilibrium configuration, an object (mass = 2.0 kg) is attached to the lower end and released from rest. What is the speed of the object after it has fallen 4.0 cm? a. 90 cm/s b. 79 cm/s c. 96 cm/s d. 83 cm/s e. 57 cm/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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20. A 2.0-kg block sliding on a horizontal, frictionless surface is attached to one end of a horizontal spring (k = 200 N/m) which has its other end fixed. If the block has a speed of 4.0 m/s as it passes through the equilibrium position, what is its speed when it is 20 cm from the equilibrium position? a. 2.6 m/s b. 3.1 m/s c. 3.5 m/s d. 1.9 m/s e. 2.3 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 21. A block (mass = 4.0 kg) sliding on a horizontal, frictionless surface is attached to one end of a horizontal spring (k = 100 N/m) which has its other end fixed. If the maximum distance the block slides from the equilibrium position is equal to 20 cm, what is the speed of the block at an instant when it is a distance of 16 cm from the equilibrium position? a. 71 cm/s b. 60 cm/s c. 80 cm/s d. 87 cm/s e. 57 cm/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 22. A 1.0-kg block is released from rest at the top of a frictionless incline that makes an angle of 37° with the horizontal.

An unknown distance down the incline from the point of release, there is a spring with k = 200 N/m. It is observed that the mass is brought momentarily to rest after compressing the spring 0.20 m. How far does the mass slide from the point of release until it is brought momentarily to rest? a. 0.98 m b. 0.68 m c. 0.82 m d. 0.55 m e. 0.20 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 23. A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed?

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a. 2.2 m/s b. 2.5 m/s c. 1.9 m/s d. 1.5 m/s e. 3.6 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 24. A spring (k = 600 N/m) is at the bottom of a frictionless plane that makes an angle of 30° with the horizontal. The upper end of the spring is depressed 0.10 m, and a 2.0-kg block is placed against the depressed spring. The system is then released from rest. What is the kinetic energy of the block at the instant it has traveled 0.10 m and the spring has returned to its uncompressed length? a. 2.0 J b. 1.8 J c. 2.2 J d. 1.6 J e. 1.0 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 25. A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. A 2.0-kg block that is initially 0.40 m above the upper end of the spring is dropped from rest onto the spring. What is the kinetic energy of the block at the instant it has fallen 0.50 m (compressing the spring 0.10 m)? a. 5.3 J b. 6.8 J c. 6.3 J d. 5.8 J e. 6.5 J ANSWER: b Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 26. A small lead sphere of mass m is hung from a spring of spring constant k. The gravitational potential energy of the system equals zero at the equilibrium position of the spring before the weight is attached. The total mechanical energy of the system when the mass is hanging at rest is a. −kx2. b.

−

2

kx .

c. 0. d.

2 + kx . e. +kx2.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 27. Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is a. mgl. b. 3mgl. c. mgl. d. 6mgl. e. 9mgl.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 28. A pendulum bob has potential energy U0 when held taut in a horizontal position. The bob falls until it is 30° away from the horizontal position, when it has potential energy UA. It continues to fall until the string is vertical, when it has potential energy UB. Compare its potential energies at O, A, and B.

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a. U0 = UA = UB. b. UA − UB = 2U0. c. UA − UB = U0 − UA. d. U0 = UB = 2UA. e. U0 − UA = 2(UA − UB).

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 29. A spring with spring constant k = 800 N/m is compressed 12 cm from its equilibrium position. A spring with spring constant k = 400 N/m has the same elastic potential energy as the first spring when its extension is a. 0.060 m. b. 0.085 m. c. 0.12 m. d. 0.17 m. e. 0.24 m.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 30. A spring with spring constant k = 800 N/m is extended 12 cm from its equilibrium position. A spring with 6.0-cm extension from equilibrium will have the same potential energy as the first spring if its spring constant is a. 200 N/m. b. 400 N/m. c. 800 N/m. d. 1 600 N/m. e. 3 200 N/m.

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ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 31. Identical masses m are attached to identical springs of spring constant k suspended from the ceiling. With both masses hanging in their equilibrium positions, mass A is pulled down 10 cm and released while mass B is pushed up 10 cm and released. Which statement is correct? a. Mass A will travel a smaller distance to its highest point than mass B will travel to its lowest point. b. Mass A will travel a greater distance to its highest point than mass B will travel to its lowest point. c. Masses A and B will travel equal distances between their highest and lowest points. d. More work was done on mass A by the extending force than on mass B by the compressing force. e. The total work done on mass A by the extending force was equal to the total work done on mass B by the compressing force.

ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 32. The solution to a problem is the equation below. Which description best fits this solution?

a. A vertical spring compressed 0.120 m shoots a 2.00-kg mass 2.90 cm above the equilibrium position of the spring. b. A vertical spring stretched 0.120 m shoots a 2.00-kg mass 9.10 cm above the equilibrium position of the spring. c. A vertical spring compressed 0.120 m shoots a 2.00-kg mass 12.0 cm above the equilibrium position of the spring. d. A vertical spring compressed 0.120 m shoots a 2.00-kg mass 14.9 cm above the equilibrium position of the spring. e. A 2.00-kg mass has fallen 0.820 m and compressed the upper end of a vertical spring 12.0 cm below the equilibrium position.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 33. Any change of the energy of a system occurs because of a. energy transfer across the boundaries of the system.

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b. combustion of fuels within the system. c. radioactive decay of elements within the system. d. all of the above. e. only (b) and (c) above.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 34. Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen equal distances, we find that a. KB = KA. b. KB = 2KA. c. KB = 4KA. d. KA = 2KB. e. KA = 4KB. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 35. Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen for equal times, we find that a. KB = KA. b. KB = 2KA. c. KB = 4KA. d. KA = 2KB. e. KA = 4KB. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 36. A surprising demonstration involves dropping an egg from a third-floor window to land on a foam-rubber pad 2 in. (5 cm) thick without breaking. If a 56-gram egg falls 12 m, and the foam pad stops the egg in 6.25 ms, by how much is the pad compressed?

ANSWER: 4.8 cm POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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37. A 70-kg high jumper leaves the ground with a vertical velocity of 6.0 m/s. How high can he jump?

ANSWER: 1.84 m POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 38. A simple pendulum, 2.0 m in length, is released from rest when the support string is at an angle of 25° from the vertical. What is the speed of the suspended mass at the bottom of the swing?

ANSWER: 1.9 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 3

39. An automobile (m = 1.00 × 10 kg) is driven into a brick wall in a safety test. The bumper behaves like a spring (k = 6 5.00 × 10 N/m), and is observed to compress a distance of 3.16 cm as the car is brought to rest. What was the initial speed of the automobile?

ANSWER: 2.23 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 40. An ore car of mass 4 000 kg starts from rest and rolls downhill on tracks from a mine. A spring with k = 400 000 N/m is located at the end of the tracks. At the spring's maximum compression, the car is at an elevation 10 m lower than its elevation at the starting point. How much is the spring compressed in stopping the ore car? Ignore friction.

ANSWER: 1.4 m POINTS: 2 DIFFICULTY: Average REFERENCES: 8.2 Analysis Model: Isolated System (Energy) HAS VARIABLES: False 41. A 1.5-kg block sliding on a rough, horizontal surface is attached to one end of a horizontal spring (k = 200 N/m) which has its other end fixed. If this system is displaced 20 cm horizontally from the equilibrium position and released from rest, the block first reaches the equilibrium position with a speed of 2.0 m/s. What is the coefficient of kinetic friction between the block and the horizontal surface on which it slides? a. 0.34 b. 0.24 c. 0.13 d. 0.44 e. 0.17 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.3 Situations Involving Kinetic Friction Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 42. A 2.0-kg block slides down a fixed, rough, curved track. The block has a speed of 5.0 m/s after its height above a horizontal surface has decreased by 1.8 m. Assume the block starts from rest. What is the change in mechanical energy of the block caused by the force of friction during this descent? a. −14 J b. −12 J c. −10 J d. −16 J e. −25 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 43. A 0.75-kg sphere is released from rest and is moving 5.0 m/s after falling 2.0 m in a viscous medium. What is the change in mechanical energy caused by the force the viscous medium exerts on the sphere during this descent? a. −6.1 J b. −4.6 J c. −5.3 J d. −6.8 J e. −2.7 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 44. A 12-kg projectile is launched with an initial vertical speed of 20 m/s. It rises to a maximum height of 18 m above the launch point. What is the change in mechanical energy caused by the dissipative (air) resistive force on the projectile during this ascent? a. −0.64 kJ b. −0.40 kJ c. −0.52 kJ d. −0.28 kJ e. −0.76 kJ ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 45. A 10-kg object is dropped from rest. After falling a distance of 50 m, it has a speed of 26 m/s. What is the change in mechanical energy caused by the dissipative (air) resistive force on the object during this descent? a. −1.3 kJ b. −1.5 kJ Copyright Cengage Learning. Powered by Cognero.

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c. −1.8 kJ d. −2.0 kJ e. −2.3 kJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 46. The block shown is released from rest when the spring is stretched a distance d. If k = 50 N/m, m = 0.50 kg, d = 10 cm, and the coefficient of kinetic friction between the block and the horizontal surface is equal to 0.25, determine the speed of the block when it first passes through the position for which the spring is unstretched.

a. 92 cm/s b. 61 cm/s c. 71 cm/s d. 82 cm/s e. 53 cm/s ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 47. A 2.0-kg block sliding on a rough, horizontal surface is attached to one end of a horizontal spring (k = 250 N/m) which has its other end fixed. The block passes through the equilibrium position with a speed of 2.6 m/s and first comes to rest at a displacement of 0.20 m from equilibrium. What is the coefficient of kinetic friction between the block and the horizontal surface? a. 0.32 b. 0.45 c. 0.58 d. 0.19 e. 0.26 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 48. In a given frictionless displacement of a particle, its kinetic energy increases by 25 J while its potential energy decreases by 10 J. Determine the work of the nonconservative forces acting on the particle during this displacement. a. −15 J Copyright Cengage Learning. Powered by Cognero.

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b. +35 J c. +15 J d. −35 J e. +55 J ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 49. A particle is acted upon by only two forces, one conservative and one nonconservative, and neither being a force of friction, as it moves from point A to point B. The kinetic energies of the particle at points A and B are equal if a. the sum of the works of the two forces is zero. b. the work of the conservative force is equal to the work of the nonconservative force. c. the work of the conservative force is zero. d. the work of the nonconservative force is zero. e. None of the above.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 50. A 1.2-kg mass is projected down a rough, circular track (radius = 2.0 m) as shown. The speed of the mass at point A is 3.2 m/s, and at point B, it is 6.0 m/s. What is the change in mechanical energy done on the system between A and B by the force of friction?

a. −8.9 J b. −7.3 J c. −8.1 J d. −6.6 J e. −24 J ANSWER: POINTS: DIFFICULTY:

c 2 Average

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REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 51. A 1.2-kg mass is projected up a rough, circular track (radius = 0.80 m) as shown. The speed of the mass at point A is 8.4 m/s, and at point B, it is 5.6 m/s. What is the change in mechanical energy between A and B caused by the force of friction?

a. −2.7 J b. −8.8 J c. −4.7 J d. −6.7 J e. −19 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 52. A 3.0-kg mass is dropped from the edge of a 50-m tall building with an initial speed of zero. The mass strikes the ground with a downward velocity of 25 m/s. Find the change in mechanical energy of the mass caused by air resistance between the point where it is dropped and the point where it strikes the ground. a. −0.46 kJ b. −0.53 kJ c. −0.61 kJ d. −0.38 kJ e. −0.81 kJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 53. A 2.0-kg mass is projected vertically upward from ground level with an initial speed of 30 m/s. The mass rises to a maximum height of 35 m above ground level. What is the change in mechanical energy of the mass caused by air resistance between the point of projection and the point of maximum height? a. −0.21 kJ Copyright Cengage Learning. Powered by Cognero.

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b. −0.47 kJ c. −0.40 kJ d. −0.34 kJ e. −0.69 kJ ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 54. A 25-kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 2.0 cm toward its equilibrium position, its kinetic energy is 12 J. What is the change in mechanical energy caused by the frictional force on the block as it moves the 2.0 cm? a. −4.0 J b. −3.5 J c. −2.4 J d. −2.9 J e. −15 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 55. The two masses in the figure are released from rest. After the 3.0-kg mass has fallen 1.5 m, it is moving with a speed of 3.8 m/s. What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0-kg mass?

a. −12 J b. −17 J c. −20 J d. −8.0 J e. −28 J ANSWER: POINTS: DIFFICULTY:

d 2 Average

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REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 56. A 2.0-kg block is projected down a plane that makes an angle of 20° with the horizontal with an initial kinetic energy of 2.0 J. If the coefficient of kinetic friction between the block and plane is 0.40, how far will the block slide down the plane before coming to rest? a. 3.0 m b. 1.8 m c. 0.30 m d. 1.0 m e. 1.3 m ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 57. A large spring is used to stop the cars after they come down the last hill of a roller coaster. The cars start at rest at the top of the hill and are caught by a mechanism at the instant their velocities at the bottom are zero. Compare the compression of the spring, xA, for a fully loaded car, with that, xB, for a lightly loaded car, when mA = 2mB.

a. xA =

xB.

b. xA = xB. c.

xA =

xB.

d. xA = 2 xB. e. xA = 4 xB. ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 58. Objects A and B, of mass M and 2M, respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value μk. At the highest point, a. KA = Fd = KB. b. KA = (F − μkMg cosθ)d; KB = (F − 2μkMg cosθ)d. c. KA = (F − Mg sinθ)d; KB = (F − 2Mg sinθ)d.

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d. KA = (F − Mg sinθ − μkMg cosθ)d; KB = (F − Mg sinθ − μkMg cosθ)d. e. KA = (F − Mg sinθ − μkMg cosθ)d; KB = (F − 2Mg sinθ − 2μkMg cosθ)d.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 59. As an object moves from point A to point B only two forces act on it: one force is nonconservative and does −30 J of work, the other force is conservative and does +50 J of work. Between A and B, a. the kinetic energy of object increases, mechanical energy decreases. b. the kinetic energy of object decreases, mechanical energy decreases. c. the kinetic energy of object decreases, mechanical energy increases. d. the kinetic energy of object increases, mechanical energy increases. e. None of the above.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 60. As an object moves from point A to point B only two forces act on it: one force is conservative and does −70 J of work, the other force is nonconservative and does +50 J of work. Between A and B, a. the kinetic energy of object increases, mechanical energy increases. b. the kinetic energy of object decreases, mechanical energy increases. c. the kinetic energy of object decreases, mechanical energy decreases. d. the kinetic energy of object increases, mechanical energy decreases. e. None of the above.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 61. An astronaut tosses a ball out in space where gravitational forces may be neglected. What will happen to the ball? a. It will stop as soon as the force the astronaut gave it is used up. b. It will stop when the energy the astronaut gave it runs out. c. It will stop after a short time because there is no gravity to keep it moving. d. It will move in a circle like a boomerang. e. It will be slowed down very gradually by collisions with molecules in space.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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62. Objects A and B, of mass M and 2M, respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value μk. At the highest point, a. KA > KB. b. KA = KB. c. KA < KB. d. The work done by F on A is greater than the work done by F on B. e. The work done by F on A is less than the work done by F on B. ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 63. The equation below describes a physical situation:

Which description best fits the equation? a. A 1.70-kg block slows down while sliding down a frictionless plane inclined at a 30° angle. b. A 1.70-kg block slows down while sliding down a plane with μk = 0.320, with the plane inclined at a 30° angle. c. A 1.70-kg block speeds up while sliding up a frictionless plane inclined at a 30° angle. d. A 1.70-kg block speeds up while sliding down a plane with μk = 0.320, with the plane inclined at a 30° angle. e. A 1.70-kg block slides over the top of an inclined plane and then descends on the other side. Both planes, inclined at a 30° angle, have μk = 0.320.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 64. A spring with spring constant 800 N/m compressed 0.200 m is released and projects a 0.800-kg mass along a frictionless surface. The mass reaches a surface area where μk = 0.400 and comes to a stop. The following student solution contains at least one error. What is the error?

a. The elastic potential energy is equal only to the kinetic energy on the right, and is never equal to the internal thermal energy. b. The elastic potential energy is equal only to the internal thermal energy on the right, and is never equal to the Copyright Cengage Learning. Powered by Cognero.

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kinetic energy. c. The elastic potential energy is equal to either the kinetic energy or the internal thermal energy on the right, but not to their sum, depending on the part of the problem being done. d. Elastic potential energy cannot end up as internal energy change caused by friction. e. The change in mechanical energy by friction cannot end up as elastic potential energy.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 65. As a result of friction between internal parts of an isolated system, a. the total mechanical energy of the system increases. b. the total mechanical energy of the system decreases. c. the total mechanical energy of the system remains the same. d. the potential energy of the system increases but the kinetic energy remains the same. e. the kinetic energy of the system increases but the potential energy of the system remains the same.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 66. A 3.50-kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer, while the belt moves at a constant speed of 0.200 m/s in the same direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is a. 5.6. b. 22.0. c. 32.9. d. 54.8. e. 76.8.

ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 67. A 3.50-kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer, while the belt moves at a constant speed of 0.200 m/s in the opposite direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is a. 5.6. b. 22.0. c. 32.9. d. 54.8. e. 76.8.

ANSWER: e Copyright Cengage Learning. Powered by Cognero.

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POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 68. A 6.0-kg block slides along a horizontal surface. If µk = 0.20 for the block and surface, at what rate is the friction force changing the mechanical energy of the block at an instant when its speed is 4.0 m/s? a. −59 W b. −47 W c. −71 W d. −82 W e. +71 W ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.4 Changes in Mechanical Energy for Nonconservative Forces HAS VARIABLES: False 69. An all-terrain vehicle of 2000-kg mass moves up a 15.0° slope at a constant velocity of 6.00 m/s. The rate of change of gravitational potential energy with time is a. 5.25 kW. b. 24.8 kW. c. 30.4 kW. d. 118 kW. e. 439 kW. ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 70. A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would have used at least ____ J of energy. a. 746 b. 3.43 × 105 c. 3.73 × 105 d. 7.46 × 105 e. 2.61 × 107 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 71. A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle Copyright Cengage Learning. Powered by Cognero.

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to the summit of a 500-m high mountain while expending power at this rate, she would reach the summit in ____ seconds. a. 1 b. 460 c. 500 d. 1 000 e. 35 000 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 72. A champion athlete can produce one horsepower (746 W) for a short period of time. The number of 16-cm-high steps a 70-kg athlete could ascend in one minute while expending one horsepower is a. 4. b. 7. c. 65. d. 408. e. 4 567.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 73. At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30° above the horizontal? a. +39 W b. −78 W c. −39 W d. +78 W e. +25 W ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 74. A 2.0-kg block slides down a plane (inclined at 40° with the horizontal) at a constant speed of 5.0 m/s. At what rate is the gravitational force on the block doing work? a. +98 W b. +63 W c. zero d. +75 W e. −75 W ANSWER: b Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 75. The speed of a 4.0-kg object is given by v = (2t) m/s, where t is in s. At what rate is the resultant force on this object doing work at t = 1 s? a. 48 W b. 40 W c. 32 W d. 56 W e. 16 W ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.5 Power HAS VARIABLES: False 76. A 3.0-kg block is on a frictionless, horizontal surface. The block is at rest when, at t = 0, a force (magnitude P = 2.0 N) acting at an angle of 22° above the horizontal is applied to the block. At what rate is the force P doing work at t = 2.0 s? a. 2.3 W b. 2.0 W c. 1.4 W d. 1.7 W e. 1.2 W ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.5 Power HAS VARIABLES: False 77. A 1.6-kg block slides down a plane (inclined at 25° with the horizontal) at a constant speed of 2.0 m/s. At what rate is the frictional force changing the mechanical energy of the block? a. +28 W b. +13 W c. −13 W d. −28 W e. +6.5 W ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 78. A 3.0-kg block is on a horizontal surface. The block is at rest when, at t = 0, a force (magnitude P = 12 N) acting parallel to the surface is applied to the block, causing it to accelerate. The coefficient of kinetic friction between the block Copyright Cengage Learning. Powered by Cognero.

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and the surface is 0.20. At what rate is the force P doing work on the block at t = 2.0 s? a. 54 W b. 49 W c. 44 W d. 59 W e. 24 W ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.5 Power HAS VARIABLES: False 79. Starting from rest at t = 0, a 5.0-kg block is pulled across a horizontal surface by a constant horizontal force having a magnitude of 12 N. If the coefficient of friction between the block and the surface is 0.20, at what rate is the 12-N force doing work at t = 5.0 s? a. 0.13 kW b. 0.14 kW c. 0.12 kW d. 26 W e. 12 W ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 80. Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are FA and FB, while the power supplied is respectively, PA and PB. Which statement is correct?

a. FB = FA; PB = PA b. FB = FA; PB = 2 PA c. FB = 2 FA; PB = PA d. FB = 2 FA; PB = 2 PA Copyright Cengage Learning. Powered by Cognero.

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e. PA = FA; PB = FB ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 7

81. A rain cloud contains 2.66 × 10 kg of water vapor. How long would it take for a 2.0-kW pump to lift the same amount of water to an altitude of 2 000 m?

ANSWER: 8.26 years POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False 82. While running, a person dissipates about 0.6 J of mechanical energy per step per kilogram of body mass. If a 60-kg person runs with a power of 70 watts during a race, how fast is the person running? Assume a running step is 1.5 m long.

ANSWER: 2.92 m/s POINTS: 3 DIFFICULTY: Challenging REFERENCES: 8.5 Power HAS VARIABLES: False 83. When an automobile moves with constant velocity, the power developed is used to overcome the frictional forces exerted by the air and the road. If the power developed in an engine is 50.0 hp, what total frictional force acts on the car at 55 mph (24.6 m/s)? One horsepower equals 746 W. ANSWER: 1 520 N POINTS: 2 DIFFICULTY: Average REFERENCES: 8.5 Power HAS VARIABLES: False

1. Two 0.20-kg balls, moving at 4 m/s, east, strike a wall. Ball A bounces backwards at the same speed. Ball B stops.

Which statement correctly describes the change in momentum of the two balls? a. . b.

.

c.

.

d. Δ B = Δ A. e. Δ B > Δ A. ANSWER: POINTS: DIFFICULTY: REFERENCES:

a 1 Easy 9.1 Linear Momentum

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HAS VARIABLES: False 2. A car of mass m1 traveling at velocity v passes a car of mass m2 parked at the side of the road. The momentum of the system of two cars is a. 0. b. m1v. c. (m1 − m2)v. d.

e. (m1 + m2)v.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.1 Linear Momentum HAS VARIABLES: False 3. A pitcher claims he can throw a baseball with as much momentum as a 3.00-g bullet moving with a speed of 1 500 m/s.

A baseball has a mass of 0.145 kg. What must be its speed if the pitcher's claim is valid?

ANSWER: 31.0 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 9.1 Linear Momentum HAS VARIABLES: False 4. A ball falls to the ground from height h and bounces to height h'. Momentum is conserved in the ball-Earth system a. no matter what height h' it reaches. b. only if h' < h. c. only if h' = h. d. only if h' > h. e. only if h' ≥ h.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.2 Analysis Model: Isolated System (Momentum) HAS VARIABLES: False 5. The law of conservation of momentum applies to a collision between two bodies since a. they exert equal and opposite forces on each other. b. they exert forces on each other respectively proportional to their masses. c. they exert forces on each other respectively proportional to their velocities. d. they exert forces on each other respectively inversely proportional to their masses. e. their accelerations are proportional to their masses.

ANSWER: a POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 9.2 Analysis Model: Isolated System (Momentum) HAS VARIABLES: False 6. Two boys in a canoe toss a baseball back and forth. What effect will this have on the canoe? Neglect (velocitydependent) frictional forces with water or air. a. None, because the ball remains in the canoe. b. The canoe will drift in the direction of the boy who throws the ball harder each time. c. The canoe will drift in the direction of the boy who throws the ball with less force each time. d. The canoe will oscillate back and forth, always moving opposite to the ball. e. The canoe will oscillate in the direction of the ball because the canoe and ball exert forces in opposite directions upon the person throwing the ball.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.2 Analysis Model: Isolated System (Momentum) HAS VARIABLES: False 7. An astronaut outside a spaceship hammers a loose rivet back in place. What happens to the astronaut as he swings the hammer? a. Nothing. The spaceship takes up the momentum of the hammer. b. He moves away from the spaceship. c. He moves towards the spaceship. d. He moves towards the spaceship as he pulls the hammer back and moves away from it as he swings the hammer forward. e. He moves away from the spaceship as he pulls the hammer back and moves toward it as he swings the hammer forward.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.2 Analysis Model: Isolated System (Momentum) HAS VARIABLES: False 8. The value of the momentum of a system is the same at a later time as at an earlier time if there are no a. collisions between particles within the system. b. inelastic collisions between particles within the system. c. changes of momentum of individual particles within the system. d. internal forces acting between particles within the system. e. external forces acting on particles of the system.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.2 Analysis Model: Isolated System (Momentum) HAS VARIABLES: False 9. A ball of mass mB is released from rest and acquires velocity of magnitude vB before hitting the ground. The ratio of the magnitude of the momentum the Earth acquires to the magnitude of the momentum the ball acquires is Copyright Cengage Learning. Powered by Cognero.

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a. 0. b. . c. . d. 1 e. .

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.2 Analysis Model: Isolated System (Momentum) HAS VARIABLES: False 10. A ball of mass mB is released from rest and acquires velocity of magnitude vB before hitting the ground. The ratio of the kinetic energy the Earth acquires to the kinetic energy the ball acquires is a. 0. b. . c. . d. 1 e. .

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.2 Analysis Model: Isolated System (Momentum) HAS VARIABLES: False 11. Two bodies of equal mass m collide and stick together. The quantities that always have equal magnitude for both masses during the collision are a. their changes in momentum. b. the force each exerts on the other. c. their changes in kinetic energy. d. all of the above. e. only (a) and (b) above.

ANSWER: e POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 9.2 Analysis Model: Isolated System (Momentum) HAS VARIABLES: False 12. Stan argues that momentum cannot be conserved when a collision is not a head-on collision. Rachel insists it is conserved because each body receives an impulse of equal magnitude. Rachel is correct because a. each body exerts an equal and opposite force on the other during the collision. b. the forces act during equal time intervals. c. the law of conservation of momentum for an isolated system is a vector equation. d. of all of the above. e. of only (a) and (b) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.2 Analysis Model: Isolated System (Momentum) HAS VARIABLES: False 13. A 2000-kg truck traveling at a speed of 6.0 m/s makes a 90° turn in a time of 4.0 s and emerges from this turn with a speed of 4.0 m/s. What is the magnitude of the average resultant force on the truck during this turn? a. 4.0 kN b. 5.0 kN c. 3.6 kN d. 6.4 kN e. 0.67 kN ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 14. A 1.2-kg object moving with a speed of 8.0 m/s collides perpendicularly with a wall and emerges with a speed of 6.0 m/s in the opposite direction. If the object is in contact with the wall for 2.0 ms, what is the magnitude of the average force on the object by the wall? a. 9.8 kN b. 8.4 kN c. 7.7 kN d. 9.1 kN e. 1.2 kN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 15. A 1.5-kg playground ball is moving with a velocity of 3.0 m/s directed 30° below the horizontal just before it strikes a horizontal surface. The ball leaves this surface 0.50 s later with a velocity of 2.0 m/s directed 60° above the horizontal.

What is the magnitude of the average resultant force on the ball?

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a. 14 N b. 11 N c. 18 N d. 22 N e. 3.0 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 16. The only force acting on a 2.0-kg object moving along the x axis is shown. If the velocity vx is −2.0 m/s at t = 0, what is the velocity at t = 4.0 s?

a. −2.0 m/s b. −4.0 m/s c. −3.0 m/s d. +1.0 m/s e. +5.0 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 17. The only force acting on a 2.0-kg object moving along the x axis is shown. If the velocity vx is +2.0 m/s at t = 0, what is the velocity at t = 4.0 s?

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a. +4.0 m/s b. +5.0 m/s c. +6.0 m/s d. +7.0 m/s e. +2.0 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 18. The speed of a 2.0-kg object changes from 30 m/s to 40 m/s during a 5.0-s time interval. During this same time interval, the velocity of the object changes its direction by 90°. What is the magnitude of the average total force acting on the object during this time interval? a. 30 N b. 20 N c. 40 N d. 50 N e. 6.0 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 19. A 3.0-kg ball with an initial velocity of (4 + 3 ) m/s collides with a wall and rebounds with a velocity of (−4 + 3 ) m/s. What is the impulse exerted on the ball by the wall? a. +24 N s b. −24 N s c. +18 N s d.

−18 N s

e.

+8.0 N s ANSWER: POINTS:

b 2

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DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 20. A 1.6-kg ball is attached to the end of a 0.40-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point of its swing, when it is moving horizontally, the ball collides with a 0.80-kg block initially at rest on a horizontal, frictionless surface. The speed of the block just after the collision is 3.0 m/s. What is the speed of the ball just after the collision? a. 1.7 m/s b. 1.1 m/s c. 1.5 m/s d. 1.3 m/s e. 2.1 m/s ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 21. A 3.00-kg stone is dropped from a 39.2-m high building. When the stone has fallen 19.6 m, the magnitude of the impulse it has received from the gravitational force is a. 9.80 N s. b. 19.6 N s. c. 29.4 N s. d. 58.8 N s. e. 118 N s.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 22. A 3.00-kg stone is dropped from a 39.2 m high building. When the stone has fallen 19.6 m, the magnitude of the impulse the Earth has received from the gravitational force exerted by the stone is a. 9.80 N s. b. 19.6 N s. c. 29.4 N s. d. 58.8 N s. e. 118 N s.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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23. A 0.28-kg stone you throw rises 34.3 m in the air. The magnitude of the impulse the stone received from your hand while being thrown is a. 0.27 N s. b. 2.7 N s. c. 7.3 N s. d. 9.6 N s. e. 34.3 N s.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 24. A 0.28-kg stone you throw rises 34.3 m in the air. The impulse your hand receives from the stone while it throws the stone is a. 2.7 N s, up. b. 2.7 N s, down. c. 7.3 N s, up. d. 7.3 N s, down. e. 9.6 N s, up.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 25. A 0.28-kg stone you throw rises 34.3 m in the air. The impulse the stone receives from your hand while being thrown is a. 2.7 N s, up. b. 2.7 N s, down. c. 7.3 N s, up. d. 7.3 N s, down. e. 9.6 N s, up.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 26. A catapult fires an 800-kg rock with an initial velocity of 100 m/s at a 40° angle to the ground. The magnitude of the horizontal impulse the catapult receives from the rock is a. 5.1 × 104 N s. b. 6.1 × 104 N s. c. 8.0 × 104 N s.

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d. 5.0 × 105 N s. e. 6.0 × 105 N s.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 27. A catapult fires an 800-kg rock with an initial velocity of 100 m/s at a 40° angle to the ground. The magnitude of the vertical impulse the catapult receives from the rock is a. 5.1 × 104 N s. b. 6.1 × 104 N s. c. 8.0 × 104 N s. d. 5.0 × 105 N s. e. 6.0 × 105 N s.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 28. When two bodies of different masses collide, the impulses they exert on each other are a. equal for all collisions. b. equal but opposite for all collisions. c. equal but opposite only for elastic collisions. d. equal but opposite only for inelastic collisions. e. equal but opposite only when the bodies have equal but opposite accelerations.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 29. If you know the impulse that has acted on a body of mass m you can calculate a. its initial velocity. b. its final velocity. c. its final momentum. d. the change in its velocity. e. its acceleration during the impulse.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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30. A ball of mass mB is released from rest and acquires velocity of magnitude vB before hitting the ground. The ratio of the impulse delivered to the Earth to the impulse delivered to the ball is a. 0. b. . c. . d. 1 e. .

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 31. A child bounces a 50-gram superball on the sidewalk. The velocity of the superball changes from 21 m/s downward to 19 m/s upward. If the contact time with the sidewalk is 1/800 s, what is the magnitude of the force exerted on the superball by the sidewalk?

ANSWER: 1 600 N POINTS: 2 DIFFICULTY: Average REFERENCES: 9.3 Analysis Model: Nonisolated System (Momentum) HAS VARIABLES: False 32. A 2.4-kg ball falling vertically hits the floor with a speed of 2.5 m/s and rebounds with a speed of 1.5 m/s. What is the magnitude of the impulse exerted on the ball by the floor? a. 9.6 N s b. 2.4 N s c. 6.4 N s d. 1.6 N s e. 1.0 N s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 33. An 8.0-kg object moving 4.0 m/s in the positive x direction has a one-dimensional collision with a 2.0-kg object moving 3.0 m/s in the opposite direction. The final velocity of the 8.0-kg object is 2.0 m/s in the positive x direction. What is the total kinetic energy of the two-mass system after the collision? a. 32 J Copyright Cengage Learning. Powered by Cognero.

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b. 52 J c. 41 J d. 25 J e. 29 J ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 34. A 4.0-kg particle is moving horizontally with a speed of 5.0 m/s when it strikes a vertical wall. The particle rebounds with a speed of 3.0 m/s. What is the magnitude of the impulse delivered to the particle? a. 24 N⋅ s b. 32 N⋅ s c. 40 N⋅ s d. 30 N⋅ s e. 8.0 N⋅ s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 35. A 2.0-kg object moving with a velocity of 5.0 m/s in the positive x direction strikes and sticks to a 3.0-kg object moving with a speed of 2.0 m/s in the same direction. How much kinetic energy is lost in this collision? a. 2.4 J b. 9.6 J c. 5.4 J d. 0.6 J e. 6.0 J ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 36. A 10-g bullet moving at 1 000 m/s strikes and passes through a 2.0-kg block initially at rest, as shown. The bullet emerges from the block with a speed of 400 m/s. To what maximum height will the block rise above its initial position?

a. 78 cm b. 66 cm Copyright Cengage Learning. Powered by Cognero.

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c. 56 cm d. 46 cm e. 37 cm ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 37. A 12-g bullet moving horizontally strikes and remains in a 3.0-kg block initially at rest on the edge of a table. The block, which is initially 80 cm above the floor, strikes the floor a horizontal distance of 120 cm from its initial position.

What was the initial speed of the bullet? a. 0.68 km/s b. 0.75 km/s c. 0.81 km/s d. 0.87 km/s e. 0.41 km/s ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 38. A 6.0-kg object moving at 5.0 m/s collides with and sticks to a 2.0-kg object. After the collision the composite object is moving at 2.0 m/s in a direction opposite to the initial direction of motion of the 6.0-kg object. Determine the speed of the 2.0-kg object before the collision. a. 15 m/s b. 7.0 m/s c. 8.0 m/s d. 23 m/s e. 11 m/s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 39. A 2.0-kg object moving at 5.0 m/s collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision. a. 20 J b. 15 J c. 30 J d. 25 J e. 5.0 J ANSWER: a POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 40. A 1.6-kg block is attached to the end of a 2.0-m string to form a pendulum. The pendulum is released from rest when the string is horizontal. At the lowest point of its swing when it is moving horizontally, the block is hit by a 10-g bullet moving horizontally in the opposite direction. The bullet remains in the block and causes the block to come to rest at the low point of its swing. What was the magnitude of the bullet's velocity just before hitting the block? a. 1.0 km/s b. 1.6 km/s c. 1.2 km/s d. 1.4 km/s e. 1.8 km/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 41. A 3.0-kg mass sliding on a frictionless surface has a velocity of 5.0 m/s east when it undergoes a one-dimensional inelastic collision with a 2.0-kg mass that has an initial velocity of 2.0 m/s west. After the collision, the 3.0-kg mass has a velocity of 1.0 m/s east. How much kinetic energy does the two-mass system lose during the collision? a. 22 J b. 24 J c. 26 J d. 20 J e. 28 J ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 42. A 3.0-kg mass is released from rest at point A of a circular, frictionless track of radius 0.40 m as shown in the figure.

The mass slides down the track and collides with a 1.4-kg mass that is initially at rest on a horizontal, frictionless surface.

If the masses stick together, what is their speed after the collision?

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a. 2.1 m/s b. 1.7 m/s c. 1.9 m/s d. 1.5 m/s e. 2.3 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 43. A 3.0-kg mass is sliding on a horizontal, frictionless surface with a speed of 3.0 m/s when it collides with a 1.0-kg mass initially at rest as shown in the figure. The masses stick together and slide up a frictionless, circular track of radius 0.40 m. To what maximum height, h, above the horizontal surface, will the masses slide?

a. 0.18 m b. 0.15 m c. 0.21 m d. 0.26 m e. 0.40 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 44. A 10-g bullet moving horizontally with a speed of 2.0 km/s strikes and passes through a 4.0-kg block moving with a speed of 4.2 m/s in the opposite direction on a horizontal, frictionless surface. If the block is brought to rest by the collision, what is the kinetic energy of the bullet as it emerges from the block? a. 0.51 kJ b. 0.29 kJ c. 0.80 kJ d. 0.13 kJ e. 20 kJ ANSWER: a POINTS: 3 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Challenging REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 45. A 10-g bullet moving horizontally with a speed of 1.8 km/s strikes and passes through a 5.0-kg block initially at rest on a horizontal, frictionless surface. The bullet emerges from the block with a speed of 1.0 km/s. What is the kinetic energy of the block immediately after the bullet emerges? a. 8.0 J b. 6.4 J c. 5.3 J d. 9.4 J e. 10 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 46. A pendulum consists of a 2.0-kg block hanging on a 1.5-m-length string. A 10-g bullet moving with a horizontal velocity of 900 m/s strikes, passes through, and emerges from the block (initially at rest) with a horizontal velocity of 300 m/s. To what maximum height above its initial position will the block swing? a. 32 cm b. 38 cm c. 46 cm d. 27 cm e. 9 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 47. A 1.0-kg ball is attached to the end of a 2.5-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point in its swing when it is moving horizontally, the ball collides elastically with a 2.0-kg block initially at rest on a horizontal frictionless surface. What is the speed of the block just after the collision? a. 2.3 m/s b. 4.7 m/s c. 3.5 m/s d. 3.0 m/s e. 7.0 m/s ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 48. A 3.0-kg object moving in the positive x direction has a one-dimensional elastic collision with a 5.0-kg object initially Copyright Cengage Learning. Powered by Cognero.

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at rest. After the collision the 5.0-kg object has a velocity of 6.0 m/s in the positive x direction. What was the initial speed of the 3.0 kg object? a. 6.0 m/s b. 7.0 m/s c. 4.5 m/s d. 8.0 m/s e. 5.5 m/s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 49. A 3.0-kg object moving 8.0 m/s in the positive x direction has a one-dimensional elastic collision with an object (mass = M) initially at rest. After the collision, the object of unknown mass has a velocity of 6.0 m/s in the positive x direction.

What is M? a. 7.5 kg b. 5.0 kg c. 6.0 kg d. 4.2 kg e. 8.0 kg ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 50. A 6.0-kg object moving 2.0 m/s in the positive x direction has a one-dimensional elastic collision with a 4.0-kg object moving 3.0 m/s in the opposite direction. What is the total kinetic energy of the two-mass system after the collision? a. 30 J b. 62 J c. 20 J d. 44 J e. 24 J ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 51. Two blocks, with masses 2.0 kg and 3.0 kg, are placed on a horizontal, frictionless surface. A light spring is placed in a horizontal position between the blocks. The blocks are pushed together, compressing the spring, and then released from rest. After contact with the spring ends, the 3.0-kg mass has a speed of 2.0 m/s. How much potential energy was stored in the spring when the blocks were released? a. 15 J b. 3.0 J c. 6.0 J Copyright Cengage Learning. Powered by Cognero.

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d. 12 J e. 9.0 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 52. Car A rear ends Car B, which has twice the mass of A, on an icy road at a speed low enough so that the collision is essentially elastic. Car B is stopped at a light when it is struck. Car A has mass m and speed v before the collision. After the collision, a. each car has half the momentum. b. car A stops and car B has momentum mv. c. car A stops and car B has momentum 2mv. d. the momentum of car B is four times as great in magnitude as that of car A. e. each car has half of the kinetic energy.

ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 53. A steel ball bearing of mass m1 and speed of magnitude v1 has a head-on elastic collision with a steel ball bearing of mass m2 at rest. Rank the speed v1 of m1 relative to v2, the magnitude of the speed of m2, after the collision when i) m1 > m2; a. v1 < v2;

ii) m1 = m2; and

iii) m1 < m2.

v1 < v2;

v1 < v2

b. v1 < v2;

v1 = v2;

v1 > v2

c. v1 < v2;

v1 > v2;

v1 > v2

d. v1 > v2;

v1 = v2;

v1 < v2

e. v1 > v2;

v1 > v2;

v1 > v2

ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 54. High-speed stroboscopic photographs show that the head of a golf club of mass 200 grams is traveling at 55.0 m/s just before it strikes a 46.0-gram golf ball at rest on a tee. After the collision, the clubhead travels (in the same direction) at 40.0 m/s. Find the speed of the golf ball just after impact.

ANSWER: 65.2 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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55. A U-238 nucleus (mass = 238 units) decays, transforming into an alpha particle (mass = 4.00 units) and a residual 7 thorium nucleus (mass = 234 units). If the uranium nucleus was at rest, and the alpha particle has a speed of 1.50 × 10 m/s, determine the recoil speed of the thorium nucleus.

5 ANSWER: 2.56 × 10 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 9.4 Collisions in One Dimension HAS VARIABLES: False 56. An 80-g particle moving with an initial speed of 50 m/s in the positive x direction strikes and sticks to a 60-g particle moving 50 m/s in the positive y direction. How much kinetic energy is lost in this collision? a. 96 J b. 89 J c. 175 J d. 86 J e. 110 J ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 57. A 2.0-kg object moving 3.0 m/s strikes a 1.0-kg object initially at rest. Immediately after the collision, the 2.0-kg object has a velocity of 1.5 m/s directed 30° from its initial direction of motion. What is the x component of the velocity of the 1.0-kg object just after the collision? a. 3.7 m/s b. 3.4 m/s c. 1.5 m/s d. 2.4 m/s e. 4.1 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 58. A 2.0-kg object moving 3.0 m/s strikes a 1.0-kg object initially at rest. Immediately after the collision, the 2.0-kg object has a velocity of 1.5 m/s directed 30° from its initial direction of motion. What is the y component of the velocity of the 1.0-kg object just after the collision? a. −3.7 m/s b. −3.4 m/s c. −1.5 m/s d. −2.4 m/s e. −4.1 m/s ANSWER: c POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 59. A 6.0-kg object, initially at rest in free space, "explodes" into three segments of equal mass. Two of these segments are observed to be moving with equal speeds of 20 m/s with an angle of 60° between their directions of motion. How much kinetic energy is released in this explosion? a. 2.4 kJ b. 2.9 kJ c. 2.0 kJ d. 3.4 kJ e. 1.2 kJ ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 60. A 5.0-g particle moving 60 m/s collides with a 2.0-g particle initially at rest. After the collision, each of the particles has a velocity that is directed 30° from the original direction of motion of the 5.0-g particle. What is the speed of the 2.0-g particle after the collision? a. 72 m/s b. 87 m/s c. 79 m/s d. 94 m/s e. 67 m/s ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 61. A 1.0-kg object moving 9.0 m/s collides with a 2.0-kg object moving 6.0 m/s in a direction that is perpendicular to the initial direction of motion of the 1.0-kg object. The two masses remain together after the collision, and this composite object then collides with and sticks to a 3.0-kg object. After these collisions, the final composite (6.0-kg) object remains at rest. What was the speed of the 3.0-kg object before the collisions? a. 15 m/s b. 10 m/s c. 5.0 m/s d. 20 m/s e. 25 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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62. A 3.0-kg mass sliding on a frictionless surface explodes into three 1.0-kg masses. After the explosion, the velocities of the three masses are: (1) 9.0 m/s, north; (2) 4.0 m/s, 30° south of west; and (3) 4.0 m/s, 30° south of east. What was the magnitude of the original velocity of the 3.0-kg mass? a. 1.7 m/s b. 1.0 m/s c. 1.3 m/s d. 2.0 m/s e. 2.8 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 63. A 3.0-kg mass moving in the positive x direction with a speed of 10 m/s collides with a 6.0-kg mass initially at rest.

After the collision, the speed of the 3.0-kg mass is 8.0 m/s, and its velocity vector makes an angle of 35° with the positive x axis. What is the magnitude of the velocity of the 6.0-kg mass after the collision? a. 2.2 m/s b. 2.9 m/s c. 4.2 m/s d. 3.5 m/s e. 4.7 m/s ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 64. A 5.0-kg mass with an initial velocity of 4.0 m/s, east, collides with a 4.0-kg mass with an initial velocity of 3.0 m/s, west. After the collision, the 5.0-kg mass has a velocity of 1.2 m/s, south. What is the magnitude of the velocity of the 4.0kg mass after the collision? a. 2.0 m/s b. 1.5 m/s c. 1.0 m/s d. 2.5 m/s e. 3.0 m/s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 65. A 4.0-kg mass has a velocity of 4.0 m/s, east, when it explodes into two 2.0-kg masses. After the explosion, one of the masses has a velocity of 3.0 m/s at an angle of 60° north of east. What is the magnitude of the velocity of the other mass after the explosion? a. 7.9 m/s b. 8.9 m/s Copyright Cengage Learning. Powered by Cognero.

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c. 7.0 m/s d. 6.1 m/s e. 6.7 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 66. A 4.2-kg object, initially at rest, "explodes" into three objects of equal mass. Two of these are determined to have velocities of equal magnitudes (5.0 m/s) with directions that differ by 90°. How much kinetic energy was released in the explosion? a. 70 J b. 53 J c. 60 J d. 64 J e. 35 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 67. A 4.0-kg mass, initially at rest on a horizontal, frictionless surface, is struck by a 2.0-kg mass moving along the x axis with a speed of 8.0 m/s. After the collision, the 2.0-kg mass has a speed of 4.0 m/s at an angle of 37° from the positive x axis. What is the speed of the 4.0-kg mass after the collision? a. 2.0 m/s b. 2.7 m/s c. 4.9 m/s d. 2.4 m/s e. 3.6 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 68. In an elastic collision between two bodies of equal mass, with body 2 initially at rest, body 1 moves off at angle θ relative to the direction of its initial velocity and body 2 at angle υ. The sine of the sum of θ and υ, sin(θ + υ), is equal to a. 0. b. 0.500. c. 0.707. d. 0.866. e. 1.00.

ANSWER: e POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 69. In an elastic collision between two bodies of mass m1 and m2, with m2 initially at rest, mass 1 moves off at angle θ relative to the direction of its initial velocity and mass 2 at angle υ. An exam paper shows the equations below: m1v1i= m1v1f cosθ + m2v2f sinυ 0= m1v1f sinθ + m2v2f cosυ What error(s) has the student made? a. In the first equation, m2v2f sinυ should be m2v2f cosυ. b. In the second equation, m2v2f cosυ should be m2v2f sinυ. c. In the second equation, the plus sign between the terms on the right should be a minus sign. d. All of the errors listed above. e. Only errors (a) and (b) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False Exhibit 9-1 Two birds of prey hurtling after the same mouse collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60° angle to the ground.

Use this exhibit to answer the following question(s).

70. Refer to Exhibit 9-1. What is the magnitude of their total momentum, in

, immediately after the collision?

a. 0 b. 6.5 c. 7.5 d. 13 e. 15 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 71. Refer to Exhibit 9-1. What is the magnitude of their velocity, in m/s, immediately after the collision?

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a. 0 b. 13 c. 15 d. 26 e. 30 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False

72. Refer to Exhibit 9-1. What is the horizontal component of their momentum, in

, immediately after the

collision? a. 0 b. 6.1 c. 7.5 d. 13 e. 15 ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 73. A 500-g firework explodes into two pieces of equal mass at an instant when it is traveling straight up at 10 m/s. If one half shoots off horizontally to the left at 20 m/s, what is the velocity, in m/s, of the other half immediately after the explosion? (The x axis is directed right; the y axis up.) a. b. c. d. e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.5 Collisions in Two Dimensions HAS VARIABLES: False 74. Three particles are placed in the xy plane. A 40-g particle is located at (3, 4) m, and a 50-g particle is positioned at (−2, −6) m. Where must a 20-g particle be placed so that the center of mass of this three-particle system is located at the origin? a. (−1, −3) m Copyright Cengage Learning. Powered by Cognero.

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b. (−1, 2) m c. (−1, 12) m d. (−1, 7) m e. (−1, 3) m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 9.6 The Center of Mass HAS VARIABLES: False 75. Three particles are placed in the xy plane. A 30-g particle is located at (3, 4) m, and a 40-g particle is located at (−2, −2) m. Where must a 20-g particle be placed so that the center of mass of the three-particle system is at the origin? a. (−3, −1) m b. (+1, +3) m c. (+3, −1) m d. (−1, −3) m e. (−0.5, −2) m ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 9.6 The Center of Mass HAS VARIABLES: False 76. Assume that the average mass of each of the approximately 1 billion people in China is 55 kg. Assume that they all 24 gather in one place and climb to the top of 2-m high ladders. The center of mass of the Earth (mE = 5.90 10 kg) is then displaced a. 0 m. b. 1.84 × 10−23 m. c. 1.84 × 10−14 m. d. 1.80 × 10−13 m. e. 2 m.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.6 The Center of Mass HAS VARIABLES: False 77. The linear density of a rod, in g/m, is given by What is the mass of the rod? a. 0.213 g b. 3.50 g c. 3.84 g d. 18.4 g e. 20.8 g ANSWER: d Copyright Cengage Learning. Powered by Cognero.

. The rod extends from the origin to x = 0.400 m.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 9.6 The Center of Mass HAS VARIABLES: False 78. The linear density of a rod, in g/m, is given by What is the location of the center of mass of the rod? a. x = 0.213 m b. x = 0.315 m c. x = 0.384 m d. x = 0.184 m e. x = 0.208 m ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.6 The Center of Mass HAS VARIABLES: False

. The rod extends from the origin to x = 0.400 m.

79. A uniform, thin wire has a length and is bent into a semicircular arc of radius R. If the wire starts at (x, y) = (R, 0) and curves counterclockwise to (x, y) = (−R, 0), what is the y coordinate of its center of mass?

ANSWER: 0.637 R POINTS: 3 DIFFICULTY: Challenging REFERENCES: 9.6 The Center of Mass HAS VARIABLES: False 2

80. At an instant when a particle of mass 50 g has an acceleration of 80 m/s in the positive x direction, a 75-g particle has 2 an acceleration of 40 m/s in the positive y direction. What is the magnitude of the acceleration of the center of mass of this two-particle system at this instant? a. 60 m/s2 b. 56 m/s2 c. 40 m/s2 d. 50 m/s2 e. 46 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 9.7 Systems of Many Particles HAS VARIABLES: False 81. At an instant when a particle of mass 80 g has a velocity of 25 m/s in the positive y direction, a 75-g particle has a velocity of 20 m/s in the positive x direction. What is the speed of the center of mass of this two-particle system at this instant? a. 16 m/s b. 45 m/s Copyright Cengage Learning. Powered by Cognero.

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c. 23 m/s d. 20 m/s e. 36 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 9.7 Systems of Many Particles HAS VARIABLES: False 82. At the instant a 2.0-kg particle has a velocity of 4.0 m/s in the positive x direction, a 3.0-kg particle has a velocity of 5.0 m/s in the positive y direction. What is the speed of the center of mass of the two-particle system? a. 3.8 m/s b. 3.4 m/s c. 5.0 m/s d. 4.4 m/s e. 4.6 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.7 Systems of Many Particles HAS VARIABLES: False 83. Two bodies with masses m1 and m2, are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2. The magnitude of the velocity of the center of mass of this system of two bodies is a. less than v1. b. equal to v1. c. equal to the average of v1 and v2. d. greater than v1 and less than v2. e. greater than v2.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.7 Systems of Many Particles HAS VARIABLES: False 84. Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than πR/2, one-quarter circle, the center of mass of the two cars a. remains at the initial point. b. travels along a diameter of the circle at speed v' < v. c. travels along a diameter of the circle at speed v' = v. d. travels along a diameter of the circle at speed v' > v. e. remains at the center of the circle.

ANSWER: b POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 9.7 Systems of Many Particles HAS VARIABLES: False 85. A rocket with an initial mass of 1 000 kg adjusts its thrust by varying the rate at which mass is ejected. The ejection 2 speed relative to the rocket is 40 km/s. If the acceleration of the rocket is to have a magnitude of 20 m/s at an instant when its mass is 80% of the original mass, at what rate is mass being ejected at that instant? Ignore any external forces on the rocket. a. 0.40 kg/s b. 0.50 kg/s c. 0.60 kg/s d. 0.70 kg/s e. 0.80 kg/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 9.9 Rocket Propulsion HAS VARIABLES: False 86. A rocket engine consumes 450 kg of fuel per minute. If the exhaust speed of the ejected fuel is 5.2 km/s, what is the thrust of the rocket? a. 42 kN b. 39 kN c. 45 kN d. 48 kN e. 35 kN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 9.9 Rocket Propulsion HAS VARIABLES: False 2

87. A rocket moving in outer space maintains a constant acceleration (magnitude = 20 m/s ) while ejecting fuel at a speed of 15 km/s relative to the rocket. If the initial mass of the rocket is 3 000 kg, what is the magnitude of the thrust after 800 kg of fuel have been consumed? a. 56 kN b. 48 kN c. 52 kN d. 44 kN e. 36 kN ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.9 Rocket Propulsion HAS VARIABLES: False 88. When the rate of burn and the exhaust velocity are constant, a rocket ascends with Copyright Cengage Learning. Powered by Cognero.

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a. decreasing acceleration. b. decreasing velocity. c. constant velocity. d. constant acceleration. e. increasing acceleration.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.9 Rocket Propulsion HAS VARIABLES: False 89. An exam paper contains the following equation for rocket propulsion: .

The error in the equation is that, instead of (v + ve), the velocity of the fuel relative to the ground should be a. −ve. b. +ve. c. v − ve. d. ve − v. e. 2ve.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 9.9 Rocket Propulsion HAS VARIABLES: False

1. A campus bird spots a member of an opposing football team in an amusement park. The football player is on a ride where he goes around at angular velocity ω at distance R from the center. The bird flies in a horizontal circle above him.

Will a dropping the bird releases while flying directly above the person's head hit him? a. Yes, because it falls straight down. b. Yes, because it maintains the acceleration of the bird as it falls. c. No, because it falls straight down and will land behind the person. d. Yes, because it maintains the angular velocity of the bird as it falls. e. No, because it maintains the tangential velocity the bird had at the instant it started falling.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 2. Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars. If the two cars are in line at t = 0, and moving at 3ω and ω respectively, at what time will they next pass each other?

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a. t = 0. b. t=

.

c. t=

.

d. t=

.

t=

.

e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 3. The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track.

Through how many radians does the car travel in the first 10 minutes?

a. 30 b. 50 c. 70 d. 90 e. 100 ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 4. The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

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a.

b.

c.

d.

e.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.

Use this exhibit to answer the following question(s).

5. Refer to Exhibit 10-1. What is her angular displacement (in rad) in the first 8 minutes? a. 0 b. π c. 4π d. 8π e. 16π ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 6. Refer to Exhibit 10-1. What is her angular displacement (in rad) in the first 12 minutes? a. 0 b. 2π c. 4π d. 16π e. 32π ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 10.1 Angular Position, Velocity, and Acceleration Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 7. Refer to Exhibit 10-1. What is her angular displacement (in rad) in the 16-minute period shown in the graph? a. 0 b. 16π c. 32π d. 40π e. 64π ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 8. Refer to Exhibit 10-1. How many revolutions does she complete in the first 12 minutes? a. 4 b. 8 c. 12 d. 16 e. 32 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 9. Refer to Exhibit 10-1. How many revolutions does she complete in the 16-minute period? a. 8 b. 12 c. 16 d. 20 e. 40 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 10. The angular speed of the minute hand of a clock, in rad/s, is a. . b. . c. .

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d. π. e. 120π.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 11. The angular speed of the hour hand of a clock, in rad/s, is a. . b. . c. . d. 1 800π. e. 7 200π.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 12. The angular speed of the hour hand of a clock, in rad/min, is a. . b. . c. . d. π. e. 120π.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track.

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Use this exhibit to answer the following question(s).

2

13. Refer to Exhibit 10-2. What is his average angular acceleration, in rad/s , in the first 10 minutes? a. 0 b. c. d. e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 2

14. Refer to Exhibit 10-2. What is his average angular acceleration, in rad/s , in the period from t = 6 min to t = 8 min? a. 0 b. c. d. e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 15. A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.

Relative to the positive direction of the axis of rotation, the angular positions of the sphere are positive, its angular Copyright Cengage Learning. Powered by Cognero.

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velocity is positive, and its angular acceleration is negative. The sphere is a. rotating clockwise and slowing down. b. rotating counterclockwise and slowing down. c. rotating clockwise and speeding up. d. rotating counterclockwise and speeding up. e. first rotating clockwise and then counterclockwise.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 16. A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.

Relative to the positive direction of the axis of rotation, the angular positions of the sphere are negative, its angular velocity is negative, and its angular acceleration is positive. The sphere is a. rotating clockwise and slowing down. b. rotating counterclockwise and slowing down. c. rotating clockwise and speeding up. d. rotating counterclockwise and speeding up. e. first rotating counterclockwise and then clockwise.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 17. A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.

Relative to the positive direction of the axis of rotation, the angular positions of the sphere are negative, its angular velocity is negative, and its angular acceleration is negative. The sphere is a. rotating clockwise and slowing down. b. rotating counterclockwise and slowing down. c. rotating clockwise and speeding up. d. rotating counterclockwise and speeding up. e. first rotating counterclockwise and then clockwise.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False Exhibit 10-3 The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s.

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Use this exhibit to answer the following question(s).

18. Refer to Exhibit 10-3. The change in angular position, Δθ, during the 7-second period is a. 21 rad, CW. b. 21 rad, CCW. c. 30 rad, CW. d. 30 rad, CCW. e. 39 rad, CCW. ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 19. Refer to Exhibit 10-3. The angular position, θ, at t = 0 s is 3.0 rad, clockwise. The angular position, θ, at t = 7 s is a. 27 rad, CW. b. 27 rad, CCW. c. 33 rad, CW. d. 33 rad, CCW. e. 36 rad, CCW. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 2

20. The graph below shows a plot of angular acceleration in rad/s versus time from t = 0 s to t = 8 s. The change in angular velocity, Δω, during this 8-second period is

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a. , CW. b. , CCW. c. , CW. d. , CCW. e. , CW. ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 2

21. The graph below shows a plot of angular acceleration in rad/s versus time from t = 0 s to t = 8 s. The angular velocity at t = 0 s is

, CCW. The angular velocity, ω, at t = 8 s is

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a. , CW. b. , CCW. c. , CW. d. , CCW. e. , CW. ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 22. A rigid rod of length l rotates about an axis perpendicular to the rod, with one end of the rod fixed to the axis. Which of the following are equal at all points on the rod? the angular position I. the angular velocity II. III. the angular acceleration IV. the centripetal acceleration the tangential acceleration V. a. I and II b. I, II, and III c. I, II, III and IV d. I, II, III, IV and V e. I, II and IV. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 23. A celestial object called a pulsar emits its light in short bursts that are synchronized with its rotation. A pulsar in the Crab Nebula is rotating at a rate of 30 revolutions/second. What is the maximum radius of the pulsar, if no part of its 8 surface can move faster than the speed of light (3 × 10 m/s)?

ANSWER: 1 590 km POINTS: 2 DIFFICULTY: Average REFERENCES: 10.1 Angular Position, Velocity, and Acceleration HAS VARIABLES: False 24. At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s. Two seconds later it has turned through 5.0 complete revolutions. What is the angular acceleration of this wheel?

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a. 17 rad/s2 b. 14 rad/s2 c. 20 rad/s2 d. 23 rad/s2 e. 13 rad/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration HAS VARIABLES: False 2

25. At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of −0.40 rad/s has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. What is the angular position of the wheel at t = 2.0 s? a. 4.9 rad b. 4.7 rad c. 4.5 rad d. 4.3 rad e. 4.1 rad ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration HAS VARIABLES: False 3

26. A wheel rotating about a fixed axis has an angular position given by θ = 3.0 − 2.0t , where θ is measured in radians and t in seconds. What is the angular acceleration of the wheel at t = 2.0 s? a. −1.0 rad/s2 b. −24 rad/s2 c. −2.0 rad/s2 d. −4.0 rad/s2 e. −3.5 rad/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration HAS VARIABLES: False 2

27. A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s turns through 2.4 revolutions during a 2.0-s time interval. What is the angular velocity at the end of this time interval? a. 9.5 rad/s b. 9.7 rad/s c. 9.3 rad/s d. 9.1 rad/s Copyright Cengage Learning. Powered by Cognero.

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e. 8.8 rad/s ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration HAS VARIABLES: False 28. The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off. The turntable comes to rest 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration. a. 12 rad b. 8.0 rad c. 10 rad d. 16 rad e. 6.8 rad ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration HAS VARIABLES: False 29. A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval, the angular velocity increases to 40 rad/s. Assume that the angular acceleration was constant during the 5.0-s interval. How many revolutions does the wheel turn through during the 5.0-s interval? a. 20 rev b. 24 rev c. 32 rev d. 28 rev e. 39 rev ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration HAS VARIABLES: False 30. A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval, the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval? a. 95 rad b. 85 rad c. 65 rad d. 75 rad e. 125 rad ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 31. A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution? a. 9.9 s b. 7.8 s c. 8.5 s d. 9.2 s e. 6.4 s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration HAS VARIABLES: False 2

32. A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s . In a 4.0-s interval the wheel turns through an angle of 80 radians. Assuming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval? a. 2.5 s b. 4.0 s c. 3.5 s d. 3.0 s e. 4.5 s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration HAS VARIABLES: False 2

33. A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s starts from rest at t = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s? a. 0.25 m/s2 b. 0.50 m/s2 c. 0.14 m/s2 d. 0.34 m/s2 e. 0.20 m/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.3 Angular and Translational Quantities HAS VARIABLES: False 2

34. A wheel rotates about a fixed axis with a constant angular acceleration of 4.0 rad/s . The diameter of the wheel is 40 cm. What is the linear speed of a point on the rim of this wheel at an instant when that point has a total linear acceleration Copyright Cengage Learning. Powered by Cognero.

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2

with a magnitude of 1.2 m/s ? a. 39 cm/s b. 42 cm/s c. 45 cm/s d. 35 cm/s e. 53 cm/s ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.3 Angular and Translational Quantities HAS VARIABLES: False 35. A disk (radius = 8.0 cm) that rotates about a fixed axis starts from rest and accelerates at a constant rate to an angular velocity of 4.0 rad/s in 2.0 s. What is the magnitude of the total linear acceleration of a point on the rim of the disk at the instant when the angular velocity of the disk is 1.5 rad/s? a. 24 cm/s2 b. 16 cm/s2 c. 18 cm/s2 d. 34 cm/s2 e. 44 cm/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.3 Angular and Translational Quantities HAS VARIABLES: False 2

36. A cylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s starts from rest at t = 0. At the instant when it has turned through 0.40 radian, what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)? a. 0.31 m/s2 b. 0.27 m/s2 c. 0.35 m/s2 d. 0.39 m/s2 e. 0.45 m/s2 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.3 Angular and Translational Quantities HAS VARIABLES: False 2

37. A wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s . At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration of a point on the rim of the wheel? a. 0.40 m/s2 Copyright Cengage Learning. Powered by Cognero.

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b. 0.29 m/s2 c. 0.69 m/s2 d. 0.49 m/s2 e. 0.35 m/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.3 Angular and Translational Quantities HAS VARIABLES: False 38. A horizontal disk with a radius of 10 cm rotates about a vertical axis through its center. The disk starts from rest at t = 2 0 and has a constant angular acceleration of 2.1 rad/s . At what value of t will the radial and tangential components of the linear acceleration of a point on the rim of the disk be equal in magnitude? a. 0.55 s b. 0.63 s c. 0.69 s d. 0.59 s e. 0.47 s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.3 Angular and Translational Quantities HAS VARIABLES: False 39. When the center of a bicycle wheel has linear velocity of point P' at the top of the wheel is

a. 0. b.

.

c.

.

d.

.

e.

relative to the ground, the velocity relative to the ground

.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.3 Angular and Translational Quantities HAS VARIABLES: False 40. A thin uniform rod (length = 1.2 m, mass = 2.0 kg) is pivoted about a horizontal, frictionless pin through one end of Copyright Cengage Learning. Powered by Cognero.

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2

the rod. (The moment of inertia of the rod about this axis is ML /3.) The rod is released when it makes an angle of 37° with the horizontal. What is the angular acceleration of the rod at the instant it is released? a. 9.8 rad/s2 b. 7.4 rad/s2 c. 8.4 rad/s2 d. 5.9 rad/s2 e. 6.5 rad/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.4 Torque HAS VARIABLES: False 41. You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee. Ignoring air resistance, the torque exerted about its center of mass by gravity is a. 0. b. mgr. c. 2mgr. d. a function of the angular velocity. e. small at first, then increasing as the Frisbee loses the torque given it by your hand.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.4 Torque HAS VARIABLES: False 42. Two forces of magnitude 50 N, as shown in the figure below, act on a cylinder of radius 4 m and mass 6.25 kg. The cylinder, which is initially at rest, sits on a frictionless surface. After 1 second, the velocity and angular velocity of the cylinder in m/s and rad/s are, respectively,

a. v = 0; ω = 0. b. v = 0; ω = 4. c. v = 0; ω = 8. d. v = 8; ω = 8. e. v = 16; ω = 8.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.4 Torque Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 43. Which of the following diagrams shows the greatest magnitude net torque with a zero net force? All the rods, of length 2r, rotate about an axis that is perpendicular to the rod and fixed in the center of the rod. All the forces are of magnitude F or 2F and all distances from the axis are r or r/2. a. b. c.

d.

e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.4 Torque HAS VARIABLES: False 44. The diagram below shows five 20-kg rods of the same 2.0-m length free to rotate about axes through the rods, as indicated. Which rod experiences the greatest magnitude gravitational torque? a.

b.

c.

d.

e.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.4 Torque HAS VARIABLES: False 45. Five identical cylinders are each acted on by forces of equal magnitude. Which force exerts the biggest torque about the central axes of the cylinders?

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a.

b.

c.

d.

e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.4 Torque HAS VARIABLES: False 46. A torque can be exerted on a body with a fixed axis of rotation a. only by a centripetal force. b. only by a force directed radially outwards. c. only by a tangential force. d. only by a force with a component directed radially outwards. e. by any force not pointing directly toward or away from the axis of rotation.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.4 Torque HAS VARIABLES: False 47. Two objects of mass m1 = 2m and m2 = m move around a rotation axis A in parallel circles of radii r1 = r and r2 = 2r with equal tangential speeds. As they rotate, forces of equal magnitude are applied opposite to their velocities to stop them. Which statement is correct?

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a. m2 will stop first because it has the larger initial angular velocity. b. m1 will stop first because it has the smaller radius. c. m2 will stop first because the torque on it is greater. d. m1 will stop first because it has the smaller moment of inertia. e. Both objects will stop at the same time because the angular accelerations are equal.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.4 Torque HAS VARIABLES: False 48. A particle located at the position vector

m has a force

N acting on it. The torque about the

origin is what? a. (1 ) N⋅ m b. (5 ) N⋅ m c. (−1 ) N⋅ m d. (−5 ) N⋅ m e. (2 + 3 ) N⋅ m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.4 The Vector Product and Torque HAS VARIABLES: False 49. A mass (M1 = 5.0 kg) is connected by a light cord to a mass (M2 = 4.0 kg) which slides on a smooth surface, as shown 2 in the figure. The pulley (radius = 0.20 m) rotates about a frictionless axle. The acceleration of M2 is 3.5 m/s . What is the moment of inertia of the pulley?

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a. 0.29 kg⋅ m2 b. 0.42 kg⋅ m2 c. 0.20 kg⋅ m2 d. 0.62 kg⋅ m2 e. 0.60 kg⋅ m2 ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 50. A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure. When released from rest the object falls with a downward acceleration 2 of 5.0 m/s . What is the moment of inertia of the wheel?

a. 0.023 kg⋅ m2 b. 0.027 kg⋅ m2 c. 0.016 kg⋅ m2 d. 0.019 kg⋅ m2 e. 0.032 kg⋅ m2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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51. A wheel (radius = 0.25 m) is mounted on a frictionless, horizontal axis. The moment of inertia of the wheel about the 2 axis is 0.040 kg⋅ m . A light cord wrapped around the wheel supports a 0.50-kg object as shown in the figure. The object is released from rest. What is the magnitude of the acceleration of the 0.50-kg object?

a. 3.0 m/s2 b. 3.4 m/s2 c. 4.3 m/s2 d. 3.8 m/s2 e. 2.7 m/s2 ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 52. A mass m = 4.0 kg is connected, as shown, by a light cord to a mass M = 6.0 kg, which slides on a smooth, horizontal 2 surface. The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a moment of inertia I = 0.090 kg⋅ m .

The cord does not slip on the pulley. What is the magnitude of the acceleration of m?

a. 2.4 m/s2 b. 2.8 m/s2 c. 3.2 m/s2 Copyright Cengage Learning. Powered by Cognero.

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d. 4.2 m/s2 e. 1.7 m/s2 ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 53. A uniform rod (mass = 2.0 kg, length = 0.60 m) is free to rotate about a frictionless pivot at one end. The rod is released from rest in the horizontal position. What is the magnitude of the angular acceleration of the rod at the instant it is 60° below the horizontal? a. 15 rad/s2 b. 12 rad/s2 c. 18 rad/s2 d. 29 rad/s2 e. 23 rad/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 54. Particles (mass of each = 0.20 kg) are placed at the 40-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the initial angular acceleration of the body? a. 12 rad/s2 b. 5.9 rad/s2 c. 8.4 rad/s2 d. 5.4 rad/s2 e. 17 rad/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 55. A wheel (radius = 12 cm) is mounted on a frictionless, horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel. A light cord wrapped around the wheel supports a 0.40-kg object. If released 2 from rest with the string taut, the object is observed to fall with a downward acceleration of 3.0 m/s . What is the moment of inertia (of the wheel) about the given axle? a. 0.023 kg⋅ m2 b. 0.013 kg⋅ m2 c. 0.020 kg⋅ m2 Copyright Cengage Learning. Powered by Cognero.

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d. 0.016 kg⋅ m2 e. 0.035 kg⋅ m2 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 56. A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular acceleration of the rod at the instant it is released? a. 4.7 rad/s2 b. 6.9 rad/s2 c. 6.4 rad/s2 d. 5.6 rad/s2 e. 4.2 rad/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 57. A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at the horizontal position. What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal? a. 3.7 rad/s2 b. 1.3 rad/s2 c. 2.5 rad/s2 d. 4.9 rad/s2 e. 1.9 rad/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 58. A uniform rod of mass M = 1.2 kg and length L = 0.80 m, lying on a frictionless, horizontal plane, is free to pivot 2 about a vertical axis through one end, as shown. The moment of inertia of the rod about this axis is given by (1/3)ML . If a force (F = 5.0 N, θ = 40°) acts as shown, what is the resulting angular acceleration about the pivot point?

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a. 16 rad/s2 b. 12 rad/s2 c. 14 rad/s2 d. 10 rad/s2 e. 33 rad/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 59. A nonuniform 2.0-kg rod is 2.0 m long. The rod is mounted to rotate freely about a horizontal axis perpendicular to 2 the rod that passes through one end of the rod. The moment of inertia of the rod about this axis is 4.0 kg⋅ m . The center of mass of the rod is 1.2 m from the axis. If the rod is released from rest in the horizontal position, what is its angular speed as it swings through the vertical position? a. 3.4 rad/s b. 4.4 rad/s c. 4.3 rad/s d. 5.8 rad/s e. 6.8 rad/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 60. When the sum of the external forces and the sum of the external torques on a body are both zero, we can conclude that a. the body is moving at constant velocity but is not rotating. b. the body is rotating at constant angular velocity but has no linear velocity. c. the body has neither linear nor angular velocity. d. the body may have constant linear or angular velocity, but not both simultaneously. e. the body may have constant linear or constant angular velocity, or both simultaneously.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 61. A horizontal force of magnitude 6.5 N is exerted tangentially on a Frisbee of mass 32 grams and radius 14.3 cm.

Assuming the Frisbee, a uniform disk, is originally at rest and the force is exerted for 0.08 s, determine the angular velocity of rotation about the central axis when the Frisbee is released.

ANSWER: 227 rad/s POINTS: 2 DIFFICULTY: Average REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 62. A force is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown. The acceleration of the center of mass of the roll of paper (when it rolls without slipping) is

a. . b. . c. . d. . e. .

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.5 Analysis Model: Rigid Object Under a Net Torque HAS VARIABLES: False 63. Two particles (m1 = 0.20 kg, m2 = 0.30 kg) are positioned at the ends of a 2.0-m long rod of negligible mass. What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass? a. 0.48 kg⋅ m2 b. 0.50 kg⋅ m2 c. 1.2 kg⋅ m2 d. 0.80 kg⋅ m2 e. 0.70 kg⋅ m2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 64. Four identical particles (mass of each = 0.24 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the center of mass of the body and is parallel to the shorter sides of the rectangle? a. 2.4 kg⋅ m2 b. 2.2 kg⋅ m2 c. 1.9 kg⋅ m2 Copyright Cengage Learning. Powered by Cognero.

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d. 2.7 kg⋅ m2 e. 8.6 kg⋅ m2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 65. Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.5 m × 4.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides? a. 2.2 kg⋅ m2 b. 2.8 kg⋅ m2 c. 2.5 kg⋅ m2 d. 3.1 kg⋅ m2 e. 1.6 kg⋅ m2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 66. Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the longer sides and is parallel to the shorter sides? a. 2.7 kg⋅ m2 b. 3.6 kg⋅ m2 c. 3.1 kg⋅ m2 d. 4.1 kg⋅ m2 e. 1.6 kg⋅ m2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 67. The rigid object shown is rotated about an axis perpendicular to the paper and through point P. The total kinetic energy of the object as it rotates is equal to 1.4 J. If M = 1.3 kg and L = 0.50 m, what is the angular velocity of the object?

Neglect the mass of the connecting rods and treat the masses as particles.

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a. 1.3 rad/s b. 1.5 rad/s c. 1.7 rad/s d. 1.2 rad/s e. 2.1 rad/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 68. If M = 0.50 kg, L = 1.2 m, and the mass of each connecting rod shown is negligible, what is the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the masses as particles.

a. 3.7 kg⋅ m2 b. 2.8 kg⋅ m2 c. 3.2 kg⋅ m2 d. 2.3 kg⋅ m2 e. 3.9 kg⋅ m2 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 69. Three particles, each of which has a mass of 80 g, are positioned at the vertices of an equilateral triangle with sides of length 60 cm. The particles are connected by rods of negligible mass. What is the moment of inertia of this rigid body about an axis that is parallel to one side of the triangle and passes through the respective midpoints of the other two sides? a. 0.018 kg⋅ m2 b. 0.020 kg⋅ m2 c. 0.016 kg⋅ m2 d. 0.022 kg⋅ m2 e. 0.032 kg⋅ m2 Copyright Cengage Learning. Powered by Cognero.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 70. A uniform meter stick is pivoted to rotate about a horizontal axis through the 25-cm mark on the stick. The stick is released from rest in a horizontal position. The moment of inertia of a uniform rod about an axis perpendicular to the rod 2 and through the center of mass of the rod is given by (1/12)ML . Determine the magnitude of the initial angular acceleration of the stick. a. 17 rad/s2 b. 13 rad/s2 c. 15 rad/s2 d. 19 rad/s2 e. 23 rad/s2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 71. A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The moment of inertia of the sphere about this axis is

a. . b. . c. . d. . e. .

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 72. A uniform cylinder of radius R, mass M, and length L rotates freely about a horizontal axis parallel and tangent to the Copyright Cengage Learning. Powered by Cognero.

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cylinder, as shown below. The moment of inertia of the cylinder about this axis is

a. . b. . c. MR2. d. . e. .

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 73. A rod of length 1.00 m has a mass per unit length given by , where is in kg/m. The rod is 2 placed on the x axis going from x = 0.00 m to x = 1.00 m. What is the moment of inertia of the rod in kg m about the y axis?

ANSWER: 0.867 POINTS: 2 DIFFICULTY: Average REFERENCES: 10.6 Calculation of Moments of Inertia HAS VARIABLES: False 74. Particles (mass of each = 0.40 kg) are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot? a. 15 m/s2 b. 9.8 m/s2 c. 5.8 m/s2 d. 12 m/s2 e. 4.7 m/s2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 75. A uniform rod (length = 2.0 m) is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through the rod at a point 0.50 m from one end of the rod. If the rod is released from rest in a horizontal Copyright Cengage Learning. Powered by Cognero.

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position, what is the angular speed of the rod as it rotates through its lowest position? a. 3.5 rad/s b. 3.8 rad/s c. 4.1 rad/s d. 2.0 rad/s e. 5.6 rad/s ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 76. Identical particles are placed at the 50-cm and 80-cm marks on a meter stick of negligible mass. This rigid body is then mounted so as to rotate freely about a pivot at the 0-cm mark on the meter stick. If this body is released from rest in a horizontal position, what is the angular speed of the meter stick as it swings through its lowest position? a. 4.2 rad/s b. 5.4 rad/s c. 4.6 rad/s d. 5.0 rad/s e. 1.7 rad/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 77. A uniform rod (mass = 1.5 kg) is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end.

The rod is released from rest in a horizontal position. What is the angular speed of the rod when the rod makes an angle of 2 30° with the horizontal? (The moment of inertia of the rod about the pin is 2.0 kg⋅ m ). a. 2.2 rad/s b. 3.6 rad/s c. 2.7 rad/s d. 3.1 rad/s e. 1.8 rad/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 78. A uniform rod is 3.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 27° above the horizontal. What is the angular speed of the rod as it passes through the horizontal position? a. 3.0 rad/s b. 2.8 rad/s c. 2.1 rad/s d. 2.5 rad/s Copyright Cengage Learning. Powered by Cognero.

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e. 3.4 rad/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 79. A uniform rod of length (L = 2.0 m) and mass (M = 1.5 kg) is pivoted about a horizontal frictionless pin through one end. The rod is released from rest at an angle of 30° below the horizontal. What is the angular speed of the rod when it 2 passes through the vertical position? (The moment of inertia of the rod about the pin is 2.0 kg⋅ m .) a. 3.5 rad/s b. 2.7 rad/s c. 3.1 rad/s d. 2.3 rad/s e. 1.6 rad/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 80. The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper. If M = 2.0 kg and L = 80 cm, what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s?

Neglect the mass of the connecting rod and treat the masses as particles.

a. 18 J b. 15 J c. 12 J d. 23 J e. 26 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 81. The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.

a. 2.9 J Copyright Cengage Learning. Powered by Cognero.

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b. 2.6 J c. 3.1 J d. 3.4 J e. 1.6 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 82. A uniform rod (length = 2.4 m) of negligible mass has a 1.0-kg point mass attached to one end and a 2.0-kg point mass attached to the other end. The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point 1.0 m from the 2.0-kg mass. The rod is released from rest when it is horizontal. What is the angular velocity of the rod at the instant the 2.0-kg mass passes through its low point? a. 1.7 rad/s b. 2.2 rad/s c. 2.0 rad/s d. 1.5 rad/s e. 3.1 rad/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 83. The net work done in accelerating a propeller from rest to an angular velocity of 200 rad/s is 3 000 J. What is the moment of inertia of the propeller?

2 ANSWER: 0.15 kg⋅ m POINTS: 2 DIFFICULTY: Average REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 84. A coin with a diameter 3.00 cm rolls up a 30.0° inclined plane. The coin starts out with an initial angular speed of 60.0 rad/s and rolls in a straight line without slipping. If the moment of inertia of the coin is

2

MR , how far will the coin roll

up the inclined plane?

ANSWER: 12.4 cm POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 85. A regulation basketball has a 25.0-cm diameter and a mass of 0.560 kg. It may be approximated as a thin, spherical shell with a moment of inertia

2

MR . Starting from rest, how long will it take a basketball to roll without slipping 4.00 m

down an incline at 30.0° to the horizontal?

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ANSWER: 1.65 s POINTS: 3 DIFFICULTY: Challenging REFERENCES: 10.8 Energy Considerations in Rotational Motion HAS VARIABLES: False 86. Two cylinders made of the same material roll down a plane inclined at an angle θ with the horizontal. Each travels the same distance. The radius of cylinder B is twice the radius of cylinder A. In what order do they reach the bottom? a. A reaches the bottom first because it has the greater acceleration. b. A reaches the bottom first because it has a smaller moment of inertia. c. B reaches the bottom first because is experiences a larger torque. d. B reaches the bottom first because it travels a larger distance in one rotation. e. They both reach the bottom at the same time, because each has the same linear acceleration.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 10.9 Rolling Motion of a Rigid Object HAS VARIABLES: False 87. When a wheel is rolling without slipping, the magnitude of its velocity relative to the ground is greatest at a. the point in contact with the ground. b. the point at the center of the wheel. c. the point at the top of the wheel opposite to the point in contact with the ground. d. the point farthest forward from the center of mass of the wheel. e. the point farthest behind the center of mass of the wheel.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.9 Rolling Motion of a Rigid Object HAS VARIABLES: False 88. A solid sphere, a solid cylinder, and a hoop all have the same mass and radius. Each are sent down identical inclined planes starting from rest. Their kinetic energies at the bottom of the incline are Ksphere, Kcylinder, and Khoop. Which of the following is true? a. Ksphere > Kcylinder b. Khoop > Ksphere c. Khoop > Kcylinder d. Kcylinder > Khoop e. No answer above is correct.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 10.9 Rolling Motion of a Rigid Object HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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89. A solid sphere, a solid cylinder, a spherical shell, and a hoop all have the same mass and radius. Each are rolling on a horizontal surface with the same center of mass speed, and then they roll up identical inclines. Which one goes the greatest distance up its incline? a. the hoop b. the solid sphere c. the spherical shell d. the cylinder e. They all go the same distance up their inclines.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.9 Rolling Motion of a Rigid Object HAS VARIABLES: False 90. A uniform solid sphere rolls without slipping along a horizontal surface. What fraction of its total kinetic energy is in the form of rotational kinetic energy about the CM? ANSWER: 2/7 POINTS: 2 DIFFICULTY: Average REFERENCES: 10.9 Rolling Motion of a Rigid Object HAS VARIABLES: False 91. A solid sphere, spherical shell, solid cylinder and a cylindrical shell all have the same mass m and radius R. If they are all released from rest at the same elevation and roll without slipping, which reaches the bottom of an inclined plane first? a. solid sphere b. spherical shell c. solid cylinder d. cylindrical shell e. all take the same time ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 10.9 Rolling Motion of a Rigid Object HAS VARIABLES: False 92. A cylindrical shell rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is what?

a. (5/7)g sin θ Copyright Cengage Learning. Powered by Cognero.

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b. (1/2)g sin θ c. (3/5)g sin θ d. (2/3)g sin θ e. (4/5)g sin θ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 10.9 Rolling Motion of a Rigid Object HAS VARIABLES: False 93. A solid cylinder rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is what?

a. (5/7)g sin θ b. (1/2)g sin θ c. (2/3)g sin θ d. (3/5)g sin θ e. (4/5)g sin θ ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 10.9 Rolling Motion of a Rigid Object HAS VARIABLES: False

1. A car of mass 1 000 kg moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its 2 angular momentum (in kg⋅ m /s) relative to the center of the race track? a. 5.0 × 102 b. 5.0 × 106 c. 2.5 × 104 d. 2.5 × 106 e. 5.0 × 103 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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2. A solid cylinder of radius R = 1.0 m and mass 10 kg rotates about its axis. When its angular velocity is 10 rad/s, what is 2 its angular momentum (in kg⋅ m /s)? a. 50 b. 20 c. 40 d. 25 e. 70 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 3. A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 2 5. What is its angular momentum (in kg⋅ m /s) relative to the origin? a. −30 b.

30 c. −15 d.

15 e.

45 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 4. A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s along the direction

. What

2

is its angular momentum (in kg⋅ m /s) relative to the origin? a.

0 b. c. d.

6

e.

−6 ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 5. A particle whose mass is 2.0 kg moves in the xy plane with a constant speed of 3.0 m/s along the direction Copyright Cengage Learning. Powered by Cognero.

.

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2

What is its angular momentum (in kg⋅ m /s) relative to the point (0, 5.0) meters? a.

12 b.

11 c.

13 d.

14 e.

21 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 6. In the figure, a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight. The string is 2 m 2 long. If the weight is released with zero initial velocity from a horizontal position, its angular momentum (in kg⋅ m /s) at the lowest point of its path relative to the center of the circle is approximately what?

a. 40 b. 10 c. 30 d. 20 e. 50 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 7. A massless rope is wrapped around a uniform cylinder that has radius R and mass M, as shown in the figure. Initially, the unwrapped portion of the rope is vertical and the cylinder is horizontal. The linear acceleration of the cylinder is what?

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a. (2/3)g b. (1/2)g c. (1/3)g d. (1/6)g e. (5/6)g ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 8. Two blocks, m1 = 1.0 kg and m2 = 2.0 kg, are connected by a light string as shown in the figure. If the radius of the 2 pulley is 1.0 m and its moment of inertia is 5.0 kg⋅ m , the acceleration of the system is what?

a. (1/6)g b. (3/8)g c. (1/8)g d. (1/2)g e. (5/8)g ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 9. A puck on a frictionless air hockey table has a mass of 5.0 kg and is attached to a cord passing through a hole in the surface as in the figure. The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The 2 angular momentum of the puck (in kg⋅ m /s) is what?

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a. 80 b. 20 c. 30 d. 60 e. 50 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 10. A pendulum bob of mass m is set into motion in a circular path in a horizontal plane as shown in the figure. The square of the angular momentum of the bob about the vertical axis through the point P is what?

a. m2 gl3 sin4 θ/cos θ b. m2 gl3 sin3 θ/cos θ c. m2 gl3 sin2 θ/cos θ d. m2 gl3 sin θ/cos θ e. m2 gl3 sin2 θ ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 11. Five objects of mass m move at velocity at a distance r from an axis of rotation perpendicular to the page through point A, as shown below. Which object has zero angular momentum about that axis?

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a.

b.

c. d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 12. The object shown below has mass m and velocity axis perpendicular to the page through point O is

. The direction of its angular momentum vector with respect to an

a. downwards. b. to the right. c. into the page. d. up out of the page. e. counterclockwise.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 13. The diagram below shows five cylinders, each cylinder rotating with constant angular velocity about its central axis.

The magnitude of the tangential speed of one point of each cylinder is shown, along with each cylinder's radius and mass.

Which cylinder has the largest angular momentum?

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a.

b.

c.

d.

e.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 14. The diagram below shows five thin cylindrical shells, each shell rotating with constant angular velocity about its central axis. The magnitude of the tangential speed of one point of each cylinder is shown, along with each cylinder's radius and mass. Which cylindrical shell has the largest angular momentum?

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a.

b.

c.

d.

e.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 15. A 0.5-kg fish, hooked as shown below, starts to swim away at a speed of 3 m/s. The angular momentum of the fish relative to the hand holding the fishing rod is about

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a. . b. . c. . d. . e. .

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False Exhibit 11-1 Two blocks of masses m1 and m2 are connected by a light cord that passes over a pulley of mass M, as shown. Block m2 slides on a frictionless, horizontal surface. The blocks and pulley are initially at rest. When m1 is released, the blocks accelerate and the pulley rotates.

Use this exhibit to answer the following question(s).

16. Refer to Exhibit 11-1. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is a. the same at all times.

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b. proportional to l1, the length of string from the pulley to m1. c. proportional to l2, the length of string from the pulley to m2. d. conserved because the Earth doesn't move. e. proportional to the speed of the blocks.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 17. Refer to Exhibit 11-1. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is a. proportional to the radius of the pulley. b. proportional to the speed of the blocks. c. proportional to the length of the string. d. to all of the above. e. only to (a) and (b) above.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 18. A 3.0-kg particle has a position vector given by

, where

is in meters and t is in seconds. What

2

is the angular momentum of the particle, in kg⋅ m /s, about the origin at t = 2 s? a.

72 b. −72 c.

24 d. −24 e.

22 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 19. If L represents angular momentum, I represents moment of inertia, p represents linear momentum, m represents mass, and r represents a distance, which of the following can represent kinetic energy? a. p2/2m b. L2/2I c. rpI d. all of the above Copyright Cengage Learning. Powered by Cognero.

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e. both (a) and (b) ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 11.1 Analysis Model: Nonisolated System (Angular Momentum) HAS VARIABLES: False 20. A puck on a frictionless air hockey table has a mass of 5.0 g and is attached to a cord passing through a hole in the surface as in the figure. The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The cord is then pulled from below, shortening the radius to 1.0 m. The new angular velocity (in rad/s) is what?

a. 4.0 b. 6.0 c. 12 d. 2.0 e. 8.0 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 21. A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is what?

a. (m + M/3)(vL/2) b. (m + M/12)(vL/2) c. (m + M/6)(vL/2) d. mvL/2 Copyright Cengage Learning. Powered by Cognero.

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e. mvL ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 22. A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision?

a. 8.1 b. 2.0 c. 6.1 d. 4.2 e. 10 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 23. A skater extends her arms horizontally, holding a 5-kg mass in each hand. She is rotating about a vertical axis with an angular velocity of one revolution per second. If she drops her hands to her sides, what will the final angular velocity (in 2 rev/s) be if her moment of inertia remains approximately constant at 5 kg⋅ m , and the distance of the masses from the axis changes from 1 m to 0.1 m? a. 6 b. 3 c. 9 d. 4 e. 7 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 2

24. A merry-go-round of radius R = 2.0 m has a moment of inertia I = 250 kg⋅ m , and is rotating at 10 rpm. A child whose mass is 25 kg jumps onto the edge of the merry-go-round, heading directly toward the center at 6.0 m/s. The new angular speed (in rpm) of the merry-go-round is approximately what? a. 10 b. 9.2 Copyright Cengage Learning. Powered by Cognero.

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c. 8.5 d. 7.1 e. 6.4 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 25. Stars originate as large bodies of slowly rotating gas. Because of gravity, these clumps of gas slowly decrease in size.

The angular velocity of a star increases as it shrinks because of a. conservation of angular momentum. b. conservation of linear momentum. c. conservation of energy. d. the law of universal gravitation. e. conservation of mass.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 26. When an object is effectively isolated from external torques, like an ice skater twirling on the tip of one skate, the angular momentum of the object a. can be increased by shifting mass out away from the axis of rotation. b. can be decreased by shifting mass out away from the axis of rotation. c. can be increased by shifting mass in toward the axis of rotation. d. can be decreased by shifting mass in toward the axis of rotation. e. cannot be changed except by friction at the point of contact.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 27. A hockey puck traveling at speed v on essentially frictionless ice collides elastically with one end of a straight stick lying flat on the ice. In this collision a. momentum is conserved. b. angular momentum is conserved. c. energy is conserved. d. all of the above are conserved. e. only momentum and angular momentum are conserved.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) Copyright Cengage Learning. Powered by Cognero.

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HAS VARIABLES: False 28. A hockey puck traveling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end. In this collision a. momentum is conserved. b. angular momentum is conserved. c. energy is conserved. d. all of the above are conserved. e. only momentum and angular momentum are conserved.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 29. A space station out beyond the solar system is rotating with constant angular velocity. A spaceship heading into the station along a diameter of the station uses its rockets to brake, and then docks inside the station at its center. When the spaceship docks, the angular momentum of the system consisting of the station and ship a. is less than the original angular momentum of the station. b. is the same as the original angular momentum of the station. c. is greater than the original angular momentum of the station. d. is less than the original angular momentum of the station, but the angular velocity increases. e. is greater than the original angular momentum of the station, but the angular velocity decreases.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 30. Halley's comet moves about the Sun in an elliptical orbit with its closest approach to the Sun being 0.59 A.U. and its furthest distance being 35 A.U. [1 Astronomical Unit (A.U.) is the Earth-Sun distance.] If the comet's speed at closest approach is 54 km/s, what is its speed when it is farthest from the Sun? ANSWER: 910 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False 22

31. What is the angular momentum of the Moon about the Earth? The mass of the Moon is 7.35 × 10 kg, the center-to5 center separation of the Earth and the Moon is 3.84 × 10 km, and the orbital period of the Moon is 27.3 days. Ignore the small offset of the center of mass of the system from the center of the Earth in your calculation.

34 2 ANSWER: 2.89 × 10 kg⋅ m /s POINTS: 2 DIFFICULTY: Average REFERENCES: 11.3 Analysis Model: Isolated System (Angular Momentum) HAS VARIABLES: False Copyright Cengage Learning. Powered by Cognero.

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32. A top is set spinning so that the rotation is counterclockwise around its axis when viewed from above. When the top is placed on a level surface it happens that its axis of rotation is not quite vertical. Viewed from above, which way does the rotational axis of the top precess? a. clockwise b. counterclockwise c. It’s random, if it starts clockwise it will continue clockwise, and vice versa, i.e., a 50% chance either way. d. The direction depends on the little shove given to the axis when the top is placed on the surface. e. In the northern hemisphere it will be clockwise, in the southern hemisphere it will be counterclockwise.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 11.4 The Motion of Gyroscopes and Tops HAS VARIABLES: False

1. The diagrams below show forces applied to a wheel that weighs 20 N. The symbol W stands for the weight. In which diagram(s) is(are) the wheel in equilibrium?

a. A b. B c. C d. D e. A and C ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.1 Analysis Model: Rigid Object in Equilibrium 2. The diagrams below show forces of magnitude F applied to an equilateral triangular block of uniform thickness. In which diagram(s) is(are) the block in equilibrium?

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c. C d. D e. A and B ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.1 Analysis Model: Rigid Object in Equilibrium 3. One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium?

a. . b. . c. . d. . e. .

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 12.1 Analysis Model: Rigid Object in Equilibrium 4. Pairs of forces of equal magnitude act on identical cylinders as shown in the figures. In which example is the cylinder in translational and rotational equilibrium? a.

b.

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c.

d.

e.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.1 Analysis Model: Rigid Object in Equilibrium 5. Angie says that an object is in equilibrium if the net torques about the center of mass is zero. Robbie says that an object is in equilibrium if the sum of external forces is zero. Which one, if either, is correct? a. Both are correct: an object is in equilibrium if either condition holds. b. Neither is correct: both conditions must hold simultaneously. c. Neither is correct: the net external force and the net external torque about any axis must be zero. d. Neither is correct: an object is in equilibrium only if its velocity is zero in all coordinate systems. e. Both are correct: if the sum of the external forces is zero, the net torque about any axis is automatically zero, and vice versa.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.1 Analysis Model: Rigid Object in Equilibrium Exhibit 12-1 A square of side

is removed from one corner of a square sandwich that has sides of length L. The center of mass of the

remainder of the sandwich moves from C to C'.

Use this exhibit to answer the following question(s).

6. Refer to Exhibit 12-1. The displacement of the x coordinate of the center of mass (from C to C') is a. .

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b. . c. . d. . e. .

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 12.2 More on the Center of Gravity 7. Refer to Exhibit 12-1. The displacement of the y coordinate of the center of mass (from C to C') is a. . b. . c. . d. . e. .

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 12.2 More on the Center of Gravity 8. Refer to Exhibit 12-1. The distance from C to C' is a. . b. . c. . d. . e. .

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 12.2 More on the Center of Gravity 9. The center of gravity of an object is at the same position as the center of mass when a. is the same at both ends of the object. b. the object is located in a region where

is uniform over the entire object.

c. the object is as large as the body that exerts the gravitational force on it. d. any of the conditions above is satisfied. e. either (a) or (b) above is satisfied.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.2 More on the Center of Gravity 10. A non-uniform meter stick is found to balance on a knife edge at the 60-cm mark. Where is the center of gravity of the meter stick? a. at the 40-cm mark b. at the 45-cm mark c. at the 50-cm mark d. at the 55-cm mark e. at a position not given ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.2 More on the Center of Gravity 11. A uniform ladder 15 ft long is leaning against a frictionless wall at an angle of 53° above the horizontal. The weight of the ladder is 30 pounds. A 75-lb boy climbs 6.0-ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor? a. 43 lb b. 34 lb c. 38 lb d. 47 lb e. 24 lb ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 12. A horizontal, uniform meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it at the 20-cm mark and a 0.30 kg mass hanging from it at the 60-cm mark. Determine the position on the meter stick at which one would hang a third mass of 0.60 kg to keep the meter stick balanced. a. 74 cm b. 70 cm Copyright Cengage Learning. Powered by Cognero.

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c. 65 cm d. 86 cm e. 62 cm ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 13. The figure shows a uniform, horizontal beam (length = 10 m, mass = 25 kg) that is pivoted at the wall, with its far end supported by a cable that makes an angle of 51° with the horizontal. If a person (mass = 60 kg) stands 3.0 m from the pivot, what is the tension in the cable?

a. 0.83 kN b. 0.30 kN c. 0.38 kN d. 0.42 kN e. 3.0 kN ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 14. A uniform, 100-lb beam is held in a vertical position by a pin at its lower end and a cable at its upper end. A horizontal force (magnitude P) acts as shown in the figure. If P = 75 lb, what is the tension in the cable?

a. 54 lb b. 69 lb c. 47 lb d. 61 lb Copyright Cengage Learning. Powered by Cognero.

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e. 75 lb ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 15. A 25-ft long crane supported at its lower end by a pin is elevated by a horizontal cable as shown in the figure. A 250lb load is suspended from the outer end of the crane. The center of gravity of the crane is 10 ft from the pin, and the crane weighs 200 lb. What is the tension in the horizontal cable?

a. 610 lb b. 540 lb c. 640 lb d. 570 lb e. 2 000 lb ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 16. A uniform beam having a mass of 60 kg and a length of 2.8 m is held in place at its lower end by a pin. Its upper end leans against a vertical, frictionless wall as shown in the figure. What is the magnitude of the force the pin exerts on the beam?

a. 0.68 kN b. 0.57 kN c. 0.74 kN Copyright Cengage Learning. Powered by Cognero.

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d. 0.63 kN e. 0.35 kN ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 17. A uniform, 120-lb beam is supported in a horizontal position by a pin and cable as shown in the figure. What is the magnitude of the force by the pin on the beam?

a. 94 lb b. 88 lb c. 63 lb d. 75 lb e. 150 lb ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 18. An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by

a. . b. . c. . d. mg.

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e.

.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 19. Sebastian has drawn a free-body diagram for a ladder of mass m leaning against a frictionless wall. His diagram is shown below. What is his error?

a. b. c. d.

is in the wrong direction. should be directed upwards, not down. should be perpendicular to the wall, not parallel to it. should be down into the floor for

to have the given direction.

e.

is correct, but there should also be a force perpendicular to the wall.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 20. A mobile is made of identical objects of mass m suspended so that the lowest row has one object, the row above two objects, and the row above three objects. All the strings are at 45° angles. What is the average tension in the strings connecting the highest row to the ceiling?

a.

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b. c. mg d.

e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 21. John is carrying a shovelful of snow. The center of mass of the 3.00 kg of snow he is holding is 15.0 cm from the end of the shovel. He is pushing down on the opposite end of the shovel with one hand and holding it up 30.0 cm from that end with his other hand. Ignore the mass of the shovel. Sarah says that his hand pushing down on the shovel must be exerting a greater force than the hand pushing up. James says it is just the reverse. Which one, if either, is correct? a. Sarah, because the hand pushing down must exert a greater force to match the torque exerted by the snow. b. James, because, depending on the location of the axis of rotation, the hand pushing down can counteract the torque exerted by the snow. c. James, because the hand pushing up must exert a force that equals the sum of the force of the hand pushing down and the weight of the snow. d. James, because both (b) and (c) above are correct. e. Neither, because the hands exert forces of equal magnitudes.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 22. The 1 560-kg solid steel door to a bank vault is 2.00 m high, 1.00-m-wide and 10 cm thick. One hinge is 60.0 cm down from the top on the left-hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the upper hinge? a. 6 950 N, left b. 6 950 N, right c. 7 640 N, left d. 7 640 N, right e. 15 300 N, left ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 23. The 1 560-kg solid steel door to a bank vault is 2.00 m high, 1.00 m wide, and 10 cm thick. One hinge is 60.0 cm down from the top on the left-hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the lower hinge? a. 6 950 N, left b. 6 950 N, right Copyright Cengage Learning. Powered by Cognero.

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c. 7 640 N, left d. 7 640 N, right e. 15 300 N, left ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 24. The free-body diagram below represents a 1 500-kg car sitting on a 3 000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below:

a. b. c.

never produces a torque on the bridge no matter where the axis of rotation is placed. never produces a torque on the bridge no matter where the axis of rotation is placed. cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge.

d. e.

Because the perpendicular distance to

from the left end of the bridge is 0, F1L should be 0.

Because the perpendicular distance to

from the right end of the bridge is 0, F2L should be 0.

ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 25. A horizontal, uniform 1.20-N meter stick is held up by two vertical strings, one at the 20-cm mark and the other at the 60-cm mark. What is the tension in the string at the 60-cm mark? a. 0.30 N b. 0.45 N c. 0.60 N d. 0.90 N e. 1.0 N ANSWER: d POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 12.3 Examples of Rigid Objects in Static Equilibrium 2

26. A 20-m long steel wire (cross-section 1.0 cm , Young's modulus 2.0 × 10 How much will the wire stretch under the load? a. 0.25 cm b. 2.5 cm c. 12.5 cm d. 25 cm e. 1.25 cm ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 12.4 Elastic Properties of Solids

11

2

N/m ), is subjected to a load of 25 000 N.

10

27. How large a force is necessary to stretch a 2.0-mm diameter copper wire (Y = 11 × 10 a. 2.1 kN b. 3.5 kN c. 6.9 kN d. 11 kN e. 5.4 kN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 12.4 Elastic Properties of Solids

2

N/m ) by 1.0%?

28. How large a pressure increase (in ATM) must be applied to water if it is to be compressed in volume by 1.0%? The 9 2 5 2 bulk modulus of water is 2.0 × 10 N/m and 1 ATM = 1.0 × 10 N/m . a. 50 ATM b. 100 ATM c. 1 100 ATM d. 400 ATM e. 200 ATM ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 12.4 Elastic Properties of Solids 29. Which one of the following cannot be a definition of an elastic modulus? a. b. c.

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d. e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.4 Elastic Properties of Solids 30. Stress is proportional to strain means that a. stress = constant × strain. b. stress = (constant 1) × strain + constant 2. c. stress = . d. stress =

.

e. stress × strain = constant.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 12.4 Elastic Properties of Solids 31. Aluminum Rod #1 has a length L and a diameter d. Aluminum Rod #2 has a length 2L and a diameter 2d. If Rod #1 is under tension T and Rod#2 is under tension 2T, how do the changes in length of the two rods compare? a. They are the same. b. Rod #1 has double the change in length that Rod #2 has. c. Rod #2 has double the change in length that Rod #1 has. d. Rod #1 has quadruple the change in length that Rod #2 has. e. Rod #2 has quadruple the change in length that Rod #1 has.

ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 12.4 Elastic Properties of Solids 32. For safety in climbing, a mountaineer uses a 50-m long nylon rope that is 1.0 cm in diameter. When supporting a 90kg climber, the rope elongates 1.6 m. Find the Young's modulus for the rope material.

8 2 ANSWER: 3.51 × 10 N/m POINTS: 2 DIFFICULTY: Average REFERENCES: 12.4 Elastic Properties of Solids 33. Find the minimum diameter of a steel wire 18 m long that will stretch no more than 9 mm when a load of 380 kg is 11 2 hung on the lower end. (Y steel = 2.0 × 10 N/m ).

ANSWER: 6.89 mm POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 12.4 Elastic Properties of Solids 3

4

34. If 1.0 m of concrete weighs 5 × 10 N, what is the height of the tallest cylindrical concrete pillar that will not collapse 7 2 under its own weight? (The compression strength of concrete is 1.7 × 10 N/m ) ANSWER: 340 m POINTS: 2 DIFFICULTY: Average REFERENCES: 12.4 Elastic Properties of Solids

1. Two stars of masses M and 6M are separated by a distance D. Determine the distance (measured from M) to a point at which the net gravitational force on a third mass would be zero. a. 0.41 D b. 0.33 D c. 0.37 D d. 0.29 D e. 0.14 D ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 13.1 Newton’s Law of Universal Gravitation Exhibit 13-1 Three 5.0-kg masses are located at points in the xy plane as shown in the figure.

Use this exhibit to answer the following question(s).

2. Refer to Exhibit 13-1. What is the magnitude of the resultant force (caused by the other two masses) on the mass at the origin? a. 2.7 × 10−8 N b. 2.1 × 10−8 N c. 1.8 × 10−8 N d. 2.4 × 10−8 N e. 2.9 × 10−8 N ANSWER:

b

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POINTS: 2 DIFFICULTY: Average REFERENCES: 13.1 Newton’s Law of Universal Gravitation 3. Refer to Exhibit 13-1. What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0.40 m, y = 0? a. 2.2 × 10−8 N b. 1.9 × 10−8 N c. 1.4 × 10−8 N d. 1.6 × 10−8 N e. 2.5 × 10−8 N ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 13.1 Newton’s Law of Universal Gravitation 4. Three 5.0-kg masses are located at points in the xy plane, as shown. What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0, y = 0.30 m?

a. 2.6 × 10−8 N b. 2.0 × 10−8 N c. 2.9 × 10−8 N d. 2.3 × 10−8 N e. 2.1 × 10−8 N ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 13.1 Newton’s Law of Universal Gravitation 41

5. Three galaxies, each of mass M = 4.0 × 10 kg, lie in a plane at the corners of an equilateral triangle with sides of 5.0 × 22 10 m length. The magnitude of the force the other two galaxies exert on each galaxy is a. 4.3 × 1027 N. b. 6.4 × 1027 N. c. 7.4 × 1027 N. Copyright Cengage Learning. Powered by Cognero.

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d. 8.6 × 1027 N. e. 4.3 × 1028 N. ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 13.1 Newton’s Law of Universal Gravitation 6. When two solid spheres of the same material and same radius r are in contact, the magnitude of the gravitational force each exerts on the other is directly proportional to a. r. b. r2. c. r3. d. r4. e. r6.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 13.1 Newton’s Law of Universal Gravitation 7

6

7. A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 × 10 m. If the radius of Roton is 5.0 × 10 m, what is the magnitude of the free-fall acceleration on the surface of Roton? a. 31 m/s2 b. 27 m/s2 c. 34 m/s2 d. 40 m/s2 e. 19 m/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 13.2 Free-Fall Acceleration and the Gravitational Force

8. What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth, where R is the radius of the Earth? a. 4.8 m/s2 b. 1.1 m/s2 c. 3.3 m/s2 d. 2.5 m/s2 e. 6.5 m/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 13.2 Free-Fall Acceleration and the Gravitational Force Copyright Cengage Learning. Powered by Cognero.

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6

at sea level and that RE = 6.37 × 10 m, we find that the value of g in

9. Knowing that

at a distance RE

from the surface of the Earth is a. 1.23. b. 2.45. c. 4.90. d. 7.35. e. 9.80.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 13.2 Free-Fall Acceleration and the Gravitational Force 10. Huygens claimed that near the surface of the Earth the velocity downwards of an object released from rest, vy, was directly proportional to the square root of the distance it had fallen,

. This is true if c is equal to

a. . b. . c. g. d.

.

e. 4g.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 13.2 Free-Fall Acceleration and the Gravitational Force 11. Isaac Newton was able to estimate a value for G, the universal gravitational constant, from the following data: the 3 2 radius of the Earth is about 6 400 km, the average density of rocks is about 5.50 g/cm , and g = 9.80 m/s near the surface of the Earth. What value did Newton obtain for G? −11 2 2 ANSWER: 6.65 × 10 N⋅ m /kg POINTS: 2 DIFFICULTY: Average REFERENCES: 13.2 Free-Fall Acceleration and the Gravitational Force 12. At the moment of a total eclipse, the Moon lies along a line from the Earth to the Sun. If your normal weight is 600 N, how much is your weight decreased by the combined pull of the Sun and Moon?

30

MSUN = 2.0 × 10 kg, 22 MMOON = 7.4 × 10 kg, ANSWER: 0.37 N POINTS: 2 DIFFICULTY: Average

8

rS-E = 1.5 × 10 km 5 rM-E = 3.8 × 10 km

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REFERENCES: 13.2 Free-Fall Acceleration and the Gravitational Force 13. When a falling meteor is at a distance above the Earth's surface of 3 times the Earth's radius, what is its acceleration due to the Earth's gravity?

2 ANSWER: 0.613 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 13.2 Free-Fall Acceleration and the Gravitational Force 14. The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 × 6 10 m. What is the mass of planet Nutron? a. 6.2 × 1028 kg b. 5.0 × 1028 kg c. 5.5 × 1028 kg d. 4.3 × 1028 kg e. 3.7 × 1028 kg ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 6

15. A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 × 10 m. What is the magnitude of the gravitational force on the satellite by planet Cruton? a. 63 N b. 58 N c. 68 N d. 73 N e. 50 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 16. A satellite is in a circular orbit about the Earth at an altitude at which air resistance is negligible. Which of the following statements is true? a. There is only one force acting on the satellite. b. There are two forces acting on the satellite, and their resultant is zero. c. There are two forces acting on the satellite, and their resultant is not zero. d. There are three forces acting on the satellite. e. None of the preceding statements are correct.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets Copyright Cengage Learning. Powered by Cognero.

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24

17. What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 × 10 m, mass = 6.0 × 10 a period of 5.0 h? a. 88 N b. 55 N c. 36 N d. 98 N e. 18 N ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 13.4 Kepler's Laws and the Motion of Planets

kg) with

18. Two satellites are placed in geosynchronous orbits, orbits with a period of 24 hours, where each satellite hovers over a spot on the Earth's equator. Satellite B has three times the mass of satellite A. What is the relationship between the magnitudes of the gravitational forces of the Earth on the two satellites? a.

FB = FA. b.

FB =

FA.

c. FB = FA. d. FB = 3FA. e. FB = 9FA. ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 19. A satellite is placed in a geosynchronous orbit. In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the equator. Which statement is true for a satellite in such an orbit? a. There is no gravitational force on the satellite. b. There is no acceleration toward the center of the Earth. c. The satellite is in a state of free fall toward the Earth. d. There is a tangential force that helps the satellite keep up with the rotation of the Earth. e. The force toward the center of the Earth is balanced by a force away from the center of the Earth.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 20. Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have a. the smaller period. b. the greater period. c. the smaller gravitational mass. d. the larger gravitational mass.

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e. the larger universal gravitational constant.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 21. The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

a. its speed is constant. b. its speed is increasing. c. its speed is decreasing. d. its speed is a maximum. e. its speed is a minimum.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 22. The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

a. its speed is constant. b. its speed is increasing. c. its speed is decreasing. d. its speed is a maximum. e. its speed is a minimum.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 23. The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

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a. its speed is constant. b. its speed is increasing. c. its speed is decreasing. d. its speed is a maximum. e. its speed is a minimum.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 24. The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

a. its speed is constant. b. its speed is increasing. c. its speed is decreasing. d. its speed is a maximum. e. its speed is a minimum.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 25. The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

a. its speed is constant. b. its speed is increasing. c. its speed is decreasing. d. its speed is a maximum. e. its speed is a minimum.

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ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 26. The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

a. its speed is decreasing. b. its angular momentum is increasing. c. the gravitational force does no work on the planet. d. all of the above are correct. e. none of the above is correct.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 27. The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a 6 6 24 22 near-Moon satellite? (RE = 6.37 × 10 m; RM = 1.74 × 10 m; ME = 5.98 × 10 kg; MM = 7.36 × 10 kg.) a. 6.03 × 10−3 min. b. 0.713 min. c. 84.3 min. d. 108 min. e. 140 min.

ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 28. An asteroid revolves around the Sun with a perihelion 0.5 AU and an aphelion of 7.5 AU. What is its period of revolution? a. 4 years b. 8 years c. 16 years d. 32 years e. 64 years ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 13.4 Kepler's Laws and the Motion of Planets Copyright Cengage Learning. Powered by Cognero.

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30

29. The planet Venus requires 225 days to orbit the Sun, which has a mass M = 1.99 × 10 kg, in an almost circular trajectory. Calculate the radius of the orbit and the orbital speed of Venus as it circles the Sun. 11 ANSWER: 1.08 × 10 m, 34.9 km/s POINTS: 3 DIFFICULTY: Challenging REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 30. Calculate the Earth's angular momentum in the approximation that treats the Earth's orbit around the Sun as a circle.

30 7 24 (MSun = 1.99 × 10 kg; T = 3.156 × 10 s; ME = 5.98 × 10 kg.)

40 2 ANSWER: 2.67 × 10 kg⋅ m /s POINTS: 3 DIFFICULTY: Challenging REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 31. What is the period of revolution of a planet in circular orbit around a star of 4.0 solar masses if it is at a distance from the star equal to that of the Earth from the Sun? ANSWER: 0.50 year POINTS: 2 DIFFICULTY: Average REFERENCES: 13.4 Kepler's Laws and the Motion of Planets 32. A spaceship of mass m circles a planet (mass = M) in an orbit of radius R. How much energy is required to transfer the spaceship to a circular orbit of radius 3R? a. GmM/(2R) b. GmM/(3R) c. GmM/(4R) d. GmM/(6R) e. 3GmM/(4R) ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 33. A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R). What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible? a. GmM/(4R) b. GmM/R c. GmM/(2R) d. GmM/(3R) e. 2GmM/(5R) ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion Copyright Cengage Learning. Powered by Cognero.

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34. A projectile is launched from the surface of a planet (mass = M, radius = R). What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere. a.

b.

c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 35. An object is released from rest at a distance h above the surface of a planet (mass = M, radius = R < h). With what speed will the object strike the surface of the planet? Disregard any dissipative effects of the atmosphere of the planet. a.

b.

c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 6

36. What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 × 10 m around the Earth?

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24

(Mass of Earth = 6.0 × 10 a. 5.0 × 109 J

kg.)

b. 1.0 × 1010 J c. 1.5 × 1010 J d. 2.0 × 1010 J e. 2.5 × 109 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 37. An object is released from rest when it is a height h above the surface of a planet of mass M and radius R. What is the 6 speed of the object just before striking the surface of the planet? Neglect any air resistance. Let h = 4.0 × 10 m, R = 5.0 × 6 24 10 m, and M = 4.0 × 10 kg. a. 7.8 km/s b. 3.5 km/s c. 5.4 km/s d. 6.9 km/s e. 4.8 km/s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 38. A 50-kg satellite circles the Earth in an orbit with a period of 120 min. What minimum energy is required to change 6 24 the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 × 10 m, mass = 6.0 × 10 kg) a. 2.9 × 108 J b. 3.5 × 108 J c. 4.1 × 108 J d. 4.7 × 108 J e. 5.9 × 108 J ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 23

6

39. Planet Roton has a mass of 4.0 × 10 kg and a radius of 2.0 × 10 m. With what speed should a space probe be 6 launched from the surface of Roton so as to achieve a maximum distance of 3.0 × 10 m from the center of Roton? a. 4.2 km/s b. 3.9 km/s c. 3.0 km/s d. 3.4 km/s e. 6.0 km/s Copyright Cengage Learning. Powered by Cognero.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 23

6

40. Planet Zero has a mass of 5.0 × 10 kg and a radius of 2.0 × 10 m. A space probe is launched vertically from the 6 surface of Zero with an initial speed of 4.0 km/s. What is the speed of the probe when it is 3.0 × 10 m from Zero's center? a. 3.0 km/s b. 2.2 km/s c. 1.6 km/s d. 3.7 km/s e. 5.9 km/s ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 23

41. What is the escape speed from a planet of mass M and radius R if M = 3.2 × 10 a. 5.5 km/s b. 4.2 km/s c. 5.2 km/s d. 4.8 km/s e. 3.7 km/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion

6

kg and R = 2.4 × 10 m?

42. A satellite of mass m circles a planet of mass M and radius R in an orbit at a height 2R above the surface of the planet.

What minimum energy is required to change the orbit to one for which the height of the satellite is 3R above the surface of the planet? a. b. c. d. e.

ANSWER: a POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 23

6

43. Planet Zero has a mass of 4.0 × 10 kg and a radius of 2.0 × 10 m. A 10-kg space probe is launched vertically from 7 the surface of Zero with an initial kinetic energy of 8.0 × 10 J. What maximum distance from the center of Zero is achieved by the probe? a. 3.2 × 106 m b. 4.0 × 106 m c. 6.0 × 106 m d. 5.0 × 106 m e. 2.5 × 106 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 44. Which of the following quantities is conserved for a planet orbiting a star in a circular orbit? Only the planet itself is to be taken as the system; the star is not included. a. Momentum and energy. b. Energy and angular momentum. c. Momentum and angular momentum. d. Momentum, angular momentum and energy. e. None of the above.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion

45. Suppose the gravitational force of the Earth on a body was

. What escape velocity ve would a body

need to escape the gravitational field of the Earth? a. . b. . c. . d. .

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e.

.

ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 46. In an isolated system of two bodies that exert gravitational forces on one another, the quantity (quantities) that remain(s) constant is(are) a. the total energy of the system. b. the total angular momentum of the system. c. the angular positions of the two bodies. d. all of the above. e. only (a) and (b) above.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 47. A satellite revolves around the Earth in a circular orbit with a mechanical energy of energy? a.

J. What is its kinetic

b. c. d. e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion 48. Carla and Jenny are arguing about whether or not it is possible to escape the gravitational field of the Earth. Carla shows Jenny a system where mass m is rE (not the Earth's radius) distant from Earth and rP (not planet P's radius) distant from planet P, the mass being on the line connecting the Earth and planet P. Carla states that the mass m has escaped if FP on m = −FE on m. Jenny disagrees. Which one, if either, is correct, and why? a. Carla, because the total gravitational force on m is zero at that point. b. Carla, because there is no gravitational force from Earth on m at that point. c. Carla, because there is no gravitational force on m from Earth when r > rE. d. Jenny, because there is a gravitational force on m from Earth no matter how great the distance from the Earth. e. Jenny, because the gravitational force from the Earth can only be blocked by a body that is larger than the Earth.

ANSWER: d POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 13.6 Energy Considerations in Planetary and Satellite Motion

2

1. A stonecutter's chisel has an edge area of 0.7 cm . If the chisel is struck with a force of 42 N, what is the pressure exerted on the stone? a. 600 N/m2 b. 30 000 N/m2 c. 300 000 N/m2 d. 600 000 N/m2 e. 6 000 N/m2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.1 Pressure 2. When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine 9 2 5 2 block if the water in there froze? The bulk modulus of ice is 2.0 × 10 N/m , and 1 ATM = 1.01 × 10 N/m . a. 18 ATM b. 360 ATM c. 1 100 ATM d. 1 800 ATM e. 600 ATM ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.1 Pressure 3. All people come very close to being able to float in water. What therefore is the volume (in cubic meters) of a 50-kg woman? a. 0.007 b. 0.035 c. 0.050 d. 0.070 e. 0.085 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 14.1 Pressure 6

5

4. What is the total mass of the Earth's atmosphere? The radius of the Earth is 6.4 × 10 m, and 1 ATM = 1.01 × 10 2 N/m . a. 5.3 × 1016 kg b. 1.1 × 1018 kg c. 5.3 × 1018 kg Copyright Cengage Learning. Powered by Cognero.

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d. 1.1 × 1020 kg e. 5.3 × 109 kg ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 14.1 Pressure 5

2

5. The pressure inside a commercial airliner is maintained at 1 ATM (1.01 × 10 N/m ). What is the outward force exerted on a 1.0 m × 2.0 m cabin door if the outside pressure (at 10 km height) is 0.3 ATM? a. 1.4 × 102 N b. 1.4 × 103 N c. 1.4 × 104 N d. 1.4 × 105 N e. 7.0 × 103 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.1 Pressure 6. Air within the funnel of a large tornado may have a pressure of only 0.2 ATM. What is the approximate outward force 5 2 on a (5 m × 10 m) wall if a tornado suddenly envelops the house? (1 ATM = 1.01 × 10 N/m .) a. 4 × 103 N b. 4 × 104 N c. 4 × 105 N d. 4 × 106 N e. 7 × 105 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.1 Pressure 7. A police crime lab is trying to determine whether someone was murdered or died as a result of an accident. The victim was struck in the temple by a 4.20-kg sculpture that is alleged to have fallen off a bookcase. The sculpture presumably fell 2 a distance of 1.43 m and the corner that struck him had an area of 0.250 cm . If the time for the sculpture to stop was 1.00 2 ms, the pressure on his temple, in N/m , was a. 8.89 × 104. b. 1.65 × 105. c. 1.65 × 106. d. 8.89 × 108. e. 1.65 × 109.

ANSWER: POINTS:

d 3

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DIFFICULTY: Challenging REFERENCES: 14.1 Pressure 8. Find the average density of a red giant star with a mass of 20 × 10 9 150 × 10 m (equal to the Earth's distance from the Sun). a. 1.41 × 10−4 kg/m3

30

kg (approximately 10 solar masses) and a radius of

b. 0.007 kg/m3 c. 1.41 kg/m3 d. 710 kg/m3 e. 1.41 × 10−3 kg/m3 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 14.2 Variation of Pressure with Depth 9. Find the pressure in atmospheres in the water at the base of Dworshak Dam if the water in the reservoir is 200 meters 5 2 deep. (1.01 × 10 N/m = 1 ATM.) a. 20.4 ATM b. 24.7 ATM c. 29.4 ATM d. 194 ATM e. 75 ATM ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 14.2 Variation of Pressure with Depth 10. Some species of whales can dive to depths of one kilometer. What is the total pressure they experience at this depth?

3 5 2 (ρsea = 1 020 kg/m and 1.01 × 10 N/m = 1 ATM.) a. 9.00 ATM b. 90.0 ATM c. 100 ATM d. 111 ATM e. 130 ATM ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 14.2 Variation of Pressure with Depth 11. A hydraulic lift raises a 2 000-kg automobile when a 500-N force is applied to the smaller piston. If the smaller piston 2 has an area of 10 cm , what is the cross-sectional area of the larger piston? a. 40 cm2 b. 80 cm2 c. 196 cm2 Copyright Cengage Learning. Powered by Cognero.

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d. 392 cm2 e. 160 cm2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.2 Variation of Pressure with Depth 12. What is the net force inward acting on a spherical bathysphere of diameter 2.00 m at an ocean depth of 1 000 m? (The 3 3 pressure inside the bathysphere is, hopefully, 1 ATM.) ρ(sea water) = 1.02 × 10 kg/m . a. 1.26 × 104 N b. 1.26 × 106 N c. 1.26 × 108 N d. 1.26 × 1010 N e. 1.26 × 102 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 14.2 Variation of Pressure with Depth 13. People can snorkel down to a depth of roughly one meter. This means that the additional pressure on the air in their lungs is roughly a. 9 800 N. b. 9 800 Pa. c. 9 800 ATM. d. 19 600 N. e. 19 600 N/m2.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 14.2 Variation of Pressure with Depth 14. The figure below shows a container filled with water to the height shown. When we compare the pressure at A to the pressure at B, we find that

a. .

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b. . c. pA = pB. d. pA = 2pB. e. pA = 4pB. ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 14.2 Variation of Pressure with Depth 15. Melanie says that when a diver enters an underwater cave of height h, the pressure on her is no greater than ρWgh. Rosalind says that if the bottom of the cave is a distance H below the water surface, the pressure on the soles of the diver's feet can reach ρWgH. Which one, if either, is correct? (The density of water is ρW.) a. Melanie, because the roof of the cave absorbs the water pressure from above. b. Melanie, because only the fluid directly above any volume of the fluid can contribute to the pressure on that volume. c. Rosalind, because a fluid exerts equal pressure in all directions at a given depth. d. Rosalind, because the pressure also depends on the density, ρc, of the material above the cave roof, so that p = ρcg(H − h) + ρWgh. e. Melanie, because the pressure equals p = ρWgH − ρcg(H − h).

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 14.2 Variation of Pressure with Depth 16. A man has built a bunker for his use in emergencies. Its dimensions are shown below. When it floods to ground level during a tropical storm, the gauge pressure at point A, in Pa, is

a. 3.92 × 105. b. 4.90 × 105. c. 5.39 × 105. d. 5.88 × 105. e. 6.89 × 105.

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ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.3 Pressure Measurements Exhibit 14-1 A man has built a bunker for his use in emergencies. Its dimensions are shown below. When it floods to ground level during a tropical storm, air is trapped above the dashed line in the bunker.

Use this exhibit to answer the following question(s).

17. Refer to Exhibit 14-1. The gauge pressure at point A, in Pa, is a. 3.92 × 105. b. 4.90 × 105. c. 5.39 × 105. d. 5.88 × 105. e. 6.89 × 105.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.3 Pressure Measurements 18. Refer to Exhibit 14-1. The absolute pressure at point A, in Pa, is a. 3.92 × 105. b. 4.90 × 105. c. 5.39 × 105. d. 5.88 × 105. e. 6.89 × 105.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 14.3 Pressure Measurements 5

2

19. The four tires of an automobile are inflated to a gauge pressure of 2.0 × 10 N/m (29 PSI). Each of the four tires has Copyright Cengage Learning. Powered by Cognero.

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2

an area of 0.024 m that is in contact with the ground. Determine the weight of the auto.

ANSWER: 19 200 N POINTS: 2 DIFFICULTY: Average REFERENCES: 14.3 Pressure Measurements 20. Find the average density of a white dwarf star if it has a mass equal to that of the Sun (2.0 × 10 6 equal to that of the Earth (6.4 × 10 m). a. 9.0 × 106 kg/m3

30

kg) and a radius

b. 1.8 × 107 kg/m3 c. 1.8 × 109 kg/m3 d. 3.6 × 1010 kg/m3 e. 9.0 × 107 kg/m3 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 3

21. A blimp is filled with 200 m of helium. How much mass can the balloon lift? The density of helium is one-seventh that of air, and the density of air is 1/800 that of water. Consider the mass of the balloon to be negligible. a. 115 kg b. 214 kg c. 315 kg d. 415 kg e. 37 kg ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 3

3

3

22. To the nearest percent, what fraction of an iceberg is submerged? (ρice = 917 kg/m , ρsea = 1.03 × 10 kg/m .) a. 95% b. 93% c. 91% d. 89% e. 77% ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 8

23. A supertanker filled with oil has a total mass of 6.1 × 10 kg. If the dimensions of the ship are those of a rectangular box 300 meters long, 80 meters wide, and 40 meters high, determine how far the bottom of the ship is below sea level.

3 (ρsea = 1 020 kg/m .)

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a. 10 m b. 15 m c. 20 m d. 25 m e. 30 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 24. Determine the minimum area of a flat ice floe 1.0 meter thick if it is to support a 2 000-kg car above seawater. (ρice = 3 3 920 kg/m , ρsea = 1 020 kg/m .) a. 20 m2 b. 40 m2 c. 60 m2 d. 80 m2 e. 100 m2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 25. A thin, rectangular piece of wood floats in water. You slowly pour oil with a density equal to that of the wood on the surface of the water until the height of the oil above the water is twice the height of the piece of wood. Which statement is correct? a. The wood floats on top of the oil, so it sticks up in the air. b. The wood does not change its position c. The wood sinks below the surface of the water. d. The wood is half in the water and half in the oil. e. The wood floats in the oil just above the water.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 26. Two identical fish, both at sea level, float in two identical aquariums with identical quantities of water. Fish A is in Alaska, so it weighs more than fish B at the equator, since g is larger at sea level in Alaska. Which statement is correct? a. A comparison is impossible unless they are both floating at the same level. b. Fish A displaces a greater quantity of water than fish B. c. Fish B displaces a greater quantity of water than fish A. d. They both displace the same quantity of water. e. Fish A has a smaller acceleration than Fish B when equal horizontal forces are applied to each, because Fish A weighs more.

ANSWER: d POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 27. A waiter in a restaurant fills a pitcher full of water and ice so that water would spill out if any more were added. As the ice starts to melt a. the water level in the pitcher falls. b. the water level in the pitcher remains the same. c. water starts to flow out the spout of the pitcher. d. the pressure on the bottom of the pitcher decreases. e. the pressure on the bottom of the pitcher increases.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 28. A wood block is placed on top of the ice in a large bowl half full of ice. The bowl is then filled to the brim with water, with the wood block riding on top of the ice. As the ice melts, a. the density of the water decreases. b. the water level falls below the rim. c. the water level rises and water spills out of the bowl. d. the water level does not change. e. the wood block descends, causing water to spill out of the bowl.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle −4

3

−4

3

29. An empty spice bottle has an inner volume of 1.31 × 10 m . It has a mass of 112 g when filled with air, and it −4 3 displaces 1.63 × 10 m of water when fully submerged. What fraction of the total volume of the bottle will be beneath the surface when it is placed in a tank of water? a. 0.69 b. 0.81 c. 0.85 d. 1.00 e. 1.46 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 30. An empty spice bottle has an inner volume of 1.31 × 10 m . It has a mass of 112 g when filled with air, and it −4 3 3 3 displaces 1.63 × 10 m of water when fully submerged. What volume of mercury (ρHg = 13.6 × 10 kg/m ) must be added to the empty bottle so that it will just submerge? a. 3.75 cm3 b. 12.0 cm3 Copyright Cengage Learning. Powered by Cognero.

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c. 101 cm3 d. 147 cm3 e. 237 cm3 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 31. The water level in identical bowls, A and B, is exactly the same. A contains only water; B contains floating ice as well as water. When we weigh the bowls, we find that a. WA < WB. b. WA = WB. c. WA > WB. d.

WB > WA if the volume of the ice cubes is greater than

the volume of the water.

e. WB > WA if the volume of the ice cubes is greater than 9 times the volume of the water.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 3

3

3

3

32. A cube of water ice (ρ = 0.917 × 10 kg/m ) is placed in mercury (ρ = 13.6 × 10 kg/m ), which is liquid at 0° Celsius. If we ignore any possible melting of the ice cube and problems with the surface tension of mercury, the fraction of the ice cube that floats above the surface of the mercury is a. 0.067 4. b. 0.073 5. c. 0.926. d. 0.933. e. 1.00.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 3

33. An iron block of density ρFe and of volume l is immersed in a fluid of density ρfluid. The block hangs from a scale which reads W as the weight. The top of the block is a height h below the surface of the fluid. The correct equation for the reading of the scale is a. W = (ρFe − ρfluid)ghl2. b. W = (ρfluid − ρFe)gl3. c. W = (ρFe − ρfluid)gl3. d. W = (ρFe + ρfluid)ghl2. e. W = (ρFe + ρfluid)gl3.

ANSWER:

c

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POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 34. A boat is floating in a small pond. The boat then sinks so that it is completely submerged. What happens to the level of the pond? a. It increases. b. It decreases. c. It stays the same. d. In some cases it would decrease, in others it would stay the same. e. In some cases it would increase, in others it would stay the same.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 35. A boat is floating in a small pond. The boat then sinks resting on the bottom, but the pond is so shallow that part of the boat is not submerged. What happens to the level of the pond? a. It increases. b. It decreases. c. It stays the same. d. In some cases it would decrease, in others it would stay the same. e. In some cases it would increase, in others it would stay the same.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 36. A vertical pipe, closed at the bottom end, is filled to a depth of 1.00 m with water and then an amount of oil of density is added to make the total depth 2.00 m. The oil and water don’t mix with the oil floating on top of the water. What is the increase in pressure at the bottom end of the pipe as a result of adding the fluids?

ANSWER: POINTS: 2 DIFFICULTY: Average REFERENCES: 14.4 Buoyant Forces and Archimedes’s Principle 37. Water is flowing at 4.0 m/s in a circular pipe. If the diameter of the pipe decreases to 1/2 its former value, what is the velocity of the water downstream? a. 1.0 m/s b. 2.0 m/s c. 8.0 m/s d. 16 m/s e. 4.0 m/s ANSWER: d POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 14.5 Fluid Dynamics 38. How much power is theoretically available from a mass flow of 1 000 kg/s of water when it falls a vertical distance of 100 meters? a. 980 kW b. 98 kW c. 4 900 W d. 980 W e. 9 600 W ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 14.5 Fluid Dynamics 39. Water is sent from a firehose at 30.0 m/s at an angle of 30.0° above the horizontal. What is the maximum height reached by the water? a. 7.50 m b. 11.5 m c. 15.0 m d. 19.0 m e. 30.0 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 14.5 Fluid Dynamics 40. A hose has been clamped so that the area at the clamp is only one quarter the area of the rest of the hose. When we ignore the viscosity of water, the ratio of the volume of water delivered per unit time when the clamp is on to the volume of water delivered per unit time without the clamp is a. . b. . c. . d. . e. 1.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 14.5 Fluid Dynamics 41. A hose has been clamped so that the area at the clamp is only one quarter the area of the rest of the hose. When we ignore the viscosity of water, the ratio of the speed of the water through the clamped area to the speed of the water when it leaves the hose is Copyright Cengage Learning. Powered by Cognero.

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a. . b. . c. 1. d. 2 e. 4.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 14.5 Fluid Dynamics 42. A natural gas pipeline with a diameter 0.250 m delivers 1.55 cubic meters of gas per second. What is the flow speed of the gas in the pipeline?

ANSWER: 31.6 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 14.5 Fluid Dynamics 43. A hole is punched in a full milk carton, 10 cm below the top. What is the initial velocity of outflow? a. 1.4 m/s b. 2.0 m/s c. 2.8 m/s d. 3.9 m/s e. 4.2 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 14.6 Bernoulli’s Equation 44. The water level in a reservoir is maintained at a constant level. What is the exit velocity in an outlet pipe 3.0 m below the water surface? a. 2.4 m/s b. 3.0 m/s c. 5.4 m/s d. 7.7 m/s e. 49 m/s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.6 Bernoulli’s Equation 5

45. Water pressurized to 3.5 × 10 Pa is flowing at 5.0 m/s in a horizontal pipe which contracts to 1/3 its former area.

What are the pressure and velocity of the water after the contraction? a. 2.5 × 105 Pa, 15 m/s Copyright Cengage Learning. Powered by Cognero.

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b. 3.0 × 105 Pa, 10 m/s c. 3.0 × 105 Pa, 15 m/s d. 4.5 × 105 Pa, 1.5 m/s e. 5.5 × 105 Pa, 1.5 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 14.6 Bernoulli’s Equation 46. A fountain sends water to a height of 100 meters. What must be the pressurization (above atmospheric) of the water 5 2 system? 1 ATM = 1.01 × 10 N/m . a. 1.0 ATM b. 4.2 ATM c. 7.2 ATM d. 9.7 ATM e. 8.2 ATM ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.6 Bernoulli’s Equation 47. A venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 m/s in the 2.0-cm section? (ρ = 1.2 3 kg/m .) a. 70 Pa b. 85 Pa c. 100 Pa d. 120 Pa e. 81 Pa ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 14.6 Bernoulli’s Equation 48. A wind of velocity 10 m/s is blowing through a wind generator with blade radius 5.00 meters. What is the maximum 3 power output if 30.0% of the wind's energy can be extracted? ρair = 1.25 kg/m . a. 7.20 kW b. 14.7 kW c. 21.3 kW d. 29.4 kW e. 39.6 kW ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 14.6 Bernoulli’s Equation Copyright Cengage Learning. Powered by Cognero.

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49. A large water storage container is filled to a depth of 3.0 m. The volume above the water is filled with air. In order to 5 2 pump the water from the container, the air pressure in the container is increased by 3.0 10 N/m . What happens to the pressure in the water at a depth of 1.0 m when the air pressure is increased? a. Nothing, it is still at a depth of 1.0 m and the pressure in the water depends only on the depth. b. It increases by 1.0 105 N/m2, since it is at 1/3 the depth of the water. c. It increases by 2.0 105 N/m2, since it is at 2/3 the depth from the bottom of the container. d. It increases by 3.0 105 N/m2. e. It increases by 3.0 105 N/m2 + 9.8 103 N/m2 since it is 1.0 m deep in the water.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 14.6 Bernoulli’s Equation 2

50. One hundred milliliters of water is poured into a U-tube that has a cross-sectional area of 1 cm . Then 100 milliliters of oil, with a density 80% that of water, is poured down one side of the U-tube so that the oil floats on the water. Find the difference in height of the liquid surfaces on the two sides of the U-tube.

ANSWER: 20 cm POINTS: 2 DIFFICULTY: Average REFERENCES: 14.6 Bernoulli’s Equation 51. A fountain sends a stream of water 20.0 m up into the air. If the base of the stream is 10.0 cm in diameter, what power is required to send the water to this height?

ANSWER: 30.5 kW POINTS: 2 DIFFICULTY: Average REFERENCES: 14.6 Bernoulli’s Equation 4

52. In a wind tunnel the pressure on the top surface of a model airplane wing is 8.8 × 10 N/m and the pressure on the 4 2 2 bottom surface is 9.0 × 10 N/m . If the area of the top and bottom surfaces of each wing is 2.0 m , what is the total lift on the model airplane? a. 2.0 × 103 N b. 8.0 × 103 N c. 1.6 × 104 N d. 3.6 × 104 N e. 1.0 × 103 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 14.8 Other Applications of Fluid Dynamics 2

53. A Boeing 737 airliner has a mass of 20 000 kg and the total area of both wings (top or bottom) is 100 m . What is the pressure difference between the top and bottom surface of each wing when the airplane is in flight at a constant altitude?

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a. 1 960 N/m2 b. 3 920 N/m2 c. 7 840 N/m2 d. 4 560 N/m2 e. 3 070 N/m2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 14.8 Other Applications of Fluid Dynamics 54. The siphon shown is used to transfer liquid from a higher level to a lower level. If the fluid is drawn up and is continuous through the tube, determine the velocity of flow of gasoline if the vertical distance from the liquid surface to the outlet is 1.0 m.

a. 1.1 m/s b. 2.2 m/s c. 4.4 m/s d. 9.8 m/s e. 6.5 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 14.8 Other Applications of Fluid Dynamics

1. A body of mass 5.0 kg is suspended by a spring which stretches 10 cm when the mass is attached. It is then displaced downward an additional 5.0 cm and released. Its position as a function of time is approximately what? a. y = −0.10 sin 9.9t b. y = 0.10 cos 9.9t c. y = −0.10 cos (9.9t + .1) d. y = 0.10 sin (9.9t + 5) e. y = −0.05 cos 9.9t ANSWER: e Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 15.1 Motion of an Object Attached to a Spring 2. The mass in the figure below slides on a frictionless surface. When the mass is pulled out, spring 1 is stretched a distance x1 from its equilibrium position and spring 2 is stretched a distance x2. The spring constants are k1 and k2 respectively. The force pulling back on the mass is:

a. −k2x1. b. −k2x2. c. −(k1x1 + k2x2). d. . e. .

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 15.1 Motion of an Object Attached to a Spring 3. An archer pulls her bow string back 0.40 m by exerting a force that increases uniformly from zero to 240 N. What is the equivalent spring constant of the bow, and how much work is done in pulling the bow?

ANSWER: 600 N/m, 48 J POINTS: 2 DIFFICULTY: Average REFERENCES: 15.1 Motion of an Object Attached to a Spring 4. A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the 2 equation x = 5.0 cos (πt). The magnitude of the acceleration (in m/s ) of the body at t = 1.0 s is approximately what? a. 3.5 b. 49 c. 14 d. 43 e. 4.3 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 5. A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the Copyright Cengage Learning. Powered by Cognero.

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equation x = 5 sin (πt + π/3). The phase (in rad) of the motion at t = 2 s is what? a. 7π/3 b. π/3 c. π d. 5π/3 e. 2π ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 6. A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5.0 sin (πt + π/3). The velocity (in m/s) of the body at t = 1.0 s is what? a. +7.9 b. −7.9 c. −14 d. +14 e. −5.0 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 7. A mass m = 2.0 kg is attached to a spring having a force constant k = 290 N/m as in the figure. The mass is displaced from its equilibrium position and released. Its frequency of oscillation (in Hz) is approximately what?

a. 12 b. 0.50 c. 0.010 d. 1.9 e. 0.080 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 8. The mass in the figure slides on a frictionless surface. If m = 2 kg, k1 = 800 N/m, and k2 = 500 N/m, the frequency of oscillation (in Hz) is approximately what?

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a. 6 b. 2 c. 4 d. 8 e. 10 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 3

9. A horizontal plank (m = 2.0 kg, L = 1.0 m) is pivoted at one end. A spring (k = 1.0 × 10 N/m) is attached at the other end, as shown in the figure. Find the angular frequency (in rad/s) for small oscillations.

a. 39 b. 44 c. 55 d. 66 e. 25 ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 10. A weight of mass m is at rest at O when suspended from a spring, as shown. When it is pulled down and released, it oscillates between positions A and B. Which statement about the system consisting of the spring and the mass is correct?

a. The gravitational potential energy of the system is greatest at A. b. The elastic potential energy of the system is greatest at O. Copyright Cengage Learning. Powered by Cognero.

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c. The rate of change of momentum has its greatest magnitude at A and B. d. The rate of change of gravitational potential energy is smallest at O. e. The rate of change of gravitational potential energy has its greatest magnitude at A and B. ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion Exhibit 15-1 A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. A point or points at which the object has positive velocity and zero acceleration is(are)

Use this exhibit to answer the following question(s).

11. Refer to Exhibit 15-1. A point or points at which the object has positive velocity and zero acceleration is (are) what? a. B b. C c. D d. B and D e. A and E ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 12. Refer to Exhibit 15-1. The point at which the object has negative velocity and zero acceleration is what? a. A b. B c. C d. D e. E ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 13. Refer to Exhibit 15-1. The point at which the object has zero velocity and positive acceleration is what? a. A Copyright Cengage Learning. Powered by Cognero.

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b. B c. C d. D e. E ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 14. Refer to Exhibit 15-1. The point at which the object has zero velocity and negative acceleration is what? a. A b. B c. C d. D e. E ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 15. In an inertia balance, a body supported against gravity executes simple harmonic oscillations in a horizontal plane under the action of a set of springs. If a 1.00-kg body vibrates at 1.00 Hz, a 2.00-kg body will vibrate at a. 0.500 Hz. b. 0.707 Hz. c. 1.00 Hz. d. 1.41 Hz. e. 2.00 Hz. ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 16. Suppose it were possible to drill a frictionless cylindrical channel along a diameter of the Earth from one side of the Earth to another. A body dropped into such a channel will only feel the gravitational pull of mass within a sphere of radius 3 3 equal to the distance of the mass from the center of the Earth. The density of the Earth is 5.52 × 10 kg/m and G = 6.67 × −11 2 2 10 N⋅ m /kg . The mass will oscillate with a period of a. 84.4 min. b. 169 min. c. 24.0 h. d. 1 130 h. e. 27.2 d.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion Copyright Cengage Learning. Powered by Cognero.

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17. Ellen says that whenever the acceleration is directly proportional to the displacement of an object from its equilibrium position, the motion of the object is simple harmonic motion. Mary says this is true only if the acceleration is opposite in direction to the displacement. Which one, if either, is correct? a. Ellen, because ω2 is directly proportional to the constant multiplying the displacement and to the mass. b. Ellen, because ω2 is directly proportional to the mass. c. Mary, because ω2 is directly proportional to the constant multiplying the displacement and to the mass. d. Mary, because ω2 is directly proportional to the mass. e. Mary, because the second derivative of an oscillatory function like sin(ωt) or cos(ωt) is always proportional to the negative of the original function.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 18. John says that the value of the function cos[ω(t + T) + ϕ], obtained one period T after time t, is greater than cos(ωt + ϕ) by 2π. Larry says that it is greater by the addition of 1.00 to cos(ωt + ϕ). Which one, if either, is correct? a. John, because ωT = 2π. b. John, because ωT = 1 radian. c. Larry, because ωT = 2π. d. Larry, because ωT = 1 radian. e. Neither, because cos(θ + 2π) = cosθ.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 19. The motion of a piston in an auto engine is simple harmonic. If the piston travels back and forth over a distance of 10 cm, and the piston has a mass of 1.5 kg, what is the maximum speed of the piston and the maximum force acting on the piston when the engine is running at 4 200 rpm?

ANSWER: 22 m/s, 14 500 N POINTS: 2 DIFFICULTY: Average REFERENCES: 15.2 Analysis Model: Particle in Simple Harmonic Motion 20. The motion of a particle connected to a spring is described by x = 10 sin (πt). At what time (in s) is the potential energy equal to the kinetic energy? a. 0 b. 0.25 c. 0.50 d. 0.79 e. 1.0 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 15.3 Energy of the Simple Harmonic Oscillator Copyright Cengage Learning. Powered by Cognero.

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21. The amplitude of a system moving with simple harmonic motion is doubled. The total energy will then be what? a. 4 times as large b. 3 times as large c. 2 times as large d. the same as it was e. half as much ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.3 Energy of the Simple Harmonic Oscillator 22. To double the total energy of a mass oscillating at the end of a spring with amplitude A, we need to a. increase the angular frequency by . b. increase the amplitude by . c. increase the amplitude by 2. d. increase the angular frequency by 2. e. increase the amplitude by 4 and decrease the angular frequency by .

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.3 Energy of the Simple Harmonic Oscillator 23. Simple harmonic oscillations can be modeled by the projection of circular motion at constant angular velocity onto the diameter of a circle. When this is done, the analog along the diameter of the acceleration of the particle executing simple harmonic motion is a. the displacement from the center of the diameter of the projection of the position of the particle on the circle. b. the projection along the diameter of the velocity of the particle on the circle. c. the projection along the diameter of tangential acceleration of the particle on the circle. d. the projection along the diameter of centripetal acceleration of the particle on the circle. e. meaningful only when the particle moving in the circle also has a non-zero tangential acceleration.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.4 Comparing Simple Harmonic Motion with Uniform Circular Motion 24. Two circus clowns (each having a mass of 50 kg) swing on two flying trapezes (negligible mass, length 25 m) shown in the figure. At the peak of the swing, one grabs the other, and the two swing back to one platform. The time for the forward and return motion is what?

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a. 10 s b. 50 s c. 15 s d. 20 s e. 25 s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 15.5 The Pendulum 25. A uniform rod (mass m = 1.0 kg and length L = 2.0 m) pivoted at one end oscillates in a vertical plane as shown below. The period of oscillation (in s) is approximately what?

a. 4.0 b. 1.6 c. 3.2 d. 2.3 e. 2.0 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 15.5 The Pendulum 26. The figure shows a uniform rod (length L = 1.0 m, mass = 2.0 kg) suspended from a pivot a distance d = 0.25 m above its center of mass. The angular frequency (in rad/s) for small oscillations is approximately what?

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a. 1.0 b. 2.5 c. 1.5 d. 4.1 e. 3.5 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 15.5 The Pendulum 27. In the figure below, a disk (radius R = 1.0 m, mass = 2.0 kg) is suspended from a pivot a distance d = 0.25 m above its center of mass. For a circular disk,

. The angular frequency (in rad/s) for small oscillations is

approximately what?

a. 4.2 b. 2.1 c. 1.5 d. 1.0 e. 3.8 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 15.5 The Pendulum 28. In the figure below, a hoop (radius R = 1.0 m, mass = 2.0 kg) having four spokes of negligible mass is suspended from a pivot a distance d = .25 m above its center of mass. The angular frequency (in rad/s) for small oscillations is approximately what?

a. 4.0 Copyright Cengage Learning. Powered by Cognero.

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b. 2.5 c. 1.5 d. 1.0 e. 0.5 ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 15.5 The Pendulum 29. A torsional pendulum consists of a solid disk (mass = 2.0 kg, radius = 1.0 m) suspended by a wire attached to a rigid support. The body oscillates about the support wire. If the torsion constant is 16 N⋅ m/rad. What is the angular frequency (in rad/s)?

a. 2 b. 4 c. 6 d. 8 e. 7 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 15.5 The Pendulum 30. A hoop, a solid cylinder, and a solid sphere all have the same mass m and the same radius R. Each is mounted to oscillate about an axis a distance 0.5R from the center. The axis is perpendicular to the circular plane of the hoop and the cylinder and to an equatorial plane of the sphere as shown below. Which is the correct ranking in order of increasing angular frequency ω?

a. hoop, cylinder, sphere b. cylinder, sphere, hoop c. sphere, cylinder, hoop d. hoop, sphere, cylinder e. sphere, hoop, cylinder ANSWER: a POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 15.5 The Pendulum 31. Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles θ1, θ2, and θ3, respectively, and released. The approximation sin θ = θ holds for all three angles, with θ3 > θ2 > θ1. How do the angular frequencies of the three pendulums compare? a. ω3 > ω2 > ω1 b. Need to know amplitudes to answer this question. c.

Need to know to answer this question. d. ω1 > ω2 > ω3 e. ω1 = ω2 = ω3 ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.5 The Pendulum 32. An object of mass m is attached to string of length L. When it is released from point A, the object oscillates between points A and B. Which statement about the system consisting of the pendulum and the Earth is correct?

a. The gravitational potential energy of the system is greatest at A and B. b. The kinetic energy of mass m is greatest at point O. c. The greatest rate of change of momentum occurs at A and B. d. All of the above are correct. e. Only (a) and (b) above are correct.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.5 The Pendulum

33. At sea level, at a latitude where

, a pendulum that takes 2.00 s for a complete swing back and forth has 2

a length of 0.993 m. What is the value of g in m/s at a location where the length of such a pendulum is 0.970 m? a. 0.098 3 b. 3.05 c. 9.57 d. 10.0 e. 38.3 ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 15.5 The Pendulum 34. A 2.00 m-long 6.00-kg ladder pivoted at the top hangs down from a platform at the circus. A 42.0-kg trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the system's natural frequency. The −1 angular frequency (in s ) of the system of ladder and woman is a. 1.01. b. 3.07. c. 4.03. d. 8.05. e. 16.2.

ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 15.5 The Pendulum 35. Which of the following combinations of variables results in the greatest period for a pendulum? a. length = L, mass = M, and maximum angular displacement = 3 degrees b. length = 2L, mass = M/2, and maximum angular displacement = 1 degree c. length = 1.5L, mass = 2M, and maximum angular displacement = 2 degrees d. length = L, mass = M, and maximum angular displacement = degrees e. length = L, mass = 4M, and maximum angular displacement = 4 degrees ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.5 The Pendulum 36. When a damping force is applied to a simple harmonic oscillator which has angular frequency ω0 in the absence of damping, the new angular frequency ω is such that a. ω < ω0. b. ω = ω0. c. ω > ω0. d. ωT < ω0T0. e. ωT > ω0T0.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.6 Damped Oscillations 37. When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of damping, the new period T is such that a. T < T0. b. T = T0. c. T > T0.

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d. ωT < ω0T0. e. ωT > ω0T0.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 15.6 Damped Oscillations 38. A damped oscillator is released from rest with an initial displacement of 10.00 cm. At the end of the first complete oscillation, the displacement reaches 9.05 cm. When 4 more oscillations are completed, what is the displacement reached? a. 7.41 cm b. 6.71 cm c. 6.07 cm d. 5.49 cm e. 5.25 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 15.6 Damped Oscillations 39. The oscillation of the 2.0-kg mass on a spring is described by x = 3.0 cos(4.0t + 0.80), where x is in centimeters and t is in seconds. What is the force constant of the spring? a. 4.0 N/m b. 0.80 N/m c. 16 N/m d. 32 N/m e. 2.0 N/m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 15.7 Forced Oscillations

1. An earthquake emits both S-waves and P-waves, which travel at different speeds through the Earth. A P-wave travels at 9 000 m/s and an S-wave travels at 5 000 m/s. If P-waves are received at a seismic station 1.00 minute before an S-wave arrives, how far away is the earthquake center? a. 88.9 km b. 1 200 km c. 675 km d. 240 km e. 480 km ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.1 Propagation of a Disturbance 2. A student attaches a length of nylon fishing line to a fence post. She stretches it out and shakes the end of the rope in Copyright Cengage Learning. Powered by Cognero.

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her hand back and forth to produce waves on the line. The most efficient way for her to increase the wavelength is to a. increase the tension on the hose and shake the end more times per second. b. decrease the tension on the hose and shake the end more times per second. c. increase the tension on the hose and shake the end fewer times per second. d. decrease the tension on the hose and shake the end fewer times per second. e. keep the tension and frequency the same but increase the length of the hose.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.1 Propagation of a Disturbance 3. Ariel claims that a pulse is described by the equation

where x and y are measured in cm and t in s. Miranda says that it is not possible to represent a pulse with this function because a wave must be a function of x + vt or x − vt. Which one, if either, is correct, and why? a. Ariel, because x2 – 6.0xt + 9t2 = (x – 3.0t)2. b. Ariel, because a pulse is not an infinite wave. c. Miranda, because (x – 3.0t)2 is the same as (3.0t – x)2. d. Miranda, because a pulse is not an infinite wave. e.

Miranda, because

is infinite when x = 0.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.1 Propagation of a Disturbance 4. You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 4 cm wide but 7 mm high. You must move your hand up and down once, a. the same distance up as before, but take a shorter time. b. the same distance up as before, but take a longer time. c. a smaller distance up, but take a shorter time. d. a greater distance up, but take a longer time. e. a greater distance up, but take the same time.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.1 Propagation of a Disturbance 5. You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide but still 5 mm high. You must move your hand up and down once, Copyright Cengage Learning. Powered by Cognero.

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a. the same distance up as before, but take a shorter time. b. the same distance up as before, but take a longer time. c. a smaller distance up, but take a shorter time. d. a greater distance up, but take a longer time. e. a greater distance up, but take the same time.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.1 Propagation of a Disturbance 6. You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide and 7 mm high. You must move your hand up and down once, a. the same distance up as before, but take a shorter time. b. the same distance up as before, but take a longer time. c. a smaller distance up, but take a shorter time. d. a greater distance up, but take a longer time. e. a greater distance up, but take the same time.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.1 Propagation of a Disturbance 7. Earthquake waves are classified as P waves and S waves. Which of the following statements is true about these waves? a. The P wave is transverse as is the S wave. b. The P wave is longitudinal as is the S wave. c. The P wave is transverse and the S wave is longitudinal. d. The P wave is longitudinal and the S wave is transverse. e. Both the P and S waves are mixtures of longitudinal and transverse waves.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.1 Propagation of a Disturbance 8. A pulse is described by

in SI units. What is the velocity of the pulse?

a. 3 m/s in the +x direction b. 2 m/s in the −x direction c. 2 m/s in the +x direction d. 4 m/s in the −x direction e. 4 m/s in the +x direction ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.1 Propagation of a Disturbance 9. A wave generated in a medium is a longitudinal wave when Copyright Cengage Learning. Powered by Cognero.

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a. there is a net transport of matter by the wave. b. the molecules of the medium are unable to exert forces on each other. c. molecular displacements are parallel to the wave velocity. d. molecular displacements are perpendicular to the wave velocity. e. the density of the medium is less than the density of water.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.1 Propagation of a Disturbance 10. Transverse waves are traveling on a 1.00-m-long piano string at 500 m/s. If the points of zero vibration occur at onehalf wavelength (where the string is fastened at both ends), find the frequency of vibration. a. 250 Hz b. 500 Hz c. 1 000 Hz d. 2 000 Hz e. 2 500 Hz ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 11. The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.00-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire? a. 0.025 kg b. 0.049 kg c. 0.051 kg d. 0.081 kg e. 0.037 kg ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 12. If y = 0.02 sin (30x − 400t) (SI units), the frequency of the wave is what? a. 30 Hz b. 15/π Hz c. 200/π Hz d. 400 Hz e. 800π Hz ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 13. If y = 0.02 sin (30x − 400t) (SI units), the wavelength of the wave is what?

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a. π/15 m b. 15/π m c. 60π m d. 4.2 m e. 30 m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 14. If y = 0.02 sin (30x − 400t) (SI units), the velocity of the wave is what? a. 3/40 m/s b. 40/3 m/s c. 60π/400 m/s d. 400/60π m/s e. 400 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 15. If y = 0.02 sin (30x − 400t) (SI units), the angular frequency of the wave is what? a. 30 rad/s b. 30/2π rad/s c. 400/2π rad/s d. 400 rad/s e. 40/3 rad/s ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.2 Analysis Model: Traveling Wave 16. If y = 0.02 sin (30x − 400t) (SI units), the wave number is what? a. 30 rad/m b. 30/2π rad/m c. 400/2π rad/m d. 400 rad/m e. 60π rad/m ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.2 Analysis Model: Traveling Wave 17. Write the equation of a wave, traveling along the +x axis with an amplitude of 0.02 m, a frequency of 440 Hz, and a speed of 330 m/s. a. y = 0.02 sin [880π(x/330 − t)] Copyright Cengage Learning. Powered by Cognero.

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b. y = 0.02 cos [880π x/330 − 440t] c. y = 0.02 sin [880π(x/330 + t)] d. y = 0.02 sin [2π(x/330 + 440t)] e. y = 0.02 cos [2π(x/330 + 440t)] ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave

18. For the wave described by

, determine the first positive x coordinate

where y is a maximum when t = 0. a. 16 m b. 8 m c. 4 m d. 2 m e. 13 m ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave

19. For the wave described by

, determine the x coordinate of the second

maximum when t = 0. a. 20 m b. 18 m c. 24 m d. 28 m e. 16 m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 20. For the wave described by y = 0.02 sin (kx) at t = 0 s, the first maximum at a positive x coordinate occurs where x = 4 m. Where on the positive x axis does the second maximum occur? a. 20 m b. 18 m c. 24 m d. 28 m e. 16 m ANSWER: a POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 16.2 Analysis Model: Traveling Wave

21. For the transverse wave described by

, determine the maximum

transverse speed of the particles of the medium. a. 0.192 m/s b. 0.6π m/s c. 9.6 m/s d. 4 m/s e. 2 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 22. Find the period of a wave of 100-m wavelength in deep water where

.

a. 5.0 s b. 8.0 s c. 12.5 s d. 15 s e. 0.125 s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave Exhibit 16-1 The figure below shows a sine wave at one point of a string as a function of time.

Use the exhibit to answer the following question(s).

23. Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and the frequency are doubled?

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a.

b.

c.

d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.2 Analysis Model: Traveling Wave 24. Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and frequency are each reduced in half? a. b.

c.

d.

e.

ANSWER:

e

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.2 Analysis Model: Traveling Wave Exhibit 16-2 The figure below shows a sine wave on a string at one instant of time.

Use this exhibit to answer the following question(s).

25. Refer to Exhibit 16-2. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled? a. b.

c.

d.

e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.2 Analysis Model: Traveling Wave 26. Refer to Exhibit 16-2. Which of the graphs below shows a wave where the wavelength is twice as large?

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a.

b.

c.

d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.2 Analysis Model: Traveling Wave Exhibit 16-3 Four wave functions are given below.

I. II. III. IV.

y(x, t) = 5sin(4x – 20t + 4) y(x, t) = 5sin(3x – 12t + 5) y(x, t) = 5cos(4x + 24t + 6) y(x, t) = 14cos(2x – 8t + 3)

Use this exhibit to answer the following question(s).

27. Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wave speeds, from least to greatest. a. IV, II, I, III b. IV = II, I, III c. III, I, II, IV d. IV, I, II, III e. III, IV, II, I ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 28. Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the frequencies of the waves, from least to greatest. a. IV, II, I, III Copyright Cengage Learning. Powered by Cognero.

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b. IV = II, I, III c. III, I, II, IV d. IV, I, II, III e. III, IV, II, I ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.2 Analysis Model: Traveling Wave 29. Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wavelengths, from least to greatest. a. IV, II, I, III b. IV, I, II, III c. I, II, III, IV d. IV, II, III = I e. I = III, II, IV ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.2 Analysis Model: Traveling Wave 30. The equation

is the same as

a. b. c. d. e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 31. What is the expression for the transverse velocity of the wave in a string given by a.

?

b. c. d. e.

ANSWER:

d

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.2 Analysis Model: Traveling Wave 32. If the breakers at a beach are separated by 5.0 m and hit shore with a frequency of 0.20 Hz, with what speed are they traveling?

ANSWER: 1.0 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 33. Bats can detect small objects such as insects that are of a size approximately that of one wavelength. If bats emit a chirp at a frequency of 60 kHz, and the speed of sound in air is 340 m/s, what is the smallest size insect they can detect?

ANSWER: 5.7 mm POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 34. A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes 0.8 s for the wave to travel the 20 m to the opposite tower. If one meter of the rope has a mass of 0.35 kg, find the tension in the tightrope.

ANSWER: 219 N POINTS: 2 DIFFICULTY: Average REFERENCES: 16.2 Analysis Model: Traveling Wave 35. Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed? a. 8.0 m/s b. 16 m/s c. 24 m/s d. 30 m/s e. 4.0 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.3 The Speed of Waves on Strings 36. A piano string of density 0.005 0 kg/m is under a tension of 1 350 N. Find the velocity with which a wave travels on the string. a. 260 m/s b. 520 m/s c. 1 040 m/s d. 2 080 m/s e. 4 160 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 16.3 The Speed of Waves on Strings 37. A 100-m-long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in 4 the cable is 3.00 × 10 N, what is the speed of transverse waves on the cable? a. 60 m/s b. 122 m/s c. 244 m/s d. 310 m/s e. 1 500 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.3 The Speed of Waves on Strings 38. Suppose that you were selected for a "Survivor"-type TV show. To help keep your group connected, you suggest that long vines can be tied together and used to transmit signals in cases of emergency. To get the signals to travel faster, you should a. select lighter vines. b. increase the tension on the vines. c. hang weights from the vines at evenly spaced intervals. d. do all of the above. e. do (a) or (b) above, preferably both.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.3 The Speed of Waves on Strings 3

2

39. The velocity of sound in sea water is 1.53 × 10 m/s. Find the bulk modulus (in N/m ) of sea water if its density is 3 3 1.03 × 10 kg/m . a. 2.57 × 109 b. 2.19 × 109 c. 2.04 × 109 d. 2.41 × 109 e. 2.82 × 109 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.3 The Speed of Waves on Strings 40. If y = 0.02 sin (30x − 400t) (SI units) and if the mass density of the string on which the wave propagates is 0.005 kg/m, then the transmitted power is what? a. 1.03 W b. 2.13 W c. 4.84 W d. 5.54 W Copyright Cengage Learning. Powered by Cognero.

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e. 106 W ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 16.4 Rate of Energy Transfer by Sinusoidal Waves on Strings 41. A piano wire of length 1.5 m vibrates so that one-half wavelength is contained on the string. If the frequency of vibration is 65 Hz, the amplitude of vibration is 3.0 mm, and the density is 15 g/m, how much energy is transmitted per second down the wire? a. 21 W b. 11 W c. 5.4 W d. 2.2 W e. 1.1 W ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.4 Rate of Energy Transfer by Sinusoidal Waves on Strings 42. To transmit four times as much energy per unit time along a string, you can a. double the frequency. b. double the amplitude. c. increase the tension by a factor of 16. d. do any one of the above. e. do only (a) or (b) above.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.4 Rate of Energy Transfer by Sinusoidal Waves on Strings

43. Which of the following is a solution to the wave equation,

?

a. b. (cos kx) (sin ωt) c. e−x sin ωt d. e−x sin (kx − ωt) e. e−x cos t ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.5 The Linear Wave Equation 44. The wave equation is written down in an exam is: Copyright Cengage Learning. Powered by Cognero.

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From dimensional considerations we see that a. 2 v should be replaced by . b.

2

v should be replaced by

.

c. v2 should be replaced by v. d. 2 v should be replaced by e. 2 v should be replaced by

. .

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.5 The Linear Wave Equation 45. It is possible to hear an approaching train before you can see it by listening to the sound wave through the track. If the 11 2 3 3 elastic modulus is 2.0 × 10 N/m and the density of steel is 7.8 × 10 kg/m , approximately how many times faster is the speed of sound in the track than in air? (vair ≈ 340 m/s.) a. 20 b. 5 c. 10 d. 15 e. 25 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.6 Sound Waves 2

46. Calculate the pressure amplitude (in N/m ) of a 500-Hz sound wave in helium if the displacement amplitude is equal -8 3 to 5.0 × 10 m. (ρ = 0.179 kg/m , v = 972 m/s.) a. 3.5 × 10-2 b. 1.6 × 10-2 c. 2.7 × 10-2 d. 4.2 × 10-2 e. 2.0 × 10-2 ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 16.6 Sound Waves 47. Calculate the displacement amplitude (in m) of a 20-kHz sound wave in helium if it has a pressure amplitude of 8.0 × -3 2 3 10 N/m . (ρ = 0.179 kg/m , v = 972 m/s.) a. 2.9 × 10-10 b. 3.7 × 10-10 c. 7.8 × 10-9 d. 2.4 × 10-9 e. 1.9 × 10-10 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.6 Sound Waves -5

48. The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10 cos 2 (6.20x − 3 000t), where x and t have units m and s, and ΔP is measured in N/m . Determine the frequency (in Hz) of the wave. a. 1 500 b. 477 c. 1.01 d. 0.32 e. 239 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.6 Sound Waves -5

49. The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10 cos 2 (6.20x − 3 000t), where x and t have units m and s, and ΔP is measured in N/m . Determine the wavelength (in m) of the wave. a. 1 500 b. 0.32 c. 477 d. 1.01 e. 0.50 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.6 Sound Waves -5

50. The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10 cos (6.20x − 3 000t), where x and t have units m and s. Determine the speed (in m/s) of the wave. a. 1 515 b. 153 c. 484 Copyright Cengage Learning. Powered by Cognero.

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d. 828 e. 101 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.6 Sound Waves 51. The speed of a 10-kHz sound wave in seawater is approximately 1 500 m/s. What is its wavelength in sea water? a. 5.0 cm b. 10 cm c. 15 cm d. 20 cm e. 29 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.7 Speed of Sound Waves 52. A sculptor strikes a piece of marble with a hammer. Find the speed of sound through the marble (in km/s). (The 9 2 3 3 Young's modulus is 50 × 10 N/m and its density is 2.7 × 10 kg/m .) a. 5.1 b. 4.3 c. 3.5 d. 1.3 e. 1.8 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.7 Speed of Sound Waves 10

53. The Young's modulus for aluminum is 7.02 × 10 3 km/s, find its density (in kg/m ). a. 11.3 × 103

2

N/m . If the speed of sound in aluminum is measured to be 5.10

b. 7.80 × 103 c. 2.70 × 103 d. 29.3 × 103 e. 1.40 × 103 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.7 Speed of Sound Waves 54. A boat sounds a fog horn on a day when both the sea water and the air temperature are 25.0° C. The speed of sound in sea water is 1 533 m/s. How much earlier (in s) does a dolphin 1 000 m from the source hear the sound than a person in a boat that is also 1 000 m distant? (Ignore the time it takes the sound to reach the water surface.)

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a. 0.652 b. 2.12 c. 2.24 d. 2.77 e. 2.90 ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.7 Speed of Sound Waves 55. A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x, t) = sm cos (kx − ωt). Its velocity can be obtained from a. ω/k b. k/ω c. k d. ω e. ωk ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.7 Speed of Sound Waves 56. Drummers like to have high-pitched cymbals that vibrate at high frequencies. To obtain the highest frequencies, a cymbal of a fixed size should be made of a material a. with a low Young's modulus and a low density. b. with a low Young's modulus and a high density. c. with a high Young's modulus and a low density. d. with a high Young's modulus and a high density. e. composed of a metal-plastic laminate.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.7 Speed of Sound Waves 2

-3

2

57. Determine the intensity (in W/m ) of a harmonic longitudinal wave with a pressure amplitude of 8.0 × 10 N/m 3 propagating down a tube filled with helium. (ρ = 0.179 kg/m , v = 972 m/s) a. 3.7 × 10-7 b. 1.8 × 10-7 c. 9.2 × 10-8 d. 4.6 × 10-8 e. 1.5 × 10-9 ANSWER: b POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 16.8 Intensity of Sound Waves -4

2

58. Calculate the intensity level in dB of a sound wave that has an intensity of 15 × 10 W/m . a. 20 b. 200 c. 92 d. 9 e. 10 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 2

59. A jet plane has a sound level of 150 dB. What is the intensity in W/m ? a. 1 b. 100 c. 10 d. 1 000 e. 10 000 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 60. By what factor will an intensity change when the corresponding sound level increases by 3 dB? a. 3 b. 0.5 c. 2 d. 4 e. 0.3 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 61. By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 20 dB, respectively? a. 1012 b. 108 c. 106 d. 1010 e. 1011 ANSWER: POINTS:

d 2

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DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 2

62. A point source emits sound with a power output of 100 watts. What is the intensity (in W/m ) at a distance of 10.0 m from the source? a. 7.96 × 10-2 b. 7.96 × 10-1 c. 7.96 × 100 d. 7.96 × 101 e. 7.96 × 10-3 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 63. A point source emits sound waves with a power output of 100 watts. What is the sound level (in dB) at a distance of 10 m? a. 139 b. 119 c. 129 d. 109 e. 10 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 64. A stone is thrown into a quiet pool of water. With no fluid friction, the amplitude of the waves falls off with distance r from the impact point as a. 1/r3 b. 1/r2 c. 1/r3/2 d. 1/r1/2 e. 1/r ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 16.8 Intensity of Sound Waves 65. To decrease the intensity of the sound you are hearing from your speaker system by a factor of 36, you can a. reduce the amplitude by a factor of 12 and increase your distance from the speaker by a factor of 3. b. reduce the amplitude by a factor of 4 and increase your distance from the speaker by a factor of 3. c. reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3. d. reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 4.

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e. reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 12.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 66. A person standing in the street is unaware of a bird dropping that is falling from a point directly above him with increasing velocity. If the dropping were producing sound of a fixed frequency, as it approaches the person would hear the sound a. drop in frequency. b. stay at the same frequency. c. increase in frequency. d. decrease in loudness. e. stay at the same loudness.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.8 Intensity of Sound Waves 67. (Do not try the following: it could kill you. This question is only about a hypothetical possibility.) If you were standing below an object emitting a fixed frequency sound falling at terminal velocity, as it approached you, you would hear the sound a. drop in frequency. b. stay at the same frequency. c. increase in frequency. d. decrease in loudness. e. stay at the same loudness.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.8 Intensity of Sound Waves 68. A spherical wave has the form

.

The amplitude of the wave a distance r from the source is a. 0.002 cm. b. . c. . d. .

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e. .

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.8 Intensity of Sound Waves 69. A spherical wave has the form

.

The wavelength of the wave is a. 0.25 m. b. 0.50 m. c. 4.0 m. d. 8.0 m. e. 4.0π m.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 70. A spherical wave has the form

.

The frequency of the wave (in Hz) is a. 3.68 × 10−4. b. 7.35 × 10−4. c. 1 360. d. 2 720. e. 2 720π.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 71. A spherical wave has the form

.

The velocity of the wave (in m/s) is a. 0.005 88.

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b. 16.0 c. 340. d. 1 360. e. 2 720.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves

72. A boy has climbed to the top of a 6.00-m-tall tree. When he shouts, the sound waves have an intensity of at a 1.00 m distance from the top of the tree. The ratio of intensity at the base of the tree to the intensity 1.00 m from the top of the tree is a. . b. . c. . d. . e. .

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 73. Which of the following does not have a precise definition in terms of the physical properties of sound waves? a. frequency b. intensity c. loudness d. sound level e. wavelength ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.8 Intensity of Sound Waves 74. A source of sound waves is placed at the center of a very large sound-reflecting wall. The source emits 0.500 W of 2 power. What is the intensity in W/m two meters from the source? a. 9.95 × 10-3. b. 1.99 × 10-2.

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c. 0.313. d. 0.399. e. 0.625.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 75. A speaker is producing 30 W of sound. At which of the following frequencies would it sound the loudest? a. 50 Hz b. 100 Hz c. 500 Hz d. 1 000 Hz e. 10 000 Hz ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 76. A microphone in the ocean is sensitive to the sounds emitted by porpoises. To produce a usable signal, sound waves -11 2 striking the microphone must have an intensity of 1.02 × 10 W/m . If porpoises emit sounds with a power of 0.049 9 W, how far away can a porpoise be and still be heard? Disregard absorption of sound waves by the water.

ANSWER: 19.7 km POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 77. The intensity level of an orchestra is 85 dB. A single violin achieves a level of 70 dB. How does the intensity of the sound of the full orchestra compare with that of the violin?

ANSWER: IOrchestra = 31.6IViolin POINTS: 2 DIFFICULTY: Average REFERENCES: 16.8 Intensity of Sound Waves 78. A car approaches a stationary police car at 36 m/s. The frequency of the siren (relative to the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car? (Assume the velocity of sound in air is 343 m/s.) a. 220 b. 448 c. 526 d. 552 e. 383 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.9 The Doppler Effect Copyright Cengage Learning. Powered by Cognero.

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79. A car moving at 36 m/s passes a stationary police car whose siren has a frequency of 500 hz. What is the change in the frequency (in Hz) heard by an observer in the moving car as he passes the police car? (The speed of sound in air is 343 m/s.) a. 416 b. 208 c. 105 d. 52 e. 552 ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 16.9 The Doppler Effect 80. A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren relative to the police car is 500 Hz, what is the frequency heard by an observer in the truck as the police car approaches the truck? (The speed of sound in air is 343 m/s.) a. 396 b. 636 c. 361 d. 393 e. 617 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.9 The Doppler Effect 81. A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the frequency heard by an observer in the truck after the police car passes the truck? (The speed of sound in air is 343 m/s.) a. 361 b. 636 c. 393 d. 396 e. 383 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.9 The Doppler Effect 82. A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the change in frequency (in Hz) heard by an observer in the truck as the two vehicles pass each other? (The speed of sound in air is 343 m/s.) a. 242 b. 238 c. 240 d. 236 e. 234 Copyright Cengage Learning. Powered by Cognero.

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ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 16.9 The Doppler Effect 83. How fast (in m/s) is the Concorde moving if it reaches Mach 1.5? (The speed of sound in air is 344 m/s.) a. 229 b. 516 c. 416 d. 728 e. 858 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.9 The Doppler Effect 84. When you hear the horn of a car that is approaching you, the frequency that you hear is larger than that heard by a person in the car, because, for the sound you hear, a. wave crests are farther apart by the distance the car travels in one period. b. wave crests are closer together by the distance the car travels in one period. c. the car gets ahead of each wave crest before it emits the next one. d. the speed of sound in air is increased by the speed of the car. e. a speeding car emits more wavecrests in each period.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.9 The Doppler Effect 85. While you are sounding a tone on a toy whistle, you notice a friend running toward you. If you want her to hear the same frequency that you hear even though she is approaching, you must a. stay put. b. run towards her at the same speed. c. run away from her at the same speed. d. stay put and play a note of higher frequency. e. run towards her and play a note of higher frequency.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.9 The Doppler Effect

86. A friend hands you an equation sheet with the following equation for the Doppler effect:

. This

version of the equation is correct with signs as given only if a. the observer and source are approaching each other. b. the observer is approaching the source while the source is moving away from the observer. c. the observer is moving away from the source while the source is approaching the observer.

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d. the observer and source are moving away from each other. e. the observer and source are moving in perpendicular directions.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 16.9 The Doppler Effect 87. On a day when the speed of sound in the upper air is 320 m/s, you fly coast to coast in the United States, a distance of about 4 850 km, in about one hour, if the Mach number for the speed of your airplane is about a. 1. b. 2 c. 3 d. 4 e. 5.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 16.9 The Doppler Effect 88. If a supersonic plane is flying at increasing speed as the temperature decreases, what happens to the Mach number in this instance? a. It stays the same. b. It increases. c. It decreases. d. It can do any of the above. e. It can do either (a) or (b) but not (c).

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.9 The Doppler Effect 89. If a plane is flying at a speed so that the apex half-angle of its shockwave is 30°, what is its speed if the speed of sound is 320 m/s? a. 960 m/s b. 640 m/s c. 320 m/s d. 160 m/s e. Choose this answer if a shock wave cannot form in this situation.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 16.9 The Doppler Effect 90. A bat, flying at 5.00 m/s, emits a chirp at 40.0 kHz. If this sound pulse is reflected by a wall, what is the frequency of the echo received by the bat? (vsound = 340 m/s.)

ANSWER: 41.2 kHz Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 16.9 The Doppler Effect 91. An airplane traveling at half the speed of sound emits sound at a frequency of 5 000 Hz. At what frequency does a stationary listener hear the sound as the plane approaches, and after it passes by? Assume the airplane is not flying very high.

ANSWER: 10 000 Hz, 3 333 Hz POINTS: 3 DIFFICULTY: Challenging REFERENCES: 16.9 The Doppler Effect

1. Two waves are described by the following equations.

When the two waves are added together, what is the amplitude of the resultant wave? a. 8.0 m b. 4.3 m c. 6.0 m d. 3.2 m e. 3.0 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 2. Two waves are described by the following equations.

When the two waves are added together, what is the frequency (in Hz) of the resultant wave? a. 300 b. 48 c. 8 d. 0.8 e. 150 ANSWER: b POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 3. Two waves are described by the following equations.

When the two waves are added together, what is the wavelength of the resultant wave? a. 3 m b. 2 m c. 1 m d. 4 m e. 6 m ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 4. Two waves are described by the following equations.

What is the phase (in rad) of the resultant wave when x = t = 0? a. 3 b. 0 c. 2 d. 1 e. 4 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 5. The path difference between two waves is 5 m. If the wavelength of the waves emitted by the two sources is 4 m, what is the phase difference (in degrees)? a. 90 b. 400 c. 1.57 d. 7.85 e. 15 Copyright Cengage Learning. Powered by Cognero.

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ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 6. Two waves are described by the following equations.

What is the magnitude of the speed (in m/s) of the two traveling waves? a. 16 b. 4.0 c. 8.0 d. 0.25 e. 2.0 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 7. Two waves are described by the following equations.

What is the magnitude of the displacement (in cm) of this wave at x = 3 cm and t = 5 sec? a. 12.0 b. 3.00 c. 6.00 d. 2.25 e. 0 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 8. Two waves are described by y1 = 6 cos 180t and y2 = 6 cos 186t (both in meters).

With what angular frequency does the maximum amplitude of the resultant wave vary with time?

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a. 366 rad/s b. 6 rad/s c. 3 rad/s d. 92 rad/s e. 180 rad/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 9. Two waves are described by y1 = 6 cos 180t and y2 = 6 cos 186t (both in meters).

What effective frequency does the resultant vibration have at a point? a. 92 Hz b. 183 Hz c. 6 Hz d. 3 Hz e. 366 Hz ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 10. Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by π radians?

a. x = 0, 1.0 m, 2.0 m b. x = 0.50 m, 1.5 m c. x = 0.50 m, 1.0 m, 1.5 m d. x = 0.75 m, 1.25 m e. x = 0.25 m, 0.75 m, 1.25 m, 1.75 m ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 17.1 Analysis Model: Waves in Interference 11. The superposition of two waves,

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,

results in a wave with a phase angle of a. 0 rad. b. 0.5 rad. c. rad. d. rad. e. π rad.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.1 Analysis Model: Waves in Interference 12. The superposition of two waves,

and ,

results in a wave with a wavelength of a. m. b. 2 m. c. π m. d. 4 m. e. 4π m.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 13. The superposition of two waves,

and

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,

results in a wave with a frequency of a. 85 Hz. b. 170 Hz. c. 85π Hz. d. 340 Hz. e. 170π Hz. ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 14. An observer stands 3 m from speaker A and 4 m from speaker B. Both speakers, oscillating in phase, produce 170-Hz waves. The speed of sound in air is 340 m/s. What is the phase difference (in radians) between the waves from A and B at the observer's location, point P?

a. 0 b. c. π d. 2π e. 4π ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 15. Transverse waves y1 = A1 sin(k1x − ω1t) and y2 = A2 sin(k2x − ω2t), with A2 > A1, start at opposite ends of a long rope when t = 0. The magnitude of the maximum displacement, y, of the rope at any point is a. A1 − A2. b. A2 − A1. c. A1 + A2.

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d. . e. .

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 16. Two speakers in an automobile emit sound waves that are in phase at the speakers. One speaker is 40 cm ahead of and 30 cm to the left of the driver's left ear. The other speaker is 50 cm ahead of and 120 cm to the right of the driver's right ear. Which of the following wavelengths is(are) in phase at the left ear for the speaker on the left and the right ear for the speaker on the right? a. 10 cm b. 20 cm c. 650 cm d. All of the wavelengths listed above. e. Only the wavelengths listed in (a) and (b).

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 17.1 Analysis Model: Waves in Interference 17. Two organ pipes, a pipe of fundamental frequency 440 Hz, closed at one end, and a pipe of fundamental frequency 660 Hz, open at both ends, produce overtones. Which choice below correctly describes overtones present in both pipes? a. After the first overtone of each pipe, every second overtone of the first pipe matches every second overtone of the second pipe. b. After the first overtone of each pipe, every second overtone of the first pipe matches every third overtone of the second pipe. c. After the first overtone of each pipe, every third overtone of the first pipe matches every second overtone of the second pipe. d. After the first overtone of each pipe, every second overtone of the first pipe matches every fourth overtone of the second pipe. e. After the first overtone of each pipe, every third overtone of the first pipe matches every fourth overtone of the second pipe.

ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 17.1 Analysis Model: Waves in Interference Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond.

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Use this exhibit to answer the following question(s).

18. Refer to Exhibit 18-1. The phase difference in radians between points A and B is a. 0. b. . c. . d. π. e. .

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.1 Analysis Model: Waves in Interference 19. Refer to Exhibit 18-1. The phase difference in radians between points A and C is a. 0. b. . c. π. d. . e. 2π ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.1 Analysis Model: Waves in Interference 20. Refer to Exhibit 18-1. The phase difference in radians between points A and D is a. π. b. 2π. c. 3π. d. 4π. e. 5π.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.1 Analysis Model: Waves in Interference Copyright Cengage Learning. Powered by Cognero.

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21. Superposition of waves can occur a. in transverse waves. b. in longitudinal waves. c. in sinusoidal waves. d. in all of the above. e. only in (a) and (c) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.1 Analysis Model: Waves in Interference 22. Two pulses are traveling towards each other at 10 cm/s on a long string at t = 0 s, as shown below.

Which diagram below correctly shows the shape of the string at 0.5 s? a.

b.

c.

d.

e.

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ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.1 Analysis Model: Waves in Interference 23. Two waves are described by the following equations.

From the choices given, determine the smallest positive value of x (in cm) corresponding to a node of the resultant standing wave. a. 3 b. 0.25 c. 0 d. 6 e. 1.5 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 24. Two waves traveling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x) cos 5t where x is in m and t is in s. What is the wavelength of the interfering waves? a. 3.14 m b. 1.00 m c. 6.28 m d. 12.0 m e. 2.00 m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 25. Two waves traveling in opposite directions interfere to produce a standing wave described by y = 4 sin (5x) cos (6t), where x is in m and t is in s. What is the approximate frequency of the interfering waves? a. 3 Hz b. 1 Hz c. 6 Hz d. 12 Hz e. 5 Hz ANSWER: b POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 26. Two waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (4x) cos (3t), where x is in m and t is in s. What is the speed (in m/s) of the interfering waves? a. 0.75 b. 0.25 c. 1.3 d. 12 e. 3.0 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 27. Two waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (πx) cos (3πt), where x is in m and t is in s. What is the distance (in m) between the first two antinodes? a. 8 b. 2 c. 4 d. 1 e. 0.5 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 28. A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the wavelength (in cm) of the first harmonic? a. 600 b. 400 c. 800 d. 1 000 e. 200 ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.2 Standing Waves 29. A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the fundamental frequency? a. 316 Hz b. 632 Hz c. 158 Hz d. 215 Hz e. 79 Hz ANSWER: c Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 30. A stretched string is observed to vibrate in three equal segments when driven by a 480-Hz oscillator. What is the fundamental frequency of vibration for this string? a. 480 Hz b. 320 Hz c. 160 Hz d. 640 Hz e. 240 Hz ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.2 Standing Waves 31. Two strings are, respectively, 1.00 m and 2.00 m long. Each has the same mass per unit length and is under the same tension. Which of the following wavelengths, in meters, could represent harmonics present on both strings? a. 0.800, 0.670, 0.500 b. 1.33, 1.00, 0.500 c. 2.00, 1.00, 0.500 d. 2.00, 1.33, 1.00 e. 4.00, 2.00, 1.25 ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 17.2 Standing Waves 32. Two identical strings have the same length and same mass per unit length. String B is stretched with four times as great a tension as that applied to string A. Which statement is correct for all n harmonics on the two strings, n = 1, 2, 3...? a. . b. . c.

.

d. fn,B = 2fn,A. e. fn,B = 4fn,A. ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 33. In a standing wave, not necessarily at the fundamental frequency, on a string of length L, the distance between nodes is a. λ/4.

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b. λ/2. c. λ. d. L/4. e. L/2.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.2 Standing Waves 34. Which of the following wavelengths could NOT be present as a harmonic on a 2-m-long string? a. 4 m b. 2 m c. 1 m d. 0.89 m e. 0.5 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 35. A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator.

Which of the following can be changed by changing the frequency of the oscillator? a. The speed of the waves traveling along the string. b. The tension in the string. c. The wavelength of the waves on the string. d. All of the above. e. None of the above.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.2 Standing Waves 36. The figure below shows the positions of particles in a longitudinal standing wave. One quarter period later the particle distribution is shown in a. b. c. d. e.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 37. A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. The wave speed is 540 m/s.

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What is the minimum frequency she should apply to set up standing waves?

ANSWER: 150 Hz POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves −3

38. Find the frequencies of the first three harmonics of a 1.0-m-long string which has a mass per unit length of 2.0 × 10 kg/m and a tension of 80 N, when both ends are fixed in place.

ANSWER: 100 Hz, 200 Hz, 300 Hz POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves

39. A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (fc = 261.6 Hz)?

ANSWER: 824 N POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 40. The fundamental frequency of a above middle C on the piano is 440 Hz. This is the tenor high A, but a convenient note in the mid-range of women's voices. When we calculate the wavelength, we find that it is a. much shorter than the length of either a man's or woman's lips. b. shorter than the length of a man's lips, but about the length of a woman's lips. c. longer than a woman's lips, but about the length of a man's lips. d. much longer than the length of either a man's or a woman's lips. e. about the same length as either a man's or woman's lips.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.2 Standing Waves 41. Two ropes are spliced together as shown.

A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in which figure? a. b. c. d. e.

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ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.3 Boundary Effects: Reflection and Transmission 42. Two ropes are spliced together as shown.

A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in which figure? a. b. c. d. e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.3 Boundary Effects: Reflection and Transmission 43. When a workman strikes a steel pipeline with a hammer, he generates both longitudinal and transverse waves. The two types of reflected waves return 2.4 s apart. How far away is the reflection point? (For steel, vL = 6.2 km/s, vT = 3.2 km/s) ANSWER: 7.9 km POINTS: 2 DIFFICULTY: Average REFERENCES: 17.3 Boundary Effects: Reflection and Transmission 44. The figure below represents a string which has a heavy section and a light section. The mass per unit length of the heavy section is 16 times as large as the mass per unit length of the light section. When the string is under tension, the speed of a pulse traveling in the heavy section is ____ times the speed of that same pulse traveling in the light section.

a. b. c. d. 2 e. 4 Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 17.3 Boundary Effects: Reflection and Transmission 45. A string with a fixed frequency vibrator at one end is undergoing resonance with 4 antinodes when under tension T1.

When the tension is slowly increased the resonance condition disappears until tension T2 is reached, there being no resonances occurring between these two tensions. How many antinodes are there in this new resonance? a. 3 b. 4, since all resonances in this situation have the same number of nodes c. 5 d. 2, since resonances only involve whole wavelengths e. 6, since resonances only involve whole wavelength ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 17.5 Resonance 46. A string with a fixed frequency vibrator at one end is subjected to varying tensions. When the tension is 20 N, a resonance with 3 antinodes results. What tension would cause a resonance with 2 antinodes in this string? a. 30 N b. 45 N c. 80 N d. 8.9 N e. 13 N ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 17.5 Resonance 47. A clarinet behaves like a tube closed at one end. If its length is 1.0 m, and the velocity of sound is 344 m/s, what is its fundamental frequency (in Hz)? a. 264 b. 140 c. 86 d. 440 e. 172 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 17.6 Standing Waves in Air Columns 48. An organ pipe open at both ends has a radius of 4.0 cm and a length of 6.0 m. What is the frequency (in Hz) of the third harmonic? (Assume the velocity of sound is 344 m/s.) a. 76 b. 86 Copyright Cengage Learning. Powered by Cognero.

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c. 54 d. 28 e. 129 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 17.6 Standing Waves in Air Columns 49. A vertical tube one meter long is open at the top. It is filled with 75 cm of water. If the velocity of sound is 344 m/s, what will the fundamental resonant frequency be (in Hz)? a. 3.4 b. 172 c. 344 d. 1.7 e. 688 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 17.6 Standing Waves in Air Columns 50. A length of organ pipe is closed at one end. If the speed of sound is 344 m/s, what length of pipe (in cm) is needed to obtain a fundamental frequency of 50 Hz? a. 28 b. 86 c. 344 d. 172 e. 688 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.6 Standing Waves in Air Columns 51. An organ pipe open at both ends is 1.5 m long. A second organ pipe that is closed at one end and open at the other is 0.75 m long. The speed of sound in the room is 330 m/s. Which of the following sets of frequencies consists of frequencies which can be produced by both pipes? a. 110 Hz, 220 Hz, 330 Hz b. 220 Hz, 440 Hz, 660 Hz c. 110 Hz, 330 Hz, 550 Hz d. 330 Hz, 440 Hz, 550 Hz e. 220 Hz, 660 Hz, 1 100 Hz ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 17.6 Standing Waves in Air Columns 52. Which of the following wavelengths could NOT be present as a standing wave in a 2-m-long organ pipe open at both ends?

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a. 4 m b. 2 m c. 1 m d. 0.89 m e. 0.5 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.6 Standing Waves in Air Columns 53. Which of the following frequencies could NOT be present as a standing wave in a 2-m-long organ pipe open at both ends? The fundamental frequency is 85 Hz. a. 85 Hz. b. 170 Hz. c. 255 Hz. d. 340 Hz. e. 382 Hz. ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 17.6 Standing Waves in Air Columns 54. As shown below, a garden room has three walls, a floor and a roof, but is open to the garden on one side. The wall widths are L and w. The roof height is h. When traveling sound waves enter the room, standing sound waves can be present in the room if the wavelength of the standing waves is

a. , where n is a positive integer. b. , where n is an odd integer. c. , where n is an even integer. d. in all cases listed above. e. given by (a) or (b) above, but not by (c).

ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 17.6 Standing Waves in Air Columns Copyright Cengage Learning. Powered by Cognero.

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55. Two tuning forks with frequencies 264 and 262 Hz produce "beats". What is the beat frequency (in Hz)? a. 4 b. 2 c. 1 d. 3 e. 0 (no beats are produced) ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.7 Beats: Interference in Time 56. Two instruments produce a beat frequency of 5 Hz. If one has a frequency of 264 Hz, what could be the frequency of the other instrument? a. 269 Hz b. 254 Hz c. 264 Hz d. 5 Hz e. 274 Hz ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 17.7 Beats: Interference in Time 57. The superposition of two waves

and

at the location x = 0 in space results in a. beats at a beat frequency of 3 Hz. b. a pure tone at a frequency of 153 Hz. c. a pure tone at a frequency of 156 Hz. d. beats at a beat frequency of 6 Hz in a 153 Hz tone. e. a tone at a frequency of 156 Hz, as well as beats at a beat frequency of 6 Hz in a 153 Hz tone.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 17.7 Beats: Interference in Time 58. A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency. At the time, the speed of sound in air is 340 m/s. How many beats per second do the people on the fire engine hear? a. 0 Copyright Cengage Learning. Powered by Cognero.

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b. 15 c. 29 d. 63 e. 250 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 17.7 Beats: Interference in Time 59. Tuning forks #1, #2, and #3 each have slightly different frequencies.When #1 and #2 are sounded together, a beat frequency of 3 Hz results. When #2 and #3 are sounded together, a beat frequency of 5 Hz results. If the frequency of #1 is 100 Hz, which of the following cannot be the frequency of #3? a. 92 Hz b. 95 Hz c. 98 Hz d. 102 Hz e. 108 Hz ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 17.7 Beats: Interference in Time

1. In order to understand the concept of temperature it is necessary to understand a. the zeroth law of thermodynamics. b. the first law of thermodynamics. c. the second law of thermodynamics. d. all of the above. e. only (b) and (c) above.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.1 Temperature and the Zeroth Law of Thermodynamics 2. In order for two objects to have the same temperature, they must a. be in thermal equilibrium. b. be in thermal contact with each other. c. have the same relative "hotness" or "coldness" when touched. d. have all of the properties listed above. e. have only properties (b) and (c) above.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.1 Temperature and the Zeroth Law of Thermodynamics 3. A bowling-ball-size probe from a spaceship and a pebble size object land on a large asteroid that is far from any star.

After a long period of time has passed, it is highly probable that the pebble and the probe Copyright Cengage Learning. Powered by Cognero.

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a. have each had the same change in temperature. b. have each had the same change in volume. c. are in thermal equilibrium with one another. d. are not in thermal equilibrium with one another. e. are in thermal equilibrium with one another, but are not at the same temperature.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.1 Temperature and the Zeroth Law of Thermodynamics 4. Two bodies can be in thermal equilibrium with one another when they are at the same temperature even if they a. absorb different quantities of thermal energy from their surroundings in equal time intervals. b. have different masses. c. have different volumes. d. have any of the properties listed above. e. have any of the properties listed above and one of them is contact with a third body at a different temperature.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.1 Temperature and the Zeroth Law of Thermodynamics 5. Steel blocks A and B, which have equal masses, are at TA = 300 °C and TB = 400 °C. Block C, with mC = 2mA, is at TC = 350 °C. Blocks A and B are placed in contact, isolated, and allowed to come into equilibrium. Then they are placed in contact with block C. At that instant, a. TA = TB < TC. b. TA = TB = TC. c. TA = TB > TC. d. TA + TB = TC. e. TA − TB = TC. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.1 Temperature and the Zeroth Law of Thermodynamics 6. A thermometer registers a change in temperature of 100°F. What change in temperature does this correspond to on the Kelvin Scale? a. 453 b. 328 c. 180 d. 55.6 e. 24.5 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale Copyright Cengage Learning. Powered by Cognero.

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7. A temperature difference of 5 K is equal to a. a difference of 9 on the Celsius scale. b. a difference of 9 on the Fahrenheit scale. c. a difference of 2.8 on the Rankine scale. d. a difference of .5 on the Fahrenheit scale. e. a difference of 2.8 on the Celsius scale.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale 8. Helium condenses into the liquid phase at approximately 4 K. What temperature, in degrees Fahrenheit, does this correspond to? a. −182 b. −269 c. −118 d. −452 e. −484 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale 9. Two thermometers are calibrated, one in degrees Celsius and the other in degrees Fahrenheit. At what temperature (in kelvins) do their readings measure the same temperature? a. 218.15 b. 233.15 c. 273.15 d. 40.15 e. 0 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale 10. A child has a temperature of 104°F. What is the temperature in degrees kelvin? a. 40 b. 406 c. 401 d. 313 e. 349 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale Copyright Cengage Learning. Powered by Cognero.

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11. At what temperature is the Celsius scale reading equal to twice the Fahrenheit scale reading? a. −12.3°F b. −24.6°F c. −12.3°C d. −6.1°C e. −20°F ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale 12. A temperature difference of 9.0 Celsius degrees is equal to a Fahrenheit temperature difference of a. 5.0 Fahrenheit degrees. b. 9.0 Fahrenheit degrees. c. 16 Fahrenheit degrees. d. 37 Fahrenheit degrees. e. 41 Fahrenheit degrees.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale 13. Death Valley in California receives many German tourists. When you convert a summer temperature reading of 130° F to the Celsius scale they use at home, you find that the Celsius temperature is about a. 26° C. b. 54° C. c. 72° C. d. 176° C e. 327° C. ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale 14. At what Fahrenheit temperature are the Kelvin and Fahrenheit temperatures numerically equal?

ANSWER: 574.6°F = 574.6 K POINTS: 2 DIFFICULTY: Average REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale 15. A student has written the equation below to convert a temperature in degrees Fahrenheit into Kelvins. What is wrong with this equation?

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a.

The factor in front of TF should be b.

The numerical factor

.

should multiply (TF − 32).

c. An additional 273.15 Kelvins must be added to the right side of the equation. d. All the corrections above are required. e. Only corrections (b) and (c) are required.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.2 Thermometers and the Celsius Temperature Scale 16. A pressure of 10.0 mm Hg is measured at the triple-point of water using a constant-volume gas thermometer. What will the pressure be (in mm Hg) at 50.0°C? a. 68.3 b. 1.80 c. 31.8 d. 11.8 e. 8.50 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 18.3 The Constant-Volume Gas Thermometer and the Absolute Temperature Scale 17. A pressure of 10.0 mm Hg is measured using a constant-volume gas thermometer at a temperature of 50.0°C. What is the pressure (in mm Hg) at the zero-point temperature? a. 31.8 b. 11.8 c. 8.45 d. 54.6 e. 68.3 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 18.3 The Constant-Volume Gas Thermometer and the Absolute Temperature Scale 18. A constant-volume gas thermometer has a pressure of 2.00 atm at 100°C. What would its pressure be at 0°C? a. 0.732 atm b. 1.46 atm c. 1.24 atm d. 1.37 atm e. More information is needed to find the answer.

ANSWER: b POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 18.3 The Constant-Volume Gas Thermometer and the Absolute Temperature Scale -6

-1

19. A bridge is made with segments of concrete 50 m long. If the linear expansion coefficient is 12 × 10 (°C) , how much spacing (in cm) is needed to allow for expansion during an extreme temperature change of 150° F? a. 10 b. 2.5 c. 7.5 d. 5.0 e. 9.5 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 20. A building made with a steel structure is 650 m high on a winter day when the temperature is 0° F. How much taller -6 -1 (in cm) is the building when it is 100° F? (The linear expansion coefficient of steel is 11 × 10 (°C) .) a. 71 b. 36 c. 40 d. 46 e. 65 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 21. A gallon container is filled with gasoline. How many gallons are lost if the temperature increases by 25°F? (The -4 -1 volume expansion of gasoline is 9.6 × 10 (°C) .) (Neglect the change in volume of the container.) a. 2.4 × 10−2 b. 1.3 × 10−2 c. 3.6 × 10−2 d. 4.8 × 10−2 e. 9.6 × 10−2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 22. A beaker is filled to the 500-ml mark with alcohol. What increase in volume (in ml) does the beaker contain when the temperature changes from 5° C to 30° C? (Neglect the expansion of the beaker, evaporation of alcohol and absorption of -4 water vapor by alcohol.) βalcohol = 1.12 × 10 /°C a. 0.47 b. 0.93 c. 1.4 d. 1.7 Copyright Cengage Learning. Powered by Cognero.

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e. 2.5 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 2

23. What is the change in area (in cm ) of a 60.0-cm by 150-cm automobile windshield when the temperature changes -6 from 0° C to 36.0° C? The coefficient of linear expansion of this glass is 9.0 × 10 /°C. a. 1.6 b. 2.9 c. 3.2 d. 4.9 e. 5.8 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 24. Angela claims that she wears a cylindrical-shaped hollow gold bracelet because it expands less than a solid one with a change in temperature. Clarissa claims that a cylindrical-shaped solid gold bracelet expands less than a hollow one. Which one, if either, is correct? a. Angela, because the bracelet expands outward on its outer surface and inward on its inner surface. b. Clarissa, because the bracelet expands outward on its outer surface and inward on its inner surface. c. Angela, because the inner circumference does not change, but the outer circumference expands. d. Clarissa, because the inner circumference does not change, but the outer circumference expands. e. Neither, because both the inner and outer circumferences increase in length.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 25. When the coefficient of linear expansion, α, and the temperature change, Tf − Ti, are large, a length Li of a solid substance expands in length to a. Lf = αLi(Tf – Ti). b. Lf = Li[1 + α(Tf – Ti)]. c. Lf = Li[1 + ln(α(Tf – Ti))]. d. . e. .

ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 18.4 Thermal Expansion of Solids and Liquids Copyright Cengage Learning. Powered by Cognero.

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2

26. A square plate has an area of 29.00 cm at 20.0°C. It will be used in a low temperature experiment at T = 10.0 K, 2 where it must have an area of 28.00 cm . What area must be removed form the plate at 20.0°C for it to have the correct -6 -1 area at 10.0 K? (The coefficient of linear expansion is 10 × 10 (°C) .) a. 0.079 3 cm2 b. 0.159 cm2 c. 0.238 cm2 d. 0.841 cm2 e. 0.921 cm2 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 27. At which of the following temperatures would one liter of water weigh the most? a. 2°C b. 4°C c. 8°C d. 90°C e. It would weigh the same at all these temperatures.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 28. A gold ring has an inner diameter of 2.168 cm at a temperature of 15.0°C. Determine its diameter at 100.0°C. (αgold = -5 1.42 × 10 /°C) ANSWER: 2.171 cm POINTS: 2 DIFFICULTY: Average REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 29. Determine the change in length of a 20-m railroad track made of steel if the temperature is changed from −15°C to -5 +35°C. (αsteel = 1.1 × 10 /°C) ANSWER: 1.1 cm POINTS: 2 DIFFICULTY: Average REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 30. Suppose the ends of a 30-m-long steel beam are rigidly clamped at 0°C to prevent expansion. The beam has a cross2 sectional area of 30 cm . What force against the clamps does the beam exert when it is heated to 40°C? (αSteel = 1.1 × 10 5 10 2 /°C, Ysteel = 20 × 10 N/m ).

5 ANSWER: 2.6 × 10 N POINTS:

3

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DIFFICULTY: Challenging REFERENCES: 18.4 Thermal Expansion of Solids and Liquids 31. An auditorium has dimensions 10 m × 10 m × 60 m. How many moles of air fill this volume at one atmosphere and 0°C? a. 2.7 × 102 b. 2.7 × 104 c. 2.7 × 103 d. 2.7 × 105 e. 2.7 × 106 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 3

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32. An auditorium has a volume of 6 × 10 m . How many molecules of air are needed to fill the auditorium at one atmosphere and 0°C? a. 1.6 × 1029 b. 1.6 × 1027 c. 1.6 × 1025 d. 1.6 × 1023 e. 1.6 × 1020 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 33. One mole of an ideal gas is held at a constant pressure of 1 atm. Find the change in volume (in liters) if the temperature changes by 50°C. a. 1 b. 2 c. 3 d. 4 e. 5 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 34. One mole of an ideal gas is held at a constant volume of 1 liter. Find the change in pressure if the temperature increases by 50°C. a. 3 atm b. 4 atm c. 2 atm Copyright Cengage Learning. Powered by Cognero.

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d. 1 atm e. 5 atm ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 35. One mole of an ideal gas has a temperature of 25°C. If the volume is held constant and the pressure is doubled, the final temperature (in °C) will be a. 174 b. 596 c. 50 d. 323 e. 25 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 36. A bicycle pump contains air at one atmosphere and 0°C. As the tire is pumped up, the volume of air decreases by 50% with each stroke. What is the new pressure of air (in atm) in the chamber after the first stroke, assuming no temperature change? a. 2 b. 1 c. 0.5 d. 0.1 e. 3 ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 3

37. A helium-filled balloon has a volume of 1 m . As it rises in the Earth's atmosphere, its volume expands. What will its 3 new volume be (in m ) if its original temperature and pressure are 20°C and 1 atm, and its final temperature and pressure are −40°C and 0.1 atm? a. 4 b. 6 c. 8 d. 10 e. 1.5 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 38. A bubble having a diameter of 1.00 cm is released from the bottom of a swimming pool, where the depth is 5.00 m.

What will the diameter of the bubble be when it reaches the surface? The temperature of the water at the surface is Copyright Cengage Learning. Powered by Cognero.

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3

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20.0°C, whereas it is 15.0°C at the bottom. (The density of water is 1.00 × 10 kg/m .) a. 1.05 cm b. 1.15 cm c. 1.45 cm d. 1.65 cm e. 1.35 cm ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 39. A scuba diver has his lungs filled to half capacity (3 liters) when 10 m below the surface. If the diver holds his breath while quietly rising to the surface, what will the volume of the lungs be (in liters) at the surface? Assume the temperature 3 3 is the same at all depths. (The density of water is 1.0 × 10 kg/m .) a. 5.9 b. 4.5 c. 6.4 d. 3.9 e. 3.1 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 40. Two identical containers, A and B, hold equal amounts of the same ideal gas at the same Po, Vo, and To. The pressure of A then decreases by a half while its volume doubles; the pressure of B doubles while its volume decreases by a half.

Which statement correctly describes the temperatures of the gases after the changes? a. TA = 0.5TB = To. b. TB = 0.5TA = To. c. TB = TA = To. d. TA = 2TB = To. e. TB = 2TA = To. ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 5

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41. A container with a one-liter capacity at 27° C is filled with helium to a pressure of 2.0 atm. (1 atm = 1.0 × 10 N/m .)

How many moles of helium does it hold? a. 0.041 b. 0.081 c. 0.45 d. 0.90 e. 1.0 ANSWER: b Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 42. Two moles of an ideal gas are placed in a container of adjustable volume. When measurements are made a. the pressure is inversely proportional to the volume at constant temperature. b. the temperature is directly proportional to the volume at constant pressure. c. the temperature is directly proportional to the pressure at constant volume. d. all the statements above are found to be correct. e. only statements (a) and (b) are found to be correct.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 43. Equal volumes of hydrogen and helium gas are at the same pressure. The atomic mass of helium is four times that of hydrogen. If the total mass of both gases is the same, the ratio of the temperature of helium (He) to that of hydrogen (H2) is a. . b. . c. 1. d. 2. e. 4.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 44. Equal masses of hydrogen and helium gas are at the same temperature in vessels of equal volume. The atomic mass of helium is four times that of hydrogen. If the total mass of both gases is the same, the ratio of the pressure of helium (He) to that of hydrogen (H2) is a. . b. . c. 1. d. 2. e. 4.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas Copyright Cengage Learning. Powered by Cognero.

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45. 48 grams of oxygen at room temperature consists of how many moles? a. 3.0 b. 1.5 c. 0.75 d. more than 3.0 e. less than 0.75 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 46. The mass of a sulfur atom is 32.0 u, and the mass of a fluorine atom is 19.0 u. What is the mass of a mole of sulfur hexafluoride (UF6)? a. 41.0 g b. 20.5 g c. 106 g d. 146 g e. 211 g ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 47. The pressure of a substance is directly proportional to its volume when the temperature is held constant and inversely proportional to its temperature when the volume is held constant. Is this substance an ideal gas? Explain why your answer is correct.

ANSWER: No. Since P = kV and P = k'/T for fixed temperature and volume, the substance obeys the law: which is different from the relation for an ideal gas.

POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas 3

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48. One mole of hydrogen, one mole of nitrogen, and one mole of oxygen are held in a 22.4 × 10 cm enclosed vessel at 2 20°C. The pressure in the vessel, in N/m , is a. 109. b. 304. c. 326. d. 1.09 × 105. e. 3.26 × 105.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 18.5 Macroscopic Description of an Ideal Gas Copyright Cengage Learning. Powered by Cognero.

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1. A 100-kg student eats a 200-Calorie doughnut. To "burn it off", he decides to climb the steps of a tall building. How 3 high (in m) would he have to climb to expend an equivalent amount of work? (1 food Calorie = 10 calories.) a. 273 b. 623 c. 418 d. 854 e. 8 400 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.1 Heat and Internal Energy 2. A 5-g coin is dropped from a 300-m building. If it reaches a terminal velocity of 45 m/s, and the rest of the energy is converted to heating the coin, what is the change in temperature (in °C) of the coin? (The specific heat of copper is 387 J/kg⋅ °C.) a. 9 b. 2 c. 5 d. 21 e. 0.5 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 19.1 Heat and Internal Energy 3. If an object feels cold to the touch, the only statement that you can make that must be correct is that a. the object has a smaller coefficient of thermal conductivity than your hand. b. the volume of the object will increase while it is in contact with your hand. c. the object contains less thermal energy than your hand. d. the object is at a lower temperature than your hand. e. the object cannot be a liquid.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.1 Heat and Internal Energy 4. Which of the following statements is correct? a. You only need to know the amount of thermal energy a body contains to calculate its temperature. b. The temperature of a body is directly proportional to the amount of work the body has performed. c. The quantity of thermal energy exchanged by two bodies in contact is inversely proportional to the difference in their temperatures. d. The quantity of thermal energy exchanged by two bodies in contact is directly proportional to the difference in their temperatures. e. Different amounts of thermal energy are transferred between two bodies in contact if different temperature scales are used to measure the temperature difference between the bodies.

ANSWER: d Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.1 Heat and Internal Energy 5. In which process will the internal energy of the system NOT change? a. An adiabatic expansion of an ideal gas. b. An isothermal compression of an ideal gas. c. An isobaric expansion of an ideal gas. d. The freezing of a quantity of liquid at its melting point. e. The evaporation of a quantity of a liquid at its boiling point.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.1 Heat and Internal Energy 6. A team of people who traveled to the North Pole by dogsled lived on butter because they needed to consume 6 000 dietician's Calories each day. Because the ice there is lumpy and irregular, they had to help the dogs by pushing and lifting the load. Assume they had a 16-hour working day and that each person could lift a 500-N load. How many times would a 2 person have to lift this weight 1.00 m upwards in a constant gravitational field, where g = 9.80 m/s , to do the work equivalent to 6 000 Calories? a. 50.2 b. 492 c. 5 130 d. 50 200 e. 492 000 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.1 Heat and Internal Energy 7. We are able to define a mechanical equivalent for heat because a. some thermal energy can be converted into mechanical energy. b. mechanical energy can be converted into thermal energy. c. work can be converted into thermal energy. d. some thermal energy can be converted into work. e. all of the above can occur.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.1 Heat and Internal Energy 8. Determine the heat capacity (in calories/°C) of a lake containing one million gallons (approximately 4 million kilograms) of water at 15°C. a. 4 × 106 b. 4 × 109 c. 4 × 103 Copyright Cengage Learning. Powered by Cognero.

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d. 1 × 103 e. 4 × 102 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 19.2 Specific Heat and Calorimetry 9. How many calories of heat are required to raise the temperature of 4 kg of water from 50°F to the boiling point? a. 6.5 × 105 b. 3.6 × 105 c. 15 × 105 d. 360 e. 4 × 104 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 19.2 Specific Heat and Calorimetry 10. A 5-gallon container of water (approximately 20 kg) having a temperature of 212°F is added to a 50-gallon tub (approximately 200 kg) of water having a temperature of 50°F. What is the final equilibrium temperature (in °C) of the mixture? a. 54 b. 36 c. 18 d. 66 e. 14 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 19.2 Specific Heat and Calorimetry 11. A 5-kg piece of lead (specific heat 0.03 cal/g⋅ °C) having a temperature of 80°C is added to 500 g of water having a temperature of 20°C. What is the final equilibrium temperature (in °C) of the system? a. 79 b. 26 c. 54 d. 34 e. 20 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.2 Specific Heat and Calorimetry 12. One gram of water is heated from 0°C to 100°C at a constant pressure of 1 atm. Determine the approximate change in internal energy (in cal) of the water.

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a. 160 b. 130 c. 100 d. 180 e. 50 ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.2 Specific Heat and Calorimetry 13. An 8 000-kg aluminum flagpole 100-m long is heated by the Sun from a temperature of 10°C to 20°C. Find the heat transferred (in J) to the aluminum if the specific heat of aluminum is 0.215 cal/g⋅ °C. a. 7.2 × 105 b. 7.2 × 107 c. 7.2 × 103 d. 7.2 × 101 e. 7.2 × 102 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 19.2 Specific Heat and Calorimetry 14. Duff states that equal masses of all substances have equal changes in internal energy when they have equal changes in temperature. Javan states that the change in internal energy is equal to a constant times the change in temperature for every ΔT, no matter how large or how small ΔT is, but that the constant is different for different substances. Which one, if either, is correct? a. Neither, because the specific heat depends on the substance and may vary with temperature. b. Neither, because a change of state may involve release or absorption of latent heat. c. Neither because a substance may do work during a temperature change. d. All of the statements above are correct. e. Only statements (a) and (b) are correct.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.2 Specific Heat and Calorimetry 15. A 100-kg marble slab falls off a skyscraper and falls 200 m to the ground without hitting anyone. Its fall stops within milliseconds, so that there is no loss of thermal energy to its surroundings if its temperature is measured immediately after it stops. By how much has its temperature changed as a result of the fall, if we ignore energy gained or lost as a result of its interaction with the atmosphere? (

.)

a. 0.57 °C b. 1.14 °C c. 2.28 °C d. 4.56 °C Copyright Cengage Learning. Powered by Cognero.

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e. 22.8 °C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 19.2 Specific Heat and Calorimetry 16. A block of material of mass m and specific heat c falls from height h and reaches speed v just before striking the ground. Its temperature is measured immediately after it strikes the ground. If we ignore any change in temperature owing to interaction with the air, the change in temperature of the block of material is a. . b. . c. . d. All of the answers above are correct. e. Only (a) and (b) above are correct.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 19.2 Specific Heat and Calorimetry 17. Which of the following substances has the greatest specific heat? a. copper b. ice c. water d. steam e. Ice, water, and steam have equal specific heats since they are the same material, and this specific heat is greater than that of copper.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.2 Specific Heat and Calorimetry 18. In braking an automobile, the friction between the brake drums and brake shoes converts the car's kinetic energy into heat. If a 1 500-kg automobile traveling at 30 m/s brakes to a halt, how much does the temperature rise in each of the four 8.0-kg brake drums? (The specific heat of each iron brake drum is 448 J/kg⋅ °C).

ANSWER: 47°C POINTS: 2 DIFFICULTY: Average REFERENCES: 19.2 Specific Heat and Calorimetry 3

19. A 300-g glass thermometer initially at 25°C is put into 200 cm of hot water at 95°C. Find the final temperature (in °C) of the thermometer, assuming no heat flows to the surroundings. (The specific heat of glass is 0.2 cal/g⋅ °C.) a. 52 Copyright Cengage Learning. Powered by Cognero.

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b. 68 c. 89 d. 79 e. 36 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.3 Latent Heat 20. How much heat (in kilocalories) is needed to convert 1.00 kg of ice at 0°C into steam at 100°C? a. 23.9 b. 79.6 c. 564 d. 643 e. 720 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 19.3 Latent Heat 21. If 25 kg of ice at 0°C is combined with 4 kg of steam at 100°C, what will be the final equilibrium temperature (in °C) of the system? a. 40 b. 20 c. 60 d. 100 e. 8 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 19.3 Latent Heat 22. How much heat (in kcal) must be removed to make ice at −10°C from 2 kg of water at 20°C? (The specific heat of ice is 0.50 cal/g⋅ °C.) a. 190 b. 200 c. 240 d. 210 e. 50 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.3 Latent Heat 23. How much heat, in joules, is required to convert 1.00 kg of ice at 0°C into steam at 100°C? (Lice = 333 J/g; Lsteam = 3 2.26 × 10 J/g.)

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a. 3.35 × 105 b. 4.19 × 105 c. 2.36 × 106 d. 2.69 × 106 e. 3.01 × 106 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 19.3 Latent Heat 24. Water at room temperature, 20°C, is pumped into a reactor core where it is converted to steam at 200°C. How much 3 heat (in J) is transferred to each kilogram of water in this process? (csteam = 2 010 J/kg⋅ °C; Lsteam = 2.26 × 10 J/g; 1 cal = 4.186 J.) a. 3.35 × 105 b. 7.53 × 105 c. 2.67 × 106 d. 2.80 × 106 e. 3.01 × 106 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.3 Latent Heat 25. A 100-g cube of ice is heated from −120°C to +120°C. In which of the following processes is the greatest amount of energy absorbed by this material? a. warming ice to the melting point b. melting the ice to become water c. warming the resulting water d. vaporizing the water to become steam e. heating the steam ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.3 Latent Heat 26. 100 grams of liquid nitrogen at 77 K is stirred into a beaker containing 200 grams of 5°C water. If the nitrogen leaves the solution as soon as it turns to gas, how much water freezes? (The heat of evaporation of nitrogen is 6.09 cal/gram and the heat of fusion of water is 80 cal/gram.)

ANSWER: none POINTS: 2 DIFFICULTY: Average REFERENCES: 19.3 Latent Heat 27. How much water at 20°C is needed to melt 1 kilogram of solid mercury at its melting point of −39°C? (The heat of fusion of mercury is 2.8 cal/gram).

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ANSWER: 23.4 grams POINTS: 2 DIFFICULTY: Average REFERENCES: 19.3 Latent Heat 28. The work done in the expansion from an initial to a final state a. is the area under the curve of a PV diagram. b. depends only on the end point. c. is independent of the path. d. is the slope of a PV curve. e. equals P(VF − Vi).

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.4 Work in Thermodynamic Processes 29. Gas in a container expands at a constant pressure of 3 atm. Find the work done (in J) by the gas if the initial volume is 5 liters and the final volume is 10 liters. a. 0 b. 150 c. 15 d. 1 500 e. 1.5 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.4 Work in Thermodynamic Processes 30. Gas in a container increases its pressure from 1 atm to 3 atm while keeping its volume constant. Find the work done (in J) by the gas if the volume is 5 liters. a. 0 b. 3 c. 5 d. 15 e. 15 × 102 ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.4 Work in Thermodynamic Processes 31. An 8 000-kg aluminum flagpole 100-m long is heated by the Sun from a temperature of 10°C to 20°C. Find the work -6 -1 3 done (in J) by the aluminum if the linear expansion coefficient is 24 × 10 (°C) . (The density of aluminum is 2.7 × 10 3 5 2 kg/m and 1 atm = 1.0 × 10 N/m .) a. 287 b. 425 c. 213 Copyright Cengage Learning. Powered by Cognero.

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d. 710 e. 626 ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 19.4 Work in Thermodynamic Processes 5

32. A gas expands from A to B as shown in the graph. Calculate the work (in joules) done by the gas. (1 atm = 1.01 × 10 2 N/m .)

a. 12 b. 24 c. 1.21 × 106 d. 2.42 × 106 e. 3.64 × 106 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.4 Work in Thermodynamic Processes 33. In an adiabatic free expansion a. no heat is transferred between a system and its surroundings. b. the pressure remains constant. c. the temperature remains constant. d. the volume remains constant. e. the process is reversible.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.5 The First Law of Thermodynamics 34. In an isothermal process a. the volume remains constant. b. the temperature remains constant. c. no heat is transferred between a system and its surroundings. d. the pressure remains constant.

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e. the internal energy is not constant.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.5 The First Law of Thermodynamics 35. In an isobaric process a. the volume remains constant. b. the temperature remains constant. c. the pressure remains constant. d. no heat is transferred between a system and its surroundings. e. the internal energy is constant.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.5 The First Law of Thermodynamics 36. In an isovolumetric process a. the temperature remains constant. b. no heat is transferred between a system and its surroundings. c. the pressure remains constant. d. the volume remains constant. e. the internal energy is constant.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.5 The First Law of Thermodynamics 37. Determine the work done by 5 moles of an ideal gas that is kept at 100°C in an expansion from 1 liter to 5 liters. a. 2.5 × 104 J b. 1.1 × 104 J c. 6.7 × 103 J d. 2.9 × 103 J e. 8.4 × 103 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 19.5 The First Law of Thermodynamics 38. Five moles of an ideal gas expand isothermally at 100°C to five times its initial volume. Find the heat flow into the system. a. 2.5 × 104 J b. 1.1 × 104 J c. 6.7 × 103 J Copyright Cengage Learning. Powered by Cognero.

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d. 2.9 × 103 J e. 7.0 × 102 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 19.5 The First Law of Thermodynamics 39. An 8 000-kg aluminum flagpole 100-m high is heated by the Sun from a temperature of 10°C to 20°C. Find the -6 -1 increase in internal energy (in J) of the aluminum. (The coefficient of linear expansion is 24 × 10 (°C) , the density is 3 3 2.7 × 10 kg/m , and the specific heat of aluminum is 0.215 cal/g⋅ °C.) a. 7.2 × 105 b. 7.2 × 107 c. 7.2 × 103 d. 7.2 × 101 e. 7.2 × 102 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 19.5 The First Law of Thermodynamics 40. Two kilograms of water at 100°C is converted to steam at 1 atm. Find the work done (in J). (The density of steam at 3 100°C is 0.598 kg/m .) a. 3.4 × 105 b. 1.2 × 105 c. 4.6 × 104 d. 2.1 × 104 e. 3.4 × 104 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 19.5 The First Law of Thermodynamics 41. Two kilograms of water at 100°C is converted to steam at 1 atm. Find the change in internal energy (in J). (Lv = 2.26 × 6 10 J/kg.) a. 2.1 × 104 b. 4.5 × 106 c. 3.4 × 105 d. 4.2 × 106 e. 2.1 × 106 ANSWER: POINTS:

d 2

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DIFFICULTY: Average REFERENCES: 19.5 The First Law of Thermodynamics 42. Which statement below regarding the first law of thermodynamics is most correct? a. A system can do work externally only if its internal energy decreases. b. The internal energy of a system that interacts with its environment must change. c. No matter what other interactions take place, the internal energy must change if a system undergoes a heat transfer. d. The only changes that can occur in the internal energy of a system are those produced by non-mechanical forces. e. The internal energy of a system cannot change if the heat transferred to the system is equal to the work done by the system.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.5 The First Law of Thermodynamics 6

5

43. A gas expands as shown in the graph. If the heat taken in during this process is 1.02 × 10 J and 1 atm = 1.01 × 10 2 N/m , the change in internal energy of the gas (in J) is

a. −2.42 × 106 b. −1.40 × 106 c. −1.02 × 106 d. 1.02 × 106 e. 1.40 × 106 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 19.5 The First Law of Thermodynamics 44. In a thermodynamic process, the internal energy of a system in a container with adiabatic walls decreases by 800 J. Which statement is correct? a. The system lost 800 J by heat transfer to its surroundings. b. The system gained 800 J by heat transfer from its surroundings. c. The system performed 800 J of work on its surroundings. d. The surroundings performed 800 J of work on the system. e. The 800 J of work done by the system was equal to the 800 J of heat transferred to the system from its Copyright Cengage Learning. Powered by Cognero.

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surroundings.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.5 The First Law of Thermodynamics 45. Which of the following statements is(are) correct when an ideal gas goes from an initial to a final state in a single process? a. No work is done on or by the gas when the volume remains constant. b. No energy is transferred into or out of the gas as heat transfer when the temperature remains constant. c. The internal energy of the gas does not change when the pressure remains constant. d. All the statements above are correct. e. Only statements (a) and (b) above are correct.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.5 The First Law of Thermodynamics 46. In an isothermal process a. P is constant. b. V is constant. c. is constant. d. PV is constant. e. is constant.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.5 The First Law of Thermodynamics 2

47. The R value of fiberglass batting, 3.5 inches thick, is 11 ft ⋅ °F⋅ h/BTU. What is the thermal conductivity (in BTU/ft⋅ °F⋅ s)? a. 7.4 × 10-6 b. 2.7 × 10-2 c. 8.9 × 10-5 d. 1.4 × 10-4 e. 3.6 × 10-3 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 48. A slab of concrete and an insulating board are in thermal contact with each other. The temperatures of their outer Copyright Cengage Learning. Powered by Cognero.

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surfaces are 68°F and 50°F. Determine the rate of heat transfer (in BTU/ft ⋅ h) if the R values are 1.93 and 8.7 2 ft ⋅ °F⋅ h/BTU, respectively. a. 9.7 b. 2.5 c. 5.3 d. 1.7 e. 28 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 49. A wall is constructed of a 2-inch layer of fiberglass board (R = 8) and six inches of fiberglass batting (R = 19). If the temperature on the outside surface of the fiberglass board is 50°F and the temperature on the inside surface of the 2 fiberglass batting is 68°F, what is the temperature (in °F) at the interface? (The units of R are ft ⋅ °F⋅ h/BTU.) a. 62 b. 58 c. 55 d. 65 e. 52 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 50. A cup of coffee is enclosed on all sides in an insulated container ½-cm thick in the shape of a cube 10 cm on a side.

The temperature of the coffee is 95°C, and the temperature of the surroundings is 21°C. Find the rate of heat loss (in J/s) -4 due to conduction if the thermal conductivity of the cup is 2 × 10 cal/s⋅ cm⋅ °C. a. 62 b. 74 c. 230 d. 160 e. 12 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 2

51. A child has a temperature of 101°F. If her total cross-sectional area is 2 m , find the energy lost each second (in W) due to radiation, assuming the emissivity is 1. (Assume the room temperature is 70°F.) a. 217 b. 180 c. 90 d. 68 e. 850 ANSWER: a Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 52. A super-insulated house is at a temperature of 20°C. The temperature outside is 0°C. The surface area of the house is 2 200 m , and the emissivity is 1. Approximately how much energy is radiated (in W) per second? a. 20 000 b. 2 000 c. 200 d. 2 e. 0.2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 53. For an astronaut working outside a spaceship, the greatest loss of heat would occur by means of a. conduction. b. convection. c. radiation. d. conduction and convection. e. conduction and radiation.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 54. If a person in Alaska were locked out of his house on a day when the temperature outside was −40°C, his thick clothing would mostly reduce the loss of thermal energy by a. conduction. b. convection. c. radiation. d. all of the above. e. convection and radiation.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 17

21

3

55. The Earth intercepts 1.27 × 10 W of radiant energy from the Sun. Suppose the Earth, of volume 1.08 × 10 m , was composed of water. How long would it take for the Earth at 0°C to reach 100°C, if none of the energy was radiated or reflected back out into space? a. 26.9 y b. 113 y c. 2.69 × 104 y d. 1.13 × 105 y Copyright Cengage Learning. Powered by Cognero.

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e. 2.69 × 107 y ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 56. Beryl states that insulation with the smallest possible thermal conductivity is best to keep a house warm in winter, but worst for keeping a house cool in summer. Sapphire insists the reverse is true: low thermal conductivity is good in the summer, but bad in the winter. Which one, if either is correct? a. Beryl, because low thermal conductivity results in low heat transfer. b. Beryl, because low thermal conductivity results in high heat transfer. c. Sapphire, because low thermal conductivity results in low heat transfer. d. Sapphire, because low thermal conductivity results in high heat transfer. e. Neither, because low heat transfer is desirable both in summer and in winter.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 57. The R-value of an insulating material is the thickness of the material divided by its thermal conductivity. When an insulating material consists of three layers with R-values R1, R2, and R3, the overall R-value of the insulation is given by a. R = R1 + R2 + R3. b. . c. . d. . e. .

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 2

58. Aluminum rod #1 is 1.0 m long with cross-section area 2.0 cm . Aluminum rod #2 is 2.0 m long with cross-section 2 2 area 4.0 cm . Aluminum rod #3 is 3.0 m long with cross-section area 9.0 cm . If each rod has the same temperature difference applied across its ends, which rod has the greatest rate of transfer of energy between its ends? a. #1 b. #2 c. #3 d. #2 = #3, both greater than #1 e. They each have the same rate.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 59. A styrofoam container used as a picnic cooler contains a block of ice at 0°C. If 225 grams of ice melts in 1 hour, how 5 much heat energy per second is passing through the walls of the container? (The heat of fusion of ice is 3.33 × 10 J/kg).

ANSWER: 20.8 J (per second) POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes 60. Star A has a radius of 200 000 km and a surface temperature of 6 000 K. Star B has a radius of 400 000 km and a surface temperature of 3 000 K. The emissivity of both stars is the same. What is the ratio of the rate of energy radiated by Star A to that of Star B? ANSWER: 4 POINTS: 2 DIFFICULTY: Average REFERENCES: 19.6 Energy Transfer Mechanisms in Thermal Processes

3

1. A container having a volume of 1.0 m holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, what is the total energy of the system? a. 2.0 × 104 J b. 2.5 × 104 J c. 1.7 × 103 J d. 1.5 × 103 J e. 4.0 × 104 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas 3

2. A container having a volume of 1.0 m holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, what is the average kinetic energy per molecule? a. 6.7 × 10-20 J b. 1.0 × 10-21 J c. 1.0 × 10-20 J d. 6.7 × 10-21 J e. 1.3 × 10-20 J ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas Copyright Cengage Learning. Powered by Cognero.

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3. What is the average kinetic energy of a nitrogen molecule at room temperature (20°C)? a. 2 × 10-21 J b. 4 × 10-21 J c. 6 × 10-21 J d. 8 × 10-21 J e. 1 × 10-20 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas 4. What is the approximate average translational speed of a nitrogen molecule at room temperature (20°C) in m/s? a. 100 b. 500 c. 300 d. 700 e. 200 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas 21

5. Suppose a box contains about 5.0 × 10 hydrogen atoms at room temperature (21°C). Determine the thermal energy of these atoms. a. 10 J b. 20 J c. 30 J d. 5.0 J e. 1.0 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas 6. Five gas molecules are found to have speeds of 100, 200, 300, 400, and 500 m/s. What is the rms speed (in m/s)? a. 390 b. 300 c. 360 d. 330 e. 320 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas Copyright Cengage Learning. Powered by Cognero.

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7. The internal energy of n moles of an ideal gas depends on a. one state variable T. b. two state variables T and V. c. two state variables T and P. d. three state variables T, P and V. e. four variables R, T, P and V. ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.1 Molecular Model of an Ideal Gas 8. A molecule in a uniform ideal gas can collide with other molecules when their centers are equal to or less than a. one radius away from its center. b. one diameter away from its center. c. two diameters away from its center. d. twice the cube root of volume away from its center. e. diameters away from its center.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.1 Molecular Model of an Ideal Gas 9. Which of the following gives the average molecular translational kinetic energy of a molecule in an ideal gas? a. kBT b.

RT c. kBT d.

RT e. kBT, where n = number of internal degrees of freedom.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.1 Molecular Model of an Ideal Gas 10. Which statement below is NOT an assumption made in the molecular model of an ideal gas? a. The average separation between molecules is large compared with the dimensions of the molecules. b. The molecules undergo inelastic collisions with one another. c. The forces between molecules are short range. d. The molecules obey Newton's laws of motion.

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e. Any molecule can move in any direction with equal probability.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.1 Molecular Model of an Ideal Gas 11. Consider a thin, horizontal layer of the atmosphere, of thickness dy, of area A, with pressure P on the bottom, with an average mass m per molecule, and nV molecules per unit volume. Which of the following gives dP, the magnitude of the difference of the pressure at the top and bottom of the layer? a. mgdy b. mgnVdy c. mgAdy d. mgnVAdy e. mgnVAPdy ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas 12. The temperature of a quantity of an ideal gas is a. one measure of its ability to transfer thermal energy to another body. b. proportional to the average molecular kinetic energy of the molecules. c. proportional to the internal energy of the gas. d. correctly described by all the statements above. e. correctly described only by (a) and (b) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.1 Molecular Model of an Ideal Gas 13. The root-mean-square speed of a gas molecule is greater than the average speed, because the former gives a greater weight to a. lighter molecules. b. heavier molecules. c. lower speeds. d. higher speeds. e. more probable speeds.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.1 Molecular Model of an Ideal Gas 14. If the rms speed of helium atoms is vrms,He at temperature T, what is the rms speed of CO2 at the same temperature? a. b.

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c. d. e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas 15. A 50-gram sample of dry ice (solid CO2) is placed in a 4-liter container. The system is sealed and allowed to reach room temperature (20°C). By approximately how much does the pressure inside the container increase when the dry ice turns to gas? (Ignore the initial volume of the sample.)

ANSWER: the pressure increases by about 7 atm POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas 16. During the volcanic eruption of Mt. Pelee in 1902, an incredibly hot "burning cloud" rolled down the mountain and incinerated the town of Saint-Pierre. From the damage done, the temperature in the cloud was estimated at 700°C. If the air temperature was 20°C and a mole of air is 29 grams, estimate the molecular weight of the gas in the "burning cloud" that made it heavier than the surrounding air. (As a follow-on, estimate the most probable composition of the cloud. Some typical volcanic gases are H2S, SO2, H2SO4, CO2, NO.) ANSWER: 96, H2SO4 (sulfuric acid) POINTS: 2 DIFFICULTY: Average REFERENCES: 20.1 Molecular Model of an Ideal Gas 4

17. Find the specific heat (in cal/mole K) of a gas kept at constant volume when it takes 1.0 × 10 J of heat to raise the temperature of 5.0 moles of the gas 200 K above the initial temperature. a. 7.5 b. 5.0 c. 2.4 d. 10 e. 20 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 20.2 Molar Specific Heat of an Ideal Gas 18. The molar specific heat at constant volume at 0°C of an ideal monatomic gas is a. . b. R. c. .

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d. 2R. e. .

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.2 Molar Specific Heat of an Ideal Gas 19. What is the molar specific heat at constant volume at 0°C of an ideal diatomic gas? a. b. R c. d. 2R e.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.2 Molar Specific Heat of an Ideal Gas 20. What is the molar specific heat at constant pressure at 0°C of an ideal monatomic gas? a. b. R c. d. 2R e.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.2 Molar Specific Heat of an Ideal Gas 21. Why is the specific heat of an ideal gas at constant pressure is greater than the specific heat of an ideal gas at constant volume? a. work is done by a gas at constant pressure. b. work is done by a gas at constant volume. c. no work is done by a gas at constant pressure. d. the temperature remains constant for a gas at constant pressure. e. the temperature remains constant for a gas at constant volume.

ANSWER: a Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.2 Molar Specific Heat of an Ideal Gas 22. If CP for an ideal gas is 35.4 J/mol⋅ K, which of the following is CV for this gas? a. 12.5 J/mol⋅ K b. 20.8 J/mol⋅ K c. 29.1 J/mol⋅ K d. 27.1 J/mol⋅ K e. 43.4 J/mol⋅ K ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 20.2 Molar Specific Heat of an Ideal Gas 23. How much energy does each degree of freedom contribute to each molecule in the system (an ideal gas), according to the theorem of equipartition of energy? a. b. c. d. e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.3 The Equipartition of Energy 24. Two tanks of gas, one of hydrogen, H2, and one of helium, He, contain equal numbers of moles of gas. The grammolecular mass of He is twice that of H2. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion? a. The total internal energy of the hydrogen is the same as that of the helium. b. The total internal energy of the hydrogen is 1.4 times that of the helium. c. The total internal energy of the helium is 1.4 times that of the hydrogen. d. The total internal energy of the hydrogen is 1.67 times that of the helium. e. The total internal energy of the helium is 1.67 times that of the hydrogen.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 20.3 The Equipartition of Energy Copyright Cengage Learning. Powered by Cognero.

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25. Two tanks of gas, one of hydrogen, H2, and one of helium, He, contain equal masses of gas. The gram-molecular mass of He is twice that of H2. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion? a. The total internal energy of the hydrogen is the same as that of the helium. b. The total internal energy of the hydrogen is 167 times that of the helium. c. The total internal energy of the helium is 1.67 times that of the hydrogen. d. The total internal energy of the hydrogen is 3.33 times that of the helium. e. The total internal energy of the helium is 3.33 times that of the hydrogen.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 20.3 The Equipartition of Energy 26. If the total translational kinetic energy of the molecules of oxygen in a container is 15 J at room temperature, what is the total rotational kinetic energy of these molecules? a. 5 J b. 10 J c. 20 J d. 25 J e. 0 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 20.3 The Equipartition of Energy 3

27. The air in an automobile engine at 20°C is compressed from an initial pressure of 1.0 atm and a volume of 200 cm to 3 a volume of 20 cm . Find the temperature if the air behaves like an ideal gas (γ = 1.4) and the compression is adiabatic. a. 730°C b. 460°C c. 25°C d. 50°C e. 20°C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 20.4 Adiabatic Processes for an Ideal Gas 28. During an adiabatic compression, a volume of air decreases to 1/4 its original size. Calculate its final pressure if its original pressure was 1 atm. (Assume the air behaves like an ideal gas with γ = 1.4.) a. 7.0 atm b. 5.6 atm c. 3.5 atm d. 2.2 atm e. 0.14 atm ANSWER: a Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 20.4 Adiabatic Processes for an Ideal Gas 29. An ideal gas is allowed to expand adiabatically until its volume increases by 50%. By approximately what factor is the pressure reduced? (γ = 5/3.) a. 1.5 b. 2.0 c. 2.5 d. 3.0 e. 3.5 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 20.4 Adiabatic Processes for an Ideal Gas 30. When we say that the speed of sound is measured under adiabatic conditions, we assume that a. the time associated with heat conduction is slow relative to the speed of the wave. b. no heat can flow between the system and its surroundings. c. the speed of the wave is directly proportional to the bulk modulus. d. the speed of the wave is proportional to the square root of the bulk modulus. e. air is an ideal gas.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.4 Adiabatic Processes for an Ideal Gas 31. Assume 3.0 moles of a diatomic gas has an internal kinetic energy of 10 kJ. Determine the temperature of the gas after it has reached equilibrium. a. 270 K b. 160 K c. 800 K d. 1 550 K e. 400 K ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 20.4 Adiabatic Processes for an Ideal Gas γ

32. The relation PV = nRT holds for all ideal gases. The additional relation PV holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: "∝" means "is proportional to".)

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a.

Isotherm:

; Adiabat:

: A is both an isotherm and an adiabat.

Isotherm:

; Adiabat:

: B is an isotherm, A is an adiabat.

Isotherm:

; Adiabat:

: A is an isotherm, B is an adiabat.

Isotherm:

; Adiabat:

: B is both an isotherm and an adiabat.

b.

c.

d.

e. cannot answer without additional information about the starting temperature.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 20.4 Adiabatic Processes for an Ideal Gas 33. One mole of helium gas expands adiabatically from 2 atm pressure to 1 atm pressure. If the original temperature of the gas is 20°C, what is the final temperature of the gas? (γ = 1.67) ANSWER: 222 K POINTS: 3 DIFFICULTY: Challenging REFERENCES: 20.4 Adiabatic Processes for an Ideal Gas 34. Air expands adiabatically (no heat in, no heat out) from T = 300 K and P = 100 atm to a final pressure of 1 atm. Treat the gas as ideal with γ = 1.4, and determine the final temperature. Compare your result to the boiling points of nitrogen (77.4 K) and oxygen (90.2 K). Could this method result in the liquification of air?

ANSWER: 80.5 K, some oxygen would liquify POINTS: 3 DIFFICULTY: Challenging REFERENCES: 20.4 Adiabatic Processes for an Ideal Gas 35. According to kinetic theory, a typical gas molecule in thermal equilibrium at room temperature has a kinetic energy K -21 -27 = 6.00 × 10 J, regardless of mass. Estimate the speed at room temperature of a hydrogen molecule H2 (m = 3.34 × 10 -25 -23 kg) and a xenon atom (m = 2.00 × 10 kg). [kB = 1.38 × 10 J/K] ANSWER: 1 895 m/s, 245 m/s POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 20.5 Distribution of Molecular Speeds

1. A gasoline engine absorbs 2 500 J of heat and performs 1 000 J of mechanical work in each cycle. The efficiency of the engine is what? a. 80% b. 40% c. 60% d. 20% e. 50% ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 21.1 Heat Engines and the Second Law of Thermodynamics 2. A gasoline engine absorbs 2 500 J of heat and performs 1 000 J of mechanical work in each cycle. The amount of heat expelled in each cycle is what? a. 1 000 J b. 1 500 J c. 2 000 J d. 500 J e. 3 000 J ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.1 Heat Engines and the Second Law of Thermodynamics 3. A new electric power plant has an efficiency of 42%. For every 100 barrels of oil needed to run the turbine, how many are essentially lost as waste heat (in barrels of oil) to the environment? a. 21 b. 42 c. 58 d. 10 e. 79 ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.1 Heat Engines and the Second Law of Thermodynamics 4. An 800-MW electric power plant has an efficiency of 30%. It loses its waste heat in large cooling towers.

Approximately how much waste heat (in MJ) is discharged to the atmosphere per second? a. 1 200 b. 1 900 c. 800 d. 560 e. 240 Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 21.1 Heat Engines and the Second Law of Thermodynamics 5. A homeowner has a new oil furnace which has an efficiency of 60%. For every 100 barrels of oil needed to heat his house, how much (in barrels of oil) goes up the chimney as waste heat? a. 20 b. 60 c. 40 d. 80 e. 10 ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.1 Heat Engines and the Second Law of Thermodynamics 6. An engine is designed to obtain energy from the temperature gradient of the ocean. What is the thermodynamic efficiency of such an engine if the temperature of the surface of the water is 59°F (15°C) and the temperature well below the surface is 41°F (5°C)? a. 3.5% b. 67% c. 31% d. 17% e. 96% ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 21.1 Heat Engines and the Second Law of Thermodynamics 7. The thermal efficiency of a heat engine is given by a. . b. . c. . d. all of the formulas above. e. only (a) or (b) above.

ANSWER: e POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 21.1 Heat Engines and the Second Law of Thermodynamics 8. A heat pump has a coefficient of performance of 4. If the heat pump absorbs 20 cal of heat from the cold outdoors in each cycle, the heat expelled (in cal) to the warm indoors is what? a. 34 b. 27 c. 36 d. 40 e. 80 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 21.2 Heat Pumps and Refrigerators 9. A refrigerator has a coefficient of performance of 4. If the refrigerator absorbs 30 cal of heat from the cold reservoir in each cycle, the heat expelled (in cal) into the heat reservoir is what? a. 40.5 b. 37.5 c. 36.5 d. 34.5 e. 22.5 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 21.2 Heat Pumps and Refrigerators 10. On a cold day, a heat pump absorbs heat from the outside air at 14°F (−10°C) and transfers it into a home at a temperature of 86°F (30°C). Determine the maximum κ of the heat pump. a. 0.2 b. 4.4 c. 0.5 d. 7.6 e. 6.7 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 21.2 Heat Pumps and Refrigerators 11. One kilogram of chilled water at 32°F (0°C) is placed in a freezer which is kept at 0°F (−18°C). Approximately how much electric energy (in kilocalories) is needed to operate the compressor to cool this water to 0°F if the room 5 3 temperature is maintained at 75°F (24°C)? (Lice = 3.33 × 10 J/kg; cice = 2.09 × 10 J/kg⋅ °C) a. 13 b. 1.5 c. 15 d. 16 e. 33 ANSWER: c Copyright Cengage Learning. Powered by Cognero.

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POINTS: 3 DIFFICULTY: Challenging REFERENCES: 21.2 Heat Pumps and Refrigerators 12. One kilogram of chilled water (0°C) is placed in a freezer which is kept at 0°F (−18°C). Approximately how much electric energy (in kilocalories) is needed just to freeze the water if the room temperature is maintained at 75°F (24°C)?

(Lice = 333 J/g; cice = 209 J/g⋅ °C.) a. 11 b. 15 c. 16 d. 13 e. 33 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 21.2 Heat Pumps and Refrigerators 13. A vessel containing 5.0 kg of water at 10°C is put into a refrigerator. The 1/7 HP motor (1 HP = 746 W) runs for 5.0 minutes to cool the liquid to the refrigerator's low temperature, 0°C. What is the κ of the refrigerator? a. 5.7 b. 4.6 c. 6.5 d. 7.2 e. 3.6 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.2 Heat Pumps and Refrigerators 14. A heat engine absorbs 2 500 J of heat from a hot reservoir and expels 1 000 J to a cold reservoir. When it is run in reverse, with the same reservoirs, the engine pumps 2 500 J of heat to the hot reservoir, requiring 1 500 J of work to do so.

Find the ratio of the work done by the heat engine to the work done by the pump. Is the heat engine reversible? a. 1.0 (no) b. 1.0 (yes) c. 1.5 (yes) d. 1.5 (no) e. 2.5 (no) ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 21.3 Reversible and Irreversible Processes 15. Which of the following is an almost reversible process? a. The explosion of hydrogen and oxygen to form water. b. Heat transfer through thick insulation. c. The adiabatic free expansion of a gas. d. A slow isothermal compression of a gas.

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e. A slow leakage of gas into an empty chamber through a small hole in a membrane.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.3 Reversible and Irreversible Processes 16. An adiabatic free expansion of a gas in a thermally isolated container is not reversible because a. work must be done on the gas to return it to its original volume. b. heat must be exchanged with the surroundings to return the gas to its original temperature. c. its internal energy has a greater value after the expanded gas is returned to its original volume and temperature. d. of all of the above. e. of (a) and (b) above only.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.3 Reversible and Irreversible Processes 17. A steam engine is operating at its theoretical maximum efficiency of 60%. If the waste heat has a temperature of 100°F (38°C), what is the temperature of the boiler? a. 350°C b. 94°C c. 225°C d. 504°C e. 775°C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 21.4 The Carnot Engine 18. A company that produces pulsed gas heaters claims their efficiency is approximately 90%. If an engine operates between 250°C and 25°C, what is its maximum thermodynamic efficiency? a. 83% b. 65% c. 43% d. 90% e. 56% ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.4 The Carnot Engine 19. An automobile engine operates with an overall efficiency of 12%. How much energy is delivered as waste heat (in gallons of gasoline) for each 10 gallons of fuel burned? a. 1.2 b. 8.8 c. 6.5 Copyright Cengage Learning. Powered by Cognero.

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d. 4.7 e. 7.5 ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.4 The Carnot Engine 20. By operating a reversible heat engine with an ideal gas as the working substance in a Carnot cycle and measuring the ratio Qc/Qh, we can calculate a. n, the number of moles of the ideal gas. b. the ratio Vc/Vh of the volumes of the ideal gas. c. the ratio Pc/Ph of the pressures of the ideal gas. d. the ratio PcVc/PhVh of the products of volumes and pressures of the ideal gas. e. the value of Avogadro's number.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.4 The Carnot Engine 21. An ideal heat engine can have an efficiency of 1 if the temperature of the low temperature reservoir is a. 0 K. b. 0°C. c. 0°F. d. 0°R. e. the same as the temperature of the heat source.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.4 The Carnot Engine 22. A Carnot cycle, operating as a heat engine, consists, in the order given, of a. an isothermal expansion, an isothermal compression, an adiabatic expansion, and an adiabatic compression. b. an adiabatic expansion, an adiabatic compression, an isothermal expansion, and an isothermal compression. c. an isothermal expansion, an adiabatic compression, an isothermal compression, and an adiabatic expansion. d. an adiabatic compression, an isothermal compression, an isothermal expansion, and an adiabatic expansion. e. an isothermal expansion, an adiabatic expansion, an isothermal compression, and an adiabatic compression.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.4 The Carnot Engine 23. All real engines are less efficient than the Carnot engine because a. they do not operate through the Otto cycle. b. they do not operate through a reversible cycle. c. the working substance does not maintain a constant volume through the cycle.

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d. the working substance does not maintain a constant pressure through the cycle. e. the working substance does not maintain a constant temperature through the cycle.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.4 The Carnot Engine 24. In a nuclear power plant, the reactor produces 500°C steam that is used to power the steam turbines which generate 1 500 MW of electrical power. The cooling tower eliminates the waste heat at 50°C. If the efficiency of the plant were that of a Carnot engine, at what rate would waste heat be vented to the atmosphere?

ANSWER: 1080 MW POINTS: 2 DIFFICULTY: Average REFERENCES: 21.4 The Carnot Engine 25. A lawn mower has a 6-horsepower engine (1 HP = 750 W). If the engine has an efficiency of 20%, and the throttle is such that the engine cycles 10 times a second, the heat that is expelled in one cycle is what? a. 1 800 J b. 2 000 J c. 2 200 J d. 2 400 J e. 2 250 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 21.5 Gasoline and Diesel Engines 26. In an engine operating in the Otto cycle, the final volume of the fuel-air mixture is one sixth the initial volume.

Assume γ = 1.4. The maximum theoretical efficiency of this cycle, in per cent, is a. 17. b. 49. c. 51. d. 56. e. 83.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.5 Gasoline and Diesel Engines 27. For a gas of N identical molecules of molecular volume Vm in total volume V at temperature T, the number of ways of locating the N molecules in the volume is a. . b. .

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c. . d. . e. .

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.6 Entropy 28. For a pair of dice, how many microstates are there that result in the macrostate of rolling a 7? a. 1 b. 5 c. 6 d. 7 e. 36 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.6 Entropy 29. What is the probability of rolling either a 7 or 11 on a single roll of a pair of dice? a. 1/6 b. 2/9 c. 3/8 d. 1/3 e. 1/2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 21.6 Entropy 30. Suppose there are 3 molecules in a container. If each molecule has a 1-in-2 chance of being in the left half of the container, what is the probability that there are exactly 2 molecules in the left half of the container? a. 1/2 b. 1/3 c. 1/8 d. 3/8 e. 3/5 ANSWER: d POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 21.6 Entropy 31. Exactly 500 grams of ice are melted at a temperature of 32°F. (Lice = 333 J/g.) The change in entropy (in J/K) is a. 321 b. 146 c. 512 d. 610 e. 5 230 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 32. When water of mass m and specific heat c is heated from absolute temperature T1 to absolute temperature T2, its change in entropy is what? a. cm ln(T2/T1) b. cm (T2/T1) c. cm (T2 − T1)/T1 d. cm (T2 − T1)/T2 e. cm (T2 − T1)/(T2 + T1) ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 33. The change in entropy of 1.00 kg of water that is heated from 50°C to 100°C is (in cal/K) what? a. 516 b. 312 c. 144 d. 946 e. 391 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 34. The change in entropy of a mass m of a solid substance which has a latent heat of fusion L and melts at a temperature T is what? a. LT/m b. mL ln(T) c. mLT d. mL/T e. L/mT ANSWER: d Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.7 Entropy in Thermodynamic Systems 35. Since Lice = 333 J/g, the change in entropy (in cal/K) when 1.00 kg of ice melts is what? a. 144 b. 291 c. 312 d. 516 e. 80 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 36. If n moles of an ideal gas are compressed isothermally from an initial volume V1 to a final volume V2, the change in entropy is what? a. nR ln (V2/V1) b. nRT ln (V2/V1) c. nkB ln (V2/V1) d. e. n Cv/T ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 37. Determine the change in entropy (in J/K) when 5.00 moles of an ideal gas at 0°C are compressed isothermally from an 3 3 initial volume of 100 cm to a final volume of 20 cm . a. −191 b. −52 c. −71 d. −67 e. −208 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 38. An ideal gas is allowed to undergo a free expansion. If its initial volume is V1 and its final volume is V2, the change in entropy is what? a. nR ln (V2/V1) b. nRT ln (V2/V1) Copyright Cengage Learning. Powered by Cognero.

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c. nk ln (V2/V1) d. 0 e. nR V2/V1 ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.7 Entropy in Thermodynamic Systems 39. Find the change in entropy (in J/K) when 5.00 moles of an ideal gas undergo a free expansion from an initial volume 3 3 of 20 cm to a final volume of 100 cm . a. 71 b. 52 c. 67 d. 191 e. 208 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 40. An ideal gas is allowed to expand adiabatically. Assume the process is reversible. The change in entropy is what? a. 0 b. nR ln (V2/V1) c. nR ln (T2/T1) d. kn ln (V2/V1) e. kn ln (T2/T1) ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.7 Entropy in Thermodynamic Systems 41. Find the change in entropy (in J/K) when 5.00 moles of an ideal monatomic gas are allowed to expand isobarically 3 3 from an initial volume of 20 cm to a final volume of 100 cm . a. 167 b. 100 c. 67 d. 52 e. 152 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 42. Ten kilograms of water at 0°C is mixed with 10 kg of water at 100°C. The change in entropy (in cal/K) of the system is what?

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a. 1 000 b. 480 c. −720 d. 240 e. −168 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 21.7 Entropy in Thermodynamic Systems 43. A vessel containing 10 kg of water is left out where it evaporates. If the temperature remains constant at 20°C, what is the change in entropy (in kcal/K)? (The latent heat of vaporization at 20°C is 585 cal/g.) a. 30 b. 10 c. 20 d. 40 e. 290 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 44. A gasoline engine absorbs 2 500 J of heat at 250°C and expels 2 000 J at a temperature of 50°C. The magnitude of the change in entropy (in J/K) for the system is what? a. 6.2 b. 4.7 c. 1.4 d. 10.9 e. 3.2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 45. 100 grams of molten lead (600°C) is used to make musket balls. If the lead shot is allowed to cool to room temperature (21°C), what is the change in entropy (in J/K) of the lead? (For the specific heat of molten and solid lead use 4 1.29 J/g⋅ °C; the latent heat of fusion and the melting point of lead are 2.45 × 10 J/kg and 327°C, respectively.) a. −145 b. −252 c. −302 d. −429 e. −100 ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 21.7 Entropy in Thermodynamic Systems Copyright Cengage Learning. Powered by Cognero.

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46. The reason that we can calculate the change in entropy of a system is that a. entropy always decreases. b. entropy always increases. c. the entropy of the universe always remains constant. d. it depends only on the properties of the initial and final equilibrium states. e. systems always follow reversible paths.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.7 Entropy in Thermodynamic Systems 47. The change in entropy when 1 kg of ice melts at 0°C is (in J/K) what? (Lice = 333 J/g) a. 335. b. 603. c. 1 220. d. 1 310. e. 2 160.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems

48. Selena states that

adiabatic free expansion. Ron says

proves that entropy has a definite value at the beginning and end of an

, where W is the number of microstates of a given

macrostate. Which one, if either, is correct? a. Only Selena, because entropy can depend only on macroscopic variables. b. Only Ron, because entropy can depend only on microscopic variables. c.

Only Selena, because

in an adiabatic free expansion.

d. Neither, because we cannot calculate changes in entropy in an adiabatic free expansion. e. Both, because entropy, which is macroscopic is a function of microscopic disorder.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.7 Entropy in Thermodynamic Systems 49. For the same temperature increase in a system, the change in entropy, ΔS, is largest in a reversible a. constant-volume process.

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b. constant-pressure process. c. adiabatic process. d. process in which no heat is transferred. e. process in which no work is performed.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 50. A 4.00-liter container is divided into two equal parts, one part containing 0.0100 mole of neon, and the other part containing 0.0100 mole of helium. The divider is removed and the gases mix. What is the change in entropy (in J/K) of this system? a. 0.057 6 b. 0.115 c. 0.173 d. 0.086 4 e. 0.144 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 3

51. Every second at Niagara Falls, some 5 000 m of water falls a distance of 50 m. What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).

ANSWER: 8 360 kJ/K POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 52. One end of a copper rod is in thermal contact with a hot reservoir at T = 500 K and the other end is in thermal contact with a cooler reservoir at T = 300 K. Find the entropy change of each reservoir, and the total entropy change, when 8 000 J of heat energy are conducted from one end of the rod to the other with no change in the temperature distribution in the rod.

ANSWER: −16.0 J/K, +26.7 J/K, +10.7 J/K POINTS: 2 DIFFICULTY: Average REFERENCES: 21.7 Entropy in Thermodynamic Systems 53. A violation of the second law of thermodynamics would occur if a. a ball lying on the ground started to bounce. b. transfer of energy by heat moved energy from an object at low temperature to an object at a higher temperature. c. a refrigerator heated the air in the room in which the refrigerator is located. d. any of the above occurred. e. (a) or (b) occurred, but not (c).

ANSWER: e POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 21.8 Entropy and the Second Law 54. A violation of the second law of thermodynamics would occur if a. a ball lying on the ground started to bounce. b. transfer of energy by heat moved energy from an object at low temperature to an object at a higher temperature. c. a motion picture was run backwards through the projector. d. any of the above occurred. e. (a) or (b) occurred, but not (c).

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.8 Entropy and the Second Law 55. Which answer below is not a statement of the second law of thermodynamics? a. Real processes proceed in a preferred direction. b. Energy does not flow spontaneously by heat from a cold to a hot reservoir. c. The entropy of the universe increases in all natural processes. d. In theory, heat engines working in a cycle employ reversible processes. e. You cannot construct a heat engine operating in a cycle that does nothing but take heat from a reservoir and perform an equal amount of work.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 21.8 Entropy and the Second Law

1. Rubber rods charged by rubbing with cat fur repel each other. Glass rods charged by rubbing with silk repel each other.

A rubber rod and a glass rod charged respectively as above attract each other. A possible explanation is that a. any two rubber rods charged this way have opposite charges on them. b. any two glass rods charged this way have opposite charges on them. c. a rubber rod and a glass rod charged this way have opposite charges on them. d. all rubber rods always have an excess of positive charge on them. e. all glass rods always have an excess of negative charge on them.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.1 Properties of Electric Charges 2. Three pith balls supported by insulating threads hang from a support. We know that ball X is positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that a. Y has a negative charge. b. Z has a negative charge. c. Y has a positive charge. d. Z has a positive charge.

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e. Z is neutral (has no net charge.)

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.1 Properties of Electric Charges 3. Three pith balls supported by insulating threads hang from a support. We know that ball X is positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that a. Y has a negative charge. b. Z has a negative charge. c. Y has a positive charge. d. Z is neutral (has no net charge.) e. Y is negatively charged or neutral (has no net charge.)

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.1 Properties of Electric Charges 4. Enrico says that positive charge is created when you rub a glass rod with silk, and that negative charge is simply the absence of positive charge. Rosetta says that negative charge is created and that positive charge is the absence of positive charge. (She has heard that Ben Franklin should have reversed the signs he associated with the charges.) Which one, if either, is correct? a. Enrico, because there really is only one kind of charge. b. Rosetta, because there really is only one kind of charge. c. Neither: although no charge is present originally, both types of charge are created through friction. d. Both: only one type of charge is created by friction at any one time. e. Neither: both negative and positive charge are present simultaneously in all solid materials on Earth and the process described involves a transfer of charge, not the creation of charge.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.1 Properties of Electric Charges 5. Three originally uncharged infinite parallel planes are arranged as shown. Then the upper plate has surface charge density σ placed on it while the lower plate receives surface charge density −σ. The net charge induced on the center plate is

a. 0. b. −σ/2. c. +σ/2. d. −σ. e. +σ.

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ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.2 Charging Objects by Induction 6. An uncharged metal sphere is placed on an insulating puck on a frictionless table. While being held parallel to the table, a rod with a charge q is brought close to the sphere, but does not touch it. As the rod is brought in, the sphere a. remains at rest. b. moves toward the rod. c. moves away from the rod. d. moves perpendicular to the velocity vector of the rod. e. moves upward off the puck.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.2 Charging Objects by Induction 7. A small metal sphere is suspended from the conducting cover of a conducting metal ice bucket by a non-conducting thread. The sphere is given a negative charge before the cover is placed on the bucket. The bucket is tilted by means of a non-conducting material so that the charged sphere touches the inside of the bucket. Which statement is correct? a. The negative charge remains on the metal sphere. b. The negative charge spreads over the outside surface of the bucket and cover. c. The negative charge spreads over the inside surface of the bucket and cover. d. The negative charge spreads equally over the inside and outside surfaces of the bucket and cover. e. The negative charge spreads equally over the sphere and the inside and outside surfaces of the bucket and cover.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.2 Charging Objects by Induction 8. Each of two small, non-conducting spheres is charged positively, the combined charge being 40 μC. When the two spheres are 50 cm apart, each sphere is repelled from the other by a force of magnitude 2.0 N. Determine the magnitude of the smaller of the two charges. a. 1.4 μC b. 1.1 μC c. 2.0 μC d. 3.3 μC e. 17 μC ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.3 Coulomb’s Law 9. A particle (charge = +40 μC) is located on the x axis at the point x = −20 cm, and a second particle (charge = −50 μC) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = −4.0 μC) placed at the origin (x = 0)?

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a. 41 N b. 16 N c. 56 N d. 35 N e. 72 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 10. In the figure, if Q = 30 μC, q = 5.0 μC, and d = 30 cm, what is the magnitude of the electrostatic force on q?

a. 15 N b. 23 N c. zero d. 7.5 N e. 38 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 11. A charge of +80 μC is placed on the x axis at x = 0. A second charge of −50 μC is placed on the x axis at x = 50 cm.

What is the magnitude of the electrostatic force on a third charge of 4.0 μC placed on the x axis at x = 30 cm? a. 13 N b. 77 N c. 39 N d. 25 N e. 45 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 12. Three point charges are positioned on the x axis. If the charges and corresponding positions are +32 μC at x = 0, +20 μC at x = 40 cm, and −60 μC at x = 60 cm, what is the magnitude of the electrostatic force on the +32-μC charge? a. 84 N b. 12 N c. 36 N d. 50 N e. 48 N ANSWER: b POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 13. A particle (m = 50 g, q = 5.0 μC) is released from rest when it is 50 cm from a second particle (Q = −20 μC).

Determine the magnitude of the initial acceleration of the 50-g particle. a. 54 m/s2 b. 90 m/s2 c. 72 m/s2 d. 65 m/s2 e. 36 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 14. A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, −Q, is placed at x = 3.0 m. If Q = 40 μC, what is the magnitude of the electrostatic force on a 30-μC charge placed at the origin? a. 7.2 N b. 3.9 N c. 1.5 N d. 14 N e. 8.1 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 15. A point charge Q is placed on the x axis at x = −2.0 m. A second point charge, −Q, is placed at x = 1.0 m. If Q = 60 μC, what is the magnitude of the electrostatic force on a 40-μC charge placed at the origin? a. 16 N b. 27 N c. 32 N d. 11 N e. 3.0 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 16. A point charge Q is placed on the x axis at the origin. An identical point charge is placed on the x axis at x = −1.0 m and another at x = +1.0 m. If Q = 40 μC, what is the magnitude of the electrostatic force on the charge at x = +1.0 m? a. 29 N b. 14 N c. 11 N d. 18 N Copyright Cengage Learning. Powered by Cognero.

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e. 7.0 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 17. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = −80 nC, and q = 36 nC in the figure, what is the magnitude of the electric force on q?

a. 5.0 N b. 4.4 N c. 3.8 N d. 5.7 N e. 0.60 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 18. If a = 3.0 mm, b = 4.0 mm, Q1 = −60 nC, Q2 = 80 nC, and q = 30 nC in the figure, what is the magnitude of the electric force on q?

a. 1.4 N b. 1.0 N c. 1.7 N d. 2.0 N e. 0.50 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 19. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 24 nC in the figure, what is the magnitude of the electric force on q?

a. 2.7 N Copyright Cengage Learning. Powered by Cognero.

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b. 1.9 N c. 2.3 N d. 1.5 N e. 0.52 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 20. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 32 nC in the figure, what is the magnitude of the electric force on q?

a. 1.6 N b. 1.3 N c. 1.9 N d. 2.2 N e. 0.040 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 21. Three point charges, two positive and one negative, each having a magnitude of 20 μC are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on the negative charge? a. 80 N b. 40 N c. 69 N d. 57 N e. 75 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 22. Three point charges, two positive and one negative, each having a magnitude of 20 μC are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on one of the positive charges? a. 69 N b. 40 N Copyright Cengage Learning. Powered by Cognero.

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c. 80 N d. 57 N e. 20 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 23. A point charge Q is placed at the origin. A second charge, 2Q, is placed on the x axis at x = −3.0 m. If Q = 50 μC, what is the magnitude of the electrostatic force on a third point charge, −Q, placed on the y axis at y = +4.0 m? a. 2.5 N b. 3.0 N c. 3.7 N d. 4.4 N e. 1.8 N ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.3 Coulomb’s Law 24. Three identical point charges Q are placed at the vertices of an equilateral triangle (length of each side = 2.0 m). If Q = 60 μC, what is the magnitude of the electrostatic force on any one of the charges? a. 25 N b. 19 N c. 14 N d. 22 N e. 16 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 25. Identical point charges Q are placed at each of the four corners of a 3.0 m × 4.0 m rectangle. If Q = 40 μC, what is the magnitude of the electrostatic force on any one of the charges? a. 3.0 N b. 2.4 N c. 1.8 N d. 3.7 N e. 2.0 N ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.3 Coulomb’s Law 26. A point charge (−5.0 μC) is placed on the x axis at x = 4.0 cm, and a second charge (+5.0 μC) is placed on the x axis at x = −4.0 cm. What is the magnitude of the electric force on a third charge (+2.5 μC) placed on the y axis at y = 3.0 cm? a. 90 N Copyright Cengage Learning. Powered by Cognero.

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b. 45 N c. 54 N d. 72 N e. 36 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 27. If Q = 25 μC, q = 10 μC, and L = 40 cm in the figure, what is the magnitude of the electrostatic force on q?

a. 28 N b. 22 N c. 20 N d. 14 N e. 10 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 28. If Q = 20 μC and L = 60 cm, what is the magnitude of the electrostatic force on any one of the charges shown?

a. 25 N b. 19 N c. 15 N d. 9.1 N e. 14 N ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.3 Coulomb’s Law

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29. Two charged particles, Q1 and Q2, are a distance r apart with Q2 = 5Q1. Compare the forces they exert on one another when

is the force Q2 exerts on Q1 and

a.

=5

b.

=

d. e.

.

= −5

c.

5

is the force Q1 exerts on Q2.

. .

=−

.

=

.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.3 Coulomb’s Law

30. The symbol

appears in Coulomb's law because we use independently defined units for

a. force and distance. b. charge and distance. c. distance and force. d. force, distance and electric charge. e. charge.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.3 Coulomb’s Law 31. Two tiny metal spheres are fixed to the ends of a non-conducting string of length . Equal charges, +q, are placed on the metal spheres. Randall says that the force on the string has magnitude

string has magnitude

. Tilden says that the tension in the

. Which one, if either, is correct?

a.

Randall, because both charges exert forces on the string, but the tension is

.

Tilden, because both charges exert forces on the string, but the net force is

.

b.

c. Both are correct, because both charges exert forces on the string. d.

Neither is correct, because both the tension and the force have magnitude Copyright Cengage Learning. Powered by Cognero.

.

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e.

Neither is correct, because the tension is

, but the net force is 0.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.3 Coulomb’s Law 32. Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00-m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the force on any one of the charges is

a. 1.88 × 10−2. b. 3.25 × 10−2. c. 3.73 × 10−2. d. 6.50 × 10−2. e. 7.50 × 10−2.

ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.3 Coulomb’s Law 33. Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00-m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the tension in any one of the strings is

a. 1.88 × 10−2. b. 3.25 × 10−2. c. 3.75 × 10−2. d. 6.50 × 10−2. e. 7.50 × 10−2.

ANSWER: POINTS:

b 3

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DIFFICULTY: Challenging REFERENCES: 22.3 Coulomb’s Law 34. Three 2.50-μC charges are placed on tiny conducting spheres at the ends of 1.00-m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the force on the knot at the center is

a. 0. b. 3.75 × 10−2. c. 5.63 × 10−2. d. 6.50 × 10−2. e. 7.50 × 10−2.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.3 Coulomb’s Law 35. An alpha particle (charge = +2e) is sent at high speed toward a gold nucleus (charge +79e). What is the electrical force -14 -19 acting on the alpha particle when it is at a distance of 2 × 10 m away from the gold nucleus? (e = 1.6 × 10 C) ANSWER: 91 N POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law 36. Imagine for a minute that the Moon is held in its orbit about the Earth by electrical forces rather than by gravitation.

What electrical charges −Q on the Earth and +Q on the Moon are necessary to hold the Moon in a circular orbit with a 22 period of 27.3 days? The Earth-Moon distance is 384 000 km and the mass of the Moon is 7.35 × 10 kg.

13 ANSWER: Q = 5.73 × 10 C POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.3 Coulomb’s Law 37. At the point of fission, a nucleus of U-238, with 92 protons is divided into two smaller spheres, each with 46 protons -15 and a radius of 5.9 × 10 m. What is the repulsive force pushing the two spheres apart when they are just touching one -25 another? (The mass of the U-238 nucleus is 3.98 × 10 kg.)

ANSWER: 3 500 N POINTS: 2 DIFFICULTY: Average REFERENCES: 22.3 Coulomb’s Law Copyright Cengage Learning. Powered by Cognero.

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38. If a = 60 cm, b = 80 cm, Q = −4.0 nC, and q = 1.5 nC, what is the magnitude of the electric field at point P?

a. 68 N/C b. 72 N/C c. 77 N/C d. 82 N/C e. 120 N/C ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 39. If a = 60 cm, b = 80 cm, Q = −6.0 nC, and q = 4.0 nC, what is the magnitude of the electric field at point P?

a. 35 N/C b. 42 N/C c. 52 N/C d. 64 N/C e. 104 N/C ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 40. If a = 60 cm, b = 80 cm, Q = −6.0 nC, and q = 6.0 nC, what is the magnitude of the electric field at point P in the figure?

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a. 65 N/C b. 55 N/C c. 60 N/C d. 52 N/C e. 67 N/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 41. If a = 60 cm, b = 80 cm, Q = −6.0 nC, and q = 3.0 nC in the figure, what is the magnitude of the electric field at point P?

a. 71 N/C b. 56 N/C c. 60 N/C d. 53 N/C e. 67 N/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric)

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42. If Q = 16 nC, a = 3.0 m, and b = 4.0 m, what is the magnitude of the electric field at point P?

a. 33 N/C b. 31 N/C c. 24 N/C d. 19 N/C e. 13 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 43. If Q = 80 nC, a = 3.0 m, and b = 4.0 m in the figure, what is the magnitude of the electric field at point P?

a. 45 N/C b. 70 N/C c. 29 N/C d. 47 N/C e. 92 N/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 44. A +2.0-nC point charge is placed at one corner of a square (1.5 m on a side), and a −3.0-nC charge is placed on a corner diagonally away from the first charge. What is the magnitude of the electric field at either of the two unoccupied corners? a. 20 N/C b. 14 N/C c. 4.0 N/C d. 12 N/C e. 8.0 N/C Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 45. A +15-nC point charge is placed on the x axis at x = 1.5 m, and a −20-nC charge is placed on the y axis at y = −2.0m.

What is the magnitude of the electric field at the origin? a. 105 N/C b. 15 N/C c. 75 N/C d. 45 N/C e. 60 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 46. A +20-nC point charge is placed on the x axis at x = 2.0 m, and a −25-nC point charge is placed on the y axis at y = −3.0 m. What is the direction of the electric field at the origin? a. 209° b. 61° c. 29° d. 241° e. 151° ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 47. A charge Q is placed on the x axis at x = +4.0 m. A second charge q is located at the origin. If Q = +75 nC and q = −8.0 nC, what is the magnitude of the electric field on the y axis at y = +3.0 m? a. 19 N/C b. 23 N/C c. 32 N/C d. 35 N/C e. 21 N/C ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 48. A charge of 80 nC is uniformly distributed along the x axis from x = 0 to x = 2.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 8.0 m. a. 30 N/C b. 15 N/C c. 48 N/C d. 90 N/C Copyright Cengage Learning. Powered by Cognero.

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e. 60 N/C ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 49. A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m. a. 81 N/C b. 74 N/C c. 61 N/C d. 88 N/C e. 20 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 50. A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle.

What is the magnitude of the electric field at the center of the circle along which the arc lies? a. 81 N/C b. 61 N/C c. 71 N/C d. 51 N/C e. 25 N/C ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 51. Charge of uniform density 4.0 nC/m is distributed along the x axis, from x = −2.0 m to x = +3.0 m. What is the magnitude of the electric field at the point x = +5.0 m on the x axis? a. 16 N/C b. 13 N/C c. 19 N/C d. 26 N/C e. 5.0 N/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 52. A uniformly charged rod (length = 2.0 m, charge per unit length = 5.0 nC/m) is bent to form one quadrant of a circle.

What is the magnitude of the electric field at the center of the circle? a. 62 N/C b. 56 N/C c. 50 N/C Copyright Cengage Learning. Powered by Cognero.

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d. 44 N/C e. 25 N/C ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 53. A uniformly charged rod (length = 2.0 m, charge per unit length = 3.0 nC/m) is bent to form a semicircle. What is the magnitude of the electric field at the center of the circle? a. 64 N/C b. 133 N/C c. 48 N/C d. 85 N/C e. 34 N/C ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 54. A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +10 m on the x axis? a.

b.

c.

d.

e. none of these ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 55. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the y component of the electric field at y = 4 m on the y axis? a.

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b.

c.

d.

e. none of these ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 56. A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis? a.

b.

c.

d.

e. none of these ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 57. A uniform linear charge of 3.0 nC/m is distributed along the y axis, from y = −3 m to y = 2 m. Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis? a.

b.

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c.

d.

e. none of these ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 58. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the x component of the electric field at y = 2 m on the y axis? a.

b.

c.

d.

e. none of these ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 59. A rod (length = 2.0 m) is uniformly charged and has a total charge of 40 nC. What is the magnitude of the electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the rod? a. 40 N/C b. 45 N/C c. 24 N/C d. 90 N/C e. 36 N/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 60. A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m. What is the magnitude of the electric field at the origin?

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a. 18 N/C b. 50 N/C c. 30 N/C d. 15 N/C e. 90 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 61. A 24-nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +8 m on the x axis? a.

b.

c.

d.

e. none of these ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 62. A uniform linear charge density of 7.0 nC/m is distributed along the y axis from y = 2 m to y = 5 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at y = 0 on the y axis? a.

b.

c.

d.

e. none of these Copyright Cengage Learning. Powered by Cognero.

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ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 63. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. What is the x component of the electric field at y = 2 m on the y axis? a. −5.0 N/C b. −4.0 N/C c. −5.7 N/C d. −6.2 N/C e. −9.0 N/C ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 64. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given

by Ex = 2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vy = 50 m/s, vx = vz = 0, what is the speed of the particle at t = 2.0 s? a. 81 m/s b. 72 m/s c. 64 m/s d. 89 m/s e. 25 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 65. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given

by Ex = −5.5 N/C, Ey = Ez = 0. If the position and velocity of the particle at t = 0 are given by x = y = z = 0 and vx = 50 m/s, vy = vz = 0, what is the distance from the origin to the particle at t = 2.0 s? a. 60 m b. 28 m c. 44 m d. 12 m e. 88 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 66. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given

by Ex = −2.3 N/C, Ey = Ez = 0. If the position and velocity of the particle at t = 0 are given by x = y = z = 0 and vz = 20 m/s, vx = vy = 0, what is the distance from the origin to the particle at t = 2.0 s?

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a. 60 m b. 54 m c. 69 m d. 78 m e. 3.2 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 67. A particle (q = 3.0 mC, m = 20 g) has a speed of 20 m/s when it enters a region where the electric field has a constant magnitude of 80 N/C and a direction which is the same as the velocity of the particle. What is the speed of the particle 3.0 s after it enters this region? a. 68 m/s b. 44 m/s c. 56 m/s d. 80 m/s e. 36 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 68. A particle (q = 4.0 mC, m = 50 g) has a velocity of 25 m/s in the positive x direction when it first enters a region where the electric field is uniform (60 N/C in the positive y direction). What is the speed of the particle 5.0 s after it enters this region? a. 49 m/s b. 35 m/s c. 32 m/s d. 44 m/s e. 24 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 69. A charge of 50-μC is placed on the y axis at y = 3.0 cm and a 77-μC charge is placed on the x axis at x = 4.0 cm. If both charges are held fixed, what is the magnitude of the initial acceleration of an electron released from rest at the origin? a. 1.2 × 1020 m/s2 b. 1.5 × 1020 m/s2 c. 1.0 × 1020 m/s2 d. 1.8 × 1020 m/s2 e. 2.0 × 1020 m/s2 ANSWER: POINTS:

a 3

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DIFFICULTY: Challenging REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 70. The velocity of a particle (m = 10 mg, q = −4.0 μC) at t = 0 is 20 m/s in the positive x direction. If the particle moves in a uniform electric field of 20 N/C in the positive x direction, what is the particle's speed at t = 5.0 s? a. 60 m/s b. 20 m/s c. 45 m/s d. 40 m/s e. 70 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 71. A particle (m = 20 mg, q = −5.0 μC) moves in a uniform electric field of 60 N/C in the positive x direction. At t = 0, the particle is moving 25 m/s in the positive x direction and is passing through the origin. How far is the particle from the origin at t = 2.0 s? a. 80 m b. 20 m c. 58 m d. 10 m e. 30 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 72. A particle (m = 20 mg, q = −5.0 μC) moves in a uniform electric field of 60 N/C in the positive x direction. At t = 0, the particle is moving 30 m/s in the positive x direction and is passing through the origin. Determine the maximum distance beyond x = 0 the particle travels in the positive x direction. a. 25 m b. 20 m c. 15 m d. 30 m e. 60 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 73. Charge Q is distributed uniformly along a semicircle of radius a. Which formula below gives the correct magnitude of the electric field at the center of the circle? a. .

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b. . c. . d. . e. .

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 74. Charge Q is distributed uniformly along a semicircle of radius a. Which formula below gives the correct magnitude of the force on a particle of charge q located at the center of the circle? a. . b. . c. . d. . e. .

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 75. Suppose a uniform electric field of 4 N/C is in the positive x direction. When a charge is placed at and fixed to the origin, the resulting electric field on the x axis at x = 2 m becomes zero. What is the magnitude of the electric field at x = 4 m on the x axis at this time? a. 0 b. 1 N/C c. 2 N/C d. 4 N/C e. More information is needed to find the resulting field magnitude at this position.

ANSWER: c Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 76. Two uniform rods, each of length 2.0 m, are bent to form semicircles. One rod has a charger per unit length of 1.5 nC/m, and the other has a charge per unit length of –1.5 nC/m. The semicircles are joined to make a circle. What is the magnitude of the electric field at the center of the circle? a. 42 N/C b. 84 N/C c. 34 N/C d. 68 N/C e. 0 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) -31

77. The electron gun in a television tube accelerates electrons (mass = 9.11 × 10 7 to 3.00 × 10 m/s within a distance of 2.00 cm. What electric field is required?

ANSWER: 128 000 N/C POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric)

kg, charge = 1.60 × 10

-19

C) from rest

4

78. A proton moving at 3 × 10 m/s is projected at an angle of 30° above a horizontal plane. If an electric field of 400 N/C is directed downwards, how long does it take the proton to return to the horizontal plane? (HINT: Ignore gravity.) [mproton -27 -19 = 1.67 × 10 kg, qproton = +1.6 × 10 C.] −7 ANSWER: 7.8 × 10 s POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 79. The nucleus of a hydrogen atom, a proton, sets up an electric field. The distance between the proton and electron is -11 about 5.1 × 10 m. What is the magnitude of the electric field at this distance from the proton? [The charge on the proton -19 is +1.6 × 10 C.] 11 ANSWER: 5.5 × 10 N/C POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 80. A 40-μC charge is positioned on the x axis at x = 4.0 cm. Where should a −60-μC charge be placed to produce a net electric field of zero at the origin? a. −5.3 cm b. 5.7 cm c. 4.9 cm d. −6.0 cm Copyright Cengage Learning. Powered by Cognero.

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e. +6.0 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 22.4 Analysis Model: Particle in a Field (Electric) 81. When gravitational, magnetic and any forces other than static electric forces are not present, electric field lines in the space surrounding a charge distribution show a. the directions of the forces that exist in space at all times. b. only the directions in which static charges would accelerate when at points on those lines c. only the directions in which moving charges would accelerate when at points on those lines. d. tangents to the directions in which either static or moving charges would accelerate when passing through points on those lines. e. the paths static or moving charges would take.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.5 Electric Field Lines 82. Which one of the diagrams below is not a possible electric field configuration for a region of space which does not contain any charges? a. b. c. d. e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.5 Electric Field Lines 83. Two identical pith balls supported by insulating threads hang side by side and close together, as shown below.

One is positively charged; the other is neutral. We can conclude that a. all field lines leaving the positively charged pith ball end on the neutral pith ball. b. some of the field lines leaving the positively charged pith ball end on the neutral pith ball. c. none of the field lines leaving the positively charged pith ball end on the neutral pith ball. d. positive charge is transferred along the field lines until both balls have equal charges. e. positive charge is transferred along the field lines until both balls hang along vertical lines.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.5 Electric Field Lines Copyright Cengage Learning. Powered by Cognero.

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84. Two imaginary spherical surfaces, of radius R and 2R, respectively, surround a positive point charge Q located at the center of the concentric spheres. When compared to the number of field lines N1 going through the sphere of radius R, the number of electric field lines N2 going through the sphere of radius 2R is a. . b. . c. N2 = N1. d. N2 = 2N1. e. N2 = 4N1.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.5 Electric Field Lines 85. In a diagram of charges and electric field lines charge has twelve field lines going outward from it and charge has three field lines going into it. If one of the charges is 100 nC, what is the other one? a. 25 nC b. 100 nC c. –25 nC d. –100 nC e. Both answers b and c can be correct.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.5 Electric Field Lines 86. A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field is uniform and is given

by Ex = −2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vx = 80 m/s, vy = vz = 0, what is the speed of the particle at t = 2.0 s? a. 40 m/s b. 20 m/s c. 60 m/s d. 80 m/s e. 180 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 22.6 Motion of a Charged Particle in a Uniform Electric Field 87. Charge Q is uniformly distributed over a line segment of length 2L, as shown below. When the x-coordinate of point P is x, the magnitude of the y-component of the electric field at point P is

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a. 0. b. . c. . d. . e. .

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.6 Motion of a Charged Particle in a Uniform Electric Field 88. When a positive charge q is placed in the field created by two other charges Q1 and Q2, each a distance r away from q, the acceleration of q is a. in the direction of the charge Q1 or Q2 of smaller magnitude. b. in the direction of the charge Q1 or Q2 of greater magnitude. c. in the direction of the negative charge if Q1 and Q2 are of opposite sign. d. in the direction of the positive charge if Q1 and Q2 are of opposite sign. e. in a direction determined by the vector sum of the electric fields of Q1 and Q2.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.6 Motion of a Charged Particle in a Uniform Electric Field 89. A positively charged particle is moving in the +y-direction when it enters a region with a uniform electric field pointing in the +x-direction. Which of the diagrams below shows its path while it is in the region where the electric field exists. The region with the field is the region between the plates bounding each figure. The field lines always point to the right. The x-direction is to the right; the y-direction is up. a. b. c. d. e.

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ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.6 Motion of a Charged Particle in a Uniform Electric Field 90. A negatively charged particle is moving in the +x-direction when it enters a region with a uniform electric field pointing in the +x-direction. Which graph gives its position as a function of time correctly? (Its initial position is x = 0 at t = 0.) a. b. c. d. e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 22.6 Motion of a Charged Particle in a Uniform Electric Field

1. Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in the region between the two planes has magnitude

. The electric field in the region to the left of A and the electric field in the region to the

right of B may have the magnitudes a. 0, 0. b. , . c. ,

.

d. given in any answer above. e. given only in answer (a) or (b) above.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.2 Electric Field of a Continuous Charge Distribution 2. Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in region I to the left of plane A has magnitude

and points to the left. The electric field in the region to the right of B has magnitude

and points to the right. The electric field in the region between the two planes has magnitude

and points to the right.

The surface charge densities on planes A and B, respectively, are a. , σ.

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b. c. d.

, σ. σ,

.

σ,

.

e. 2σ, σ.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 23.2 Electric Field of a Continuous Charge Distribution 3. A uniform electric field

is present in the region between the infinite parallel planes of charge A and B, and a uniform

electric field is present in the region between the infinite parallel planes of charge B and C. When the planes are vertical and the fields are both non-zero, a. and are both directed to the right. b. c. d.

and

are both directed to the left.

points to the right and

to the left.

points to the left and

to the right.

e. Any one of the above is possible.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.2 Electric Field of a Continuous Charge Distribution 4. A uniform electric field field

is present in the region between infinite parallel plane plates A and B and a uniform electric

is present in the region between infinite parallel plane plates B, and C. When the plates are vertical,

to the right and

is directed

to the left. The signs of the charges on plates A, B and C may be

a. −, −, −. b. +, −, −. c. +, −, +. d. +, +, +. e. any one of the above.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.2 Electric Field of a Continuous Charge Distribution 5. Three infinite planes of charge, A, B, and C, are vertical and parallel to one another. There is a uniform electric field Copyright Cengage Learning. Powered by Cognero.

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to the left of plane A and a uniform electric field

to the right of plane C. The field

points to the left and the field

points to the right. The signs of the charges on plates A, B, and C may be a. −, −, −. b. +, −, −. c. +, −, +. d. +, +, +. e. any one of the above.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.2 Electric Field of a Continuous Charge Distribution 6. The nucleus of lead-208,

, has 82 protons within a sphere of radius 6.34 × 10

-15

. Each electric charge has a value

-19

of 1.60 × 10 C. Assuming that the protons create a spherically symmetric distribution of charge, calculate the electric field at the surface of the nucleus.

21 ANSWER: 2.94 × 10 N/C POINTS: 2 DIFFICULTY: Average REFERENCES: 23.2 Electric Field of a Continuous Charge Distribution 7. A Geiger counter is like an electroscope that discharges whenever ions formed by a radioactive particle produce a conducting path. A typical Geiger counter consists of a thin conducting wire of radius 0.002 cm stretched along the axis of -10 a conducting cylinder of radius 2.0 cm. The wire and the cylinder carry equal and opposites charges of 8.0 × 10 C all along their length of 10.0 cm. What is the magnitude of the electric field at the surface of the wire?

6 ANSWER: 7.2 × 10 N/C POINTS: 2 DIFFICULTY: Average REFERENCES: 23.2 Electric Field of a Continuous Charge Distribution 8. Two charges of 15 pC and −40 pC are inside a cube with sides that are of 0.40-m length. Determine the net electric flux through the surface of the cube. a. +2.8 N ⋅ m2/C b. −1.1 N ⋅ m2/C c. +1.1 N ⋅ m2/C d. −2.8 N ⋅ m2/C e. −0.47 N ⋅ m2/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 9. The total electric flux through a closed cylindrical (length = 1.2 m, diameter = 0.20 m) surface is equal to −5.0 N ⋅ 2 m /C. Determine the net charge within the cylinder.

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a. −62 pC b. −53 pC c. −44 pC d. −71 pC e. −16 pC ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 10. Charges q and Q are placed on the x axis at x = 0 and x = 2.0 m, respectively. If q = −40 pC and Q = +30 pC, determine the net flux through a spherical surface (radius = 1.0 m) centered on the origin. a. −9.6 N ⋅ m2/C b. −6.8 N ⋅ m2/C c. −8.5 N ⋅ m2/C d. −4.5 N ⋅ m2/C e. −1.1 N ⋅ m2/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 11. A uniform linear charge density of 4.0 nC/m is distributed along the entire x axis. Consider a spherical (radius = 5.0 cm) surface centered on the origin. Determine the electric flux through this surface. a. 68 N ⋅ m2/C b. 62 N ⋅ m2/C c. 45 N ⋅ m2/C d. 79 N ⋅ m2/C e. 23 N ⋅ m2/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 3

12. A uniform charge density of 500 nC/m is distributed throughout a spherical volume (radius = 16 cm). Consider a cubical (4.0 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface. a. 7.1 N ⋅ m2/C b. 3.6 N ⋅ m2/C c. 12 N ⋅ m2/C d. 19 N ⋅ m2/C e. 970 N ⋅ m2/C ANSWER:

b

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POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 13. A point charge +Q is located on the x axis at x = a, and a second point charge −Q is located on the x axis at x = −a. A Gaussian surface with radius r = 2a is centered at the origin. The flux through this Gaussian surface is a. zero, because the negative flux over one hemisphere is equal to the positive flux over the other. b. greater than zero. c. zero, because at every point on the surface the electric field has no component perpendicular to the surface. d. zero, because the electric field is zero at every point on the surface. e. none of the above.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.3 Electric Flux 2

14. The xy plane is "painted" with a uniform surface charge density which is equal to 40 nC/m . Consider a spherical surface with a 4.0-cm radius that has a point in the xy plane as its center. What is the electric flux through that part of the spherical surface for which z > 0? a. 14 N ⋅ m2/C b. 11 N ⋅ m2/C c. 17 N ⋅ m2/C d. 20 N ⋅ m2/C e. 23 N ⋅ m2/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 15. A long cylinder (radius = 3.0 cm) is filled with a nonconducting material which carries a uniform charge density of 1.3 3 μC/m . Determine the electric flux through a spherical surface (radius = 2.0 cm) which has a point on the axis of the cylinder as its center. a. 5.7 N ⋅ m2/C b. 4.9 N ⋅ m2/C c. 6.4 N ⋅ m2/C d. 7.2 N ⋅ m2/C e. 15 N ⋅ m2/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 2

16. Charge of uniform surface density (4.0 nC/m ) is distributed on a spherical surface (radius = 2.0 cm). What is the total electric flux through a concentric spherical surface with a radius of 4.0 cm?

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a. 2.8 N ⋅ m2/C b. 1.7 N ⋅ m2/C c. 2.3 N ⋅ m2/C d. 4.0 N ⋅ m2/C e. 9.1 N ⋅ m2/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 3

17. A charge of uniform volume density (40 nC/m ) fills a cube with 8.0-cm edges. What is the total electric flux through the surface of this cube? a. 2.9 N ⋅ m2/C b. 2.0 N ⋅ m2/C c. 2.6 N ⋅ m2/C d. 2.3 N ⋅ m2/C e. 1.8 N ⋅ m2/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 18. A charge of 0.80 nC is placed at the center of a cube that measures 4.0 m along each edge. What is the electric flux through one face of the cube? a. 90 N ⋅ m2/C b. 15 N ⋅ m2/C c. 45 N ⋅ m2/C d. 23 N ⋅ m2/C e. 64 N ⋅ m2/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 19. A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface? a. πR2E b. 4πR2E/3 c. 2πR2E/3 d. πR2E/2 e. πR2E/3 Copyright Cengage Learning. Powered by Cognero.

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ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.3 Electric Flux 20. Two concentric, imaginary, spherical surfaces of radius R and 2R, respectively, surround a positive point charge Q located at the center of the surfaces. When compared to the electric flux Φ1 through the surface of radius R, the electric flux Φ2 through the surface of radius 2R is a. . b. . c. Φ2 = Φ1. d. Φ2 = 2Φ1. e. Φ2 = 4Φ1.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.3 Electric Flux 21. Two concentric, imaginary, spherical surfaces of radius R and 2R, respectively, surround a negative point charge −Q located at the center of the surfaces. When compared to the electric flux Φ1 through the surface of radius R, the electric flux Φ2 through the surface of radius 2R is a. . b. . c. Φ2 = Φ1. d. Φ2 = 2Φ1. e. Φ2 = 4Φ1.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.3 Electric Flux

22. When a cube is inscribed in a sphere of radius r, the length L of a side of the cube is

. If a positive point

charge Q is placed at the center of the spherical surface, the ratio of the electric flux Φsphere at the spherical surface to the flux Φcube at the surface of the cube is a. .

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b. . c. 1. d. . e. .

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.3 Electric Flux 23. The electric flux through the two adjacent spherical surfaces shown below is known to be the same.

It is also known that there is no charge inside either spherical surface. We can conclude that a. there is no electric field present in this region of space. b. there is a constant E field present in this region of space. c. the electric flux has a constant value of zero. d. any of the above may be correct. e. only (a) and (b) above may be correct.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.3 Electric Flux 24. A constant electric field

is present throughout a region of space that includes the plane bounded by the 2

x and y axes and the lines x = 30 cm and y = 50 cm. The electric flux through the plane's surface, in N ⋅ m /C, is a. 0. b. 0.25. c. 25. d. 50. e. 100.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.3 Electric Flux 25. A constant electric field

is present throughout a region of space that includes the plane bounded by the 2

y and z axes and the lines y = 50 cm and z = 50 cm. The electric flux through the plane's surface, in N ⋅ m /C, is Copyright Cengage Learning. Powered by Cognero.

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a. 0. b. 0.25. c. 25. d. 50. e. 100.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 26. An constant electric field,

2

N/C, goes through a surface with area 2

can also be expressed as an area of 10 m with the direction of the unit vector ( the electric flux through this area? a. 24 N ⋅ m2/C

m . (This surface ). What is the magnitude of

b. 48 N ⋅ m2/C c. 0.24 N ⋅ m2/C d. 0.48 N ⋅ m2/C e. 0 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 27. A point charge is located at the origin. Centered along the x axis is a cylindrical closed surface of radius 10 cm with one end surface located at x = 2 m and the other end surface located at x = 4 m. If the magnitude of the electric flux 2 through the surface at x = 2 m is 4 N ⋅ m /C, what is the magnitude of the electric flux through the surface at x = 4 m? a. 1 N ⋅ m2/C b. 2 N ⋅ m2/C c. 4 N ⋅ m2/C d. 16 N ⋅ m2/C e. The correct value is not given.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 23.3 Electric Flux 28. Which one of the following cannot be a statement of Gauss's law for some physical situation? a. 4πr2ε0E = Q. b. 2πrLε0E = Q. c. d.

. .

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e.

.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.4 Gauss’s Law 29. Which one of the following is not an expression for electric charge? a.

b.

c.

d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.4 Gauss’s Law

30. You are told that

summed over both the surface areas of sphere A and sphere B below totals to

. You

can conclude that

a. Sphere A contains charge qin = −Q. b. Sphere B contains charge qin = −Q. c. Sphere B contains charge qin = +Q. d.

Each sphere contains charge

.

e. The sum of the charges contained in both spheres is −Q. ANSWER: e POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 23.4 Gauss’s Law

31. If we define the gravitational field a. b.

, where is a unit radial vector, then Gauss's law for gravity is

. .

c.

.

d.

.

e.

.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.4 Gauss’s Law 32. Gino says that the analog of Gauss's law for the flow of an incompressible fluid of density ρ at constant velocity

is

for an imaginary surface within the fluid. Lorenzo says that it is true only if the area where the fluid enters the surface and the area where it leaves the surface are both perpendicular to the velocity of the fluid. Which one, if either, is correct? a. Gino, because as much fluid leaves as enters. b.

Lorenzo, because is not equal to zero if the fluid enters or exits at angles other than 90°. c. Lorenzo, because this is true only when the fluid executes rotational motion. d. Gino, because it is true only when the fluid is enclosed on all sides, not when it is flowing. e. Lorenzo, because it is true only when the fluid is enclosed on all sides, not when it is flowing.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.4 Gauss’s Law 33. A student has made the statement that the electric flux through one half of a Gaussian surface is always equal and opposite to the flux through the other half of the Gaussian surface. This is a. never true. b. never false. c. true whenever enclosed charge is symmetrically located at a center point, or on a center line or centrally placed plane. d. true whenever no charge is enclosed within the Gaussian surface. e. true only when no charge is enclosed within the Gaussian surface.

ANSWER: e POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 23.4 Gauss’s Law 34. A student has made the statement that the electric flux through one half of a Gaussian surface is always equal to the flux through the other half of the Gaussian surface. This is a. never true. b. never false. c. true whenever enclosed charge is symmetrically located at a center point, on a center line, or on a centrally placed plane. d. true whenever no charge is enclosed within the Gaussian surface. e. true only when no charge is enclosed within the Gaussian surface.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.4 Gauss’s Law 35. Whitney says that Gauss's law can be used to find the electric field of a sufficiently symmetrical distribution of charge as long as over the whole Gaussian surface. Algie says that the electric field must be a constant vector over the entire Gaussian surface. Which one, if either, is correct? a. Whitney, because that means no charge is enclosed within the Gaussian surface. b.

Algie, because a constant electric field means that . c. Both, because the conditions in (a) and (b) are equivalent. d.

Neither, because the electric field can be found from Gauss's law only if of the Gaussian surface. e.

Neither, because the charge distribution must be symmetric if ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.4 Gauss’s Law 36. The electric field in the region of space shown is given by magnitude of the electric flux through the top face of the cube shown?

holds only over a portion anywhere on the surface.

N/C, where y is in m. What is the

a. 90 N ⋅ m2/C Copyright Cengage Learning. Powered by Cognero.

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b. 6.0 N ⋅ m2/C c. 54 N ⋅ m2/C d. 12 N ⋅ m2/C e. 126 N ⋅ m2/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

37. Charge of uniform surface density (0.20 nC/m ) is distributed over the entire xy plane. Determine the magnitude of the electric field at any point having z = 2.0 m. a. 17 N/C b. 11 N/C c. 23 N/C d. 28 N/C e. 40 N/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

2

38. Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m and −0.60 nC/m . What is the magnitude of the electric field at a point between the two surfaces? a. 34 N/C b. 23 N/C c. 45 N/C d. 17 N/C e. 90 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 39. Two infinite, uniformly charged, flat surfaces are mutually perpendicular. One of the sheets has a charge density of 2 2 +60 pC/m , and the other carries a charge density of −80 pC/m . What is the magnitude of the electric field at any point not on either surface? a. 1.1 N/C b. 5.6 N/C c. 7.9 N/C d. 3.8 N/C e. 4.0 N/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions Copyright Cengage Learning. Powered by Cognero.

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2

40. Charge of a uniform density (8.0 nC/m ) is distributed over the entire xy plane. A charge of uniform density (3.0 2 nC/m ) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 3.0 m. a. 0.79 kN/C b. 0.17 kN/C c. 0.62 kN/C d. 0.34 kN/C e. 0.28 kN/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

41. Charge of a uniform density (8.0 nC/m ) is distributed over the entire xy plane. A charge of uniform density (5.0 2 nC/m ) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 1.0 m. a. 0.45 kN/C b. 0.17 kN/C c. 0.28 kN/C d. 0.73 kN/C e. 0.62 kN/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

2

42. Charge of uniform density (0.30 nC/m ) is distributed over the xy plane, and charge of uniform density (−0.40 nC/m ) is distributed over the yz plane. What is the magnitude of the resulting electric field at any point not in either of the two charged planes? a. 40 N/C b. 34 N/C c. 28 N/C d. 46 N/C e. 6.0 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 3

43. A long, nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m ) distributed throughout its column. Determine the magnitude of the electric field 5.0 cm from the axis of the cylinder. a. 25 N/C b. 20 N/C c. 14 N/C d. 31 N/C Copyright Cengage Learning. Powered by Cognero.

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e. 34 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 3

44. A long, nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m ) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the axis of the cylinder. a. 20 N/C b. 27 N/C c. 16 N/C d. 12 N/C e. 54 N/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 45. Each 2.0-m length of a long cylinder (radius = 4.0 mm) has a charge of 4.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point 5.0 mm from the axis of the cylinder? a. 9.9 kN/C b. 8.1 kN/C c. 9.0 kN/C d. 7.2 kN/C e. 18 kN/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

46. A long, nonconducting cylinder (radius = 6.0 mm) has a nonuniform volume charge density given by αr , where α = 5 6.2 mC/m and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis? a. 1.4 N/C b. 1.6 N/C c. 1.8 N/C d. 2.0 N/C e. 5.4 N/C ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 47. A long, cylindrical shell (radius = 2.0 cm) has a charge uniformly distributed on its surface. If the magnitude of the electric field at a point 8.0 cm radially outward from the axis of the shell is 85 N/C, how much charge is distributed on a 2.0-m length of the charged cylindrical surface?

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a. 0.38 nC b. 0.76 nC c. 0.19 nC d. 0.57 nC e. 0.98 nC ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 48. Charge of uniform linear density (4.0 nC/m) is distributed along the entire x axis. Determine the magnitude of the electric field on the y axis at y = 2.5 m. a. 36 N/C b. 29 N/C c. 43 N/C d. 50 N/C e. 58 N/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 3

49. Charge of uniform density (80 nC/m ) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 2.0 mm from the symmetry axis. a. 7.9 N/C b. 9.0 N/C c. 5.9 N/C d. 6.8 N/C e. 18 N/C ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 3

50. Charge of uniform density (80 nC/m ) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 4.0 mm from the symmetry axis. a. 7.9 N/C b. 10 N/C c. 9.0 N/C d. 8.9 N/C e. 17 N/C ANSWER: c POINTS: 3 DIFFICULTY: Challenging Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

51. Charge of uniform density (20 nC/m ) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial 2 surface (radius = 3.0 cm) carries a uniform charge density of −12 nC/m . Determine the magnitude of the electric field at a point 2.0 cm from the symmetry axis of the two surfaces. a. 2.3 kN/C b. 1.1 kN/C c. 1.7 kN/C d. 3.4 kN/C e. 4.5 kN/C ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

52. Charge of uniform density (20 nC/m ) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial 2 surface (radius = 3.0 cm) carries a uniform charge density of −12 nC/m . Determine the magnitude of the electric field at a point 4.0 cm from the symmetry axis of the two surfaces. a. 0.45 kN/C b. 1.0 kN/C c. 0.73 kN/C d. 0.56 kN/C e. 2.3 kN/C ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

53. Charge of uniform density (40 pC/m ) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric 2 spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m . What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces? a. 3.8 N/C b. 4.1 N/C c. 3.5 N/C d. 3.2 N/C e. 0.28 N/C ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 3

54. A solid, nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m ) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the center of the sphere. a. 22 N/C b. 49 N/C c. 31 N/C Copyright Cengage Learning. Powered by Cognero.

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d. 87 N/C e. 26 N/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 55. A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) which has a charge of −8.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere? a. 1.8 × 105 N/C b. 9.0 × 104 N/C c. 3.6 × 105 N/C d. 2.7 × 105 N/C e. 7.2 × 105 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 56. A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of −2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces. a. 30 N/C b. 50 N/C c. 40 N/C d. 20 N/C e. 70 N/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 57. A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of −3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces. a. 14 N/C b. 11 N/C c. 22 N/C d. 18 N/C e. 40 N/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions Copyright Cengage Learning. Powered by Cognero.

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58. A point charge (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm), and a charge of 3.0 pC is spread uniformly upon this surface. Determine the magnitude of the electric field 1.0 cm from the point charge. a. 0.72 kN/C b. 0.45 kN/C c. 0.63 kN/C d. 0.90 kN/C e. 0.18 kN/C ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

59. Charge of uniform density (40 pC/m ) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric 2 spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m . What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces? a. 1.1 N/C b. 4.5 N/C c. 1.4 N/C d. 5.6 N/C e. 0.50 N/C ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 60. A 4.0-pC point charge is placed at the center of a hollow (inner radius = 2.0 cm, outer radius = 4.0 cm) conducting sphere which has a net charge of 4.0 pC. Determine the magnitude of the electric field at a point which is 6.0 cm from the point charge. a. 35 N/C b. 25 N/C c. 30 N/C d. 20 N/C e. 10 N/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 61. The axis of a long, hollow, metallic cylinder (inner radius = 1.0 cm, outer radius = 2.0 cm) coincides with a long wire.

The wire has a linear charge density of −8.0 pC/m, and the cylinder has a net charge per unit length of −4.0 pC/m.

Determine the magnitude of the electric field 3.0 cm from the axis. a. 5.4 N/C b. 7.2 N/C c. 4.3 N/C d. 3.6 N/C e. 2.4 N/C ANSWER: b Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 2

62. A long, straight, metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m . Determine the magnitude of the electric field 3.0 mm from the axis. a. 18 N/C b. 23 N/C c. 30 N/C d. 15 N/C e. 60 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 63. If the electric field just outside a thin conducting sheet is equal to 1.5 N/C, determine the surface charge density on the conductor. a. 53 pC/m2 b. 27 pC/m2 c. 35 pC/m2 d. 13 pC/m2 e. 6.6 pC/m2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 64. The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C. What is the charge density on the surface of the cylinder? a. 2.7 nC/m2 b. 1.8 nC/m2 c. 3.5 nC/m2 d. 4.4 nC/m2 e. 0.90 nC/m2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 65. A spherical conductor (radius = 1.0 cm) with a charge of 2.0 pC is within a concentric hollow spherical conductor (inner radius = 3.0 cm, outer radius = 4.0 cm) which has a total charge of −3.0 pC. What is the magnitude of the electric field 2.0 cm from the center of these conductors? a. 23 N/C Copyright Cengage Learning. Powered by Cognero.

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b. zero c. 45 N/C d. 90 N/C e. 110 N/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 66. A long cylindrical conductor (radius = 1.0 mm) carries a charge density of 4.0 pC/m and is inside a coaxial, hollow, cylindrical conductor (inner radius = 3.0 mm, outer radius = 4.0 mm) that has a total charge of −8.0 pC/m. What is the magnitude of the electric field 2.0 mm from the axis of these conductors? a. 24 N/C b. 18 N/C c. zero d. 36 N/C e. 226 N/C ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 67. The electric field just outside the surface of a hollow conducting sphere of radius 20 cm has a magnitude of 500 N/C and is directed outward. An unknown charge Q is introduced into the center of the sphere and it is noted that the electric field is still directed outward but has decreased to 100 N/C. What is the magnitude of the charge Q? a. 1.5 nC b. 1.8 nC c. 1.3 nC d. 1.1 nC e. 2.7 nC ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 68. A point charge of 6.0 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm, outer radius = 2.0 cm) which has a net charge of −4.0 nC. Determine the resulting charge density on the inner surface of the conducting sphere. a. +4.8 μC/m2 b. −4.8 μC/m2 c. −9.5 μC/m2 d. +9.5 μC/m2 e. −8.0 μC/m2 ANSWER: POINTS:

b 2

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DIFFICULTY: Average REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 69. A spaceship encounters a single plane of charged particles, with the charge per unit area equal to σ. The electric field a short distance above the plane has magnitude ____ and is directed ____ to the plane. a. , parallel b. , perpendicular c. , parallel d. , perpendicular e. , parallel ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions 70. A beam of electrons moves at velocity

. The number of particles per unit volume in the beam of area A is ρ. If we

imagine a cylindrical Gaussian surface of radius r and length centered on the beam, the electron flux through the surface is a. 0. b. ρvfA. c. 2ρvfA. d. ρvf(A+2πr ). e. 2ρvf(A+πr ).

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 23.5 Application of Gauss’s Law to Various Charge Distributions

1. A charged particle (q = −8.0 mC), which moves in a region where the only force acting on the particle is an electric force, is released from rest at point A. At point B, the kinetic energy of the particle is equal to 4.8 J. What is the electric potential difference VB − VA? a. −0.60 kV b. +0.60 kV c. +0.80 kV d. −0.80 kV e. +0.48 kV Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference 2. A particle (charge = 50 μC) moves in a region where the only force on it is an electric force. As the particle moves 25 cm from point A to point B, its kinetic energy increases by 1.5 mJ. Determine the electric potential difference, VB − VA. a. −50 V b. −40 V c. −30 V d. −60 V e. +15 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference 3. Points A [at (2, 3) m] and B [at (5, 7) m] are in a region where the electric field is uniform and given by N/C. What is the potential difference VA − VB? a. 33 V b. 27 V c. 30 V d. 24 V e. 11 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference 4. A particle (charge = +2.0 mC) moving in a region where only electric forces act on it has a kinetic energy of 5.0 J at point A. The particle subsequently passes through point B which has an electric potential of +1.5 kV relative to point A. Determine the kinetic energy of the particle as it moves through point B. a. 3.0 J b. 2.0 J c. 5.0 J d. 8.0 J e. 10.0 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference −27

−19

5

5. A particle (mass = 6.7 × 10 kg, charge = 3.2 × 10 C) moves along the positive x axis with a speed of 4.8 × 10 m/s. It enters a region of uniform electric field parallel to its motion and comes to rest after moving 2.0 m into the field.

What is the magnitude of the electric field? a. 2.0 kN/C Copyright Cengage Learning. Powered by Cognero.

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b. 1.5 kN/C c. 1.2 kN/C d. 3.5 kN/C e. 2.4 kN/C ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference −27

−19

6. A proton (mass = 1.67 × 10 kg, charge = 1.60 × 10 C) moves from point A to point B under the influence of an electrostatic force only. At point A, the proton moves with a speed of 50 km/s. At point B, the speed of the proton is 80 km/s. Determine the potential difference VB − VA. a. +20 V b. −20 V c. −27 V d. +27 V e. −40 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference 7. What is the speed of a proton that has been accelerated from rest through a potential difference of 4.0 kV? a. 1.1 × 106 m/s b. 9.8 × 105 m/s c. 8.8 × 105 m/s d. 1.2 × 106 m/s e. 6.2 × 105 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference -31

-19

6

8. An electron (m = 9.1 × 10 kg, q = −1.6 × 10 C) starts from rest at point A and has a speed of 5.0 × 10 m/s at point B. Only electric forces act on it during this motion. Determine the electric potential difference VA − VB. a. −71 V b. +71 V c. −26 V d. +26 V e. −140 V ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference Copyright Cengage Learning. Powered by Cognero.

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-27

-19

9. A proton (m = 1.7 × 10 kg, q = +1.6 × 10 C) starts from rest at point A and has a speed of 40 km/s at point B. Only electric forces act on it during this motion. Determine the electric potential difference VB − VA. a. +8.5 V b. −8.5 V c. −4.8 V d. +4.8 V e. −17 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference 10. A particle (m = 2.0 μg, q = −5.0 μC) has a speed of 30 m/s at point A and moves (with only electric forces acting on it) to point B where its speed is 80 m/s. Determine the electric potential difference VA − VB. a. −2.2 kV b. +1.1 kV c. −1.1 kV d. +2.2 kV e. +1.3 kV ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference -27

-19

11. An alpha particle (m = 6.7 × 10 kg, q = +3.2 × 10 C) has a speed of 20 km/s at point A and moves to point B where it momentarily stops. Only electric forces act on the particle during this motion. Determine the electric potential difference VA − VB. a. +4.2 V b. −4.2 V c. −9.4 V d. +9.4 V e. −8.4 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference 12. Which statement is always correct when applied to a charge distribution located in a finite region of space? a. Electric potential is always zero at infinity. b. Electric potential is always zero at the origin. c. Electric potential is always zero at a boundary surface to a charge distribution. d. Electric potential is always infinite at a boundary surface to a charge distribution. e. The location where electric potential is zero may be chosen arbitrarily.

ANSWER: e Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.1 Electric Potential and Potential Difference 13. The electric field in the region defined by the y-z plane and the negative x axis is given by E = −ax, where a is a constant. (There is no field for positive values of x.) As −x increases in magnitude, relative to V = 0 at the origin, the electric potential in the region defined above is a. a decreasing function proportional to −|x2|. b. a decreasing function proportional to −|x|. c. constant. d. an increasing function proportional to +|x|. e. an increasing function proportional to +|x2|.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.1 Electric Potential and Potential Difference 14. The electric field in the region defined by the y-z plane and the positive x axis is given by E = ax, where a is a constant. (There is no field for negative values of x.) As x increases in magnitude, relative to V = 0 at the origin, the electric potential in the region defined above is a. a decreasing function proportional to −|x2|. b. a decreasing function proportional to −|x|. c. constant. d. an increasing function proportional to +|x|. e. an increasing function proportional to +|x2|.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.1 Electric Potential and Potential Difference 15. In the Bohr model of the hydrogen atom, the electron circles the proton at a distance of 0.529 × 10 potential at the position of the electron.

ANSWER: 27.2 Volts POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference

-10

m. Find the

5

16. To recharge a 12-V battery, a battery charger must move 3.6 × 10 C of charge from the negative to the positive terminal. What amount of work is done by the battery charger? How many kilowatt hours is this?

ANSWER: 4.3 MJ, 1.2 kWh POINTS: 2 DIFFICULTY: Average REFERENCES: 24.1 Electric Potential and Potential Difference 17. Points A [at (3, 6) m] and B [at (8, −3) m] are in a region where the electric field is uniform and given by N/C. What is the electric potential difference VA − VB? Copyright Cengage Learning. Powered by Cognero.

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a. +60 V b. −60 V c. +80 V d. −80 V e. +50 V ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 18. A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributed uniformly on its surface. If point A is located at the center of the sphere and point B is 15 cm from the center, what is the magnitude of the electric potential difference between these two points? a. 23 V b. 30 V c. 15 V d. 45 V e. 60 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 3

19. Charge of uniform density 50 nC/m is distributed throughout the inside of a long, nonconducting cylindrical rod (radius = 5.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis). a. 2.7 V b. 2.0 V c. 2.4 V d. 1.7 V e. 3.4 V ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 3

20. Charge of uniform density 90 nC/m is distributed throughout the inside of a long, nonconducting cylindrical rod (radius = 2.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis). a. 1.9 V b. 1.4 V c. 2.2 V d. 2.8 V e. 4.0 V ANSWER: b POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 3

21. A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m . What is the magnitude of the potential difference between the center and a point 4.0 cm away? a. 12 V b. 6.8 V c. 3.0 V d. 4.7 V e. 2.2 V ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 22. Two flat conductors are placed with their inner faces separated by 6.0 mm. If the surface charge density on one of the 2 inner faces is 40 pC/m , what is the magnitude of the electric potential differences between the two conductors? a. 36 mV b. 18 mV c. 32 mV d. 27 mV e. 14 mV ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 23. An electron is released form rest in a region of space where a uniform electric field is present. Joanna claims that its kinetic and potential energies both increase as it moves from its initial position to its final position. Sonya claims that they both decrease. Which one, if either, is correct? a. Joanna, because the electron moves opposite to the direction of the field. b. Sonya, because the electron moves opposite to the direction of the field. c. Joanna, because the electron moves in the direction of the field. d. Sonya, because the electron moves in the direction of the field. e. Neither, because the kinetic energy increases while the electron moves to a point at a higher potential.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 24. Four electrons move from point A to point B in a uniform electric field as shown below. Rank the electrons in diagrams I through IV by the changes in potential energy from most positive to most negative when traveling from A to B.

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a. I = II = III = IV. b. II = III > I > IV. c. III > I = IV > II. d. II > I = IV > III. e. I > II = III > IV. ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 25. Four electrons move from point A to point B in a uniform electric field as shown below. Rank the electrons in diagrams I through IV by the changes in potential from most positive to most negative when traveling from A to B.

a. I = II = III = IV. b. II = III > I > IV. c. III > I = IV > II. d. II > I = IV > III. e. I > II = III > IV. ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field

26. An infinite plane of charge with

is tilted at a 45° angle to the vertical direction as shown below. The

potential difference, VB − VA, in volts, between points A and B, a 4.50-m distance apart, is

a. −7.06.

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b. −9.98. c. −14.11. d. +7.06. e. +9.98.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field

27. An infinite plane of charge with

is tilted at a 45° angle to the vertical direction as shown below. The

potential difference, VA − VB, in volts, between points A and B, a 4.50 m distance apart, is

a. −7.06. b. −9.98. c. −14.11. d. +7.06. e. +9.98.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 28. The gap between electrodes in a spark plug is 0.06 cm. In order to produce an electric spark in a gasoline-air mixture, 6 the electric field must reach a value of 3 × 10 V/m. What minimum voltage must be supplied by the ignition circuit when starting the car?

ANSWER: 1 800 V POINTS: 2 DIFFICULTY: Average REFERENCES: 24.2 Potential Difference in a Uniform Electric Field 29. If a = 30 cm, b = 20 cm, q = +2.0 nC, and Q = −3.0 nC in the figure, what is the potential difference VA − VB?

a. +60 V b. +72 V c. +84 V Copyright Cengage Learning. Powered by Cognero.

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d. +96 V e. +48 V ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 30. Several charges in the neighborhood of point P produce an electric potential of 6.0 kV (relative to zero at infinity) and an electric field of N/C at point P. Determine the work required of an external agent to move a 3.0-μC charge along the x axis from infinity to point P without any net change in the kinetic energy of the particle. a. 21 mJ b. 18 mJ c. 24 mJ d. 27 mJ e. 12 mJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 31. Point charges q and Q are positioned as shown. If q = +2.0 nC, Q = −2.0 nC, a = 3.0 m, and b = 4.0 m, what is the electric potential difference, VA − VB?

a. 8.4 V b. 6.0 V c. 7.2 V d. 4.8 V e. 0 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 32. Three charged particles are positioned in the xy plane: a 50-nC charge at y = 6 m on the y axis, a −80-nC charge at x = −4 m on the x axis, and a 70-nc charge at y = −6 m on the y axis. What is the electric potential (relative to a zero at infinity) at the point x = 8 m on the x axis? a. +81 V b. +48 V c. +5.8 V d. −72 V Copyright Cengage Learning. Powered by Cognero.

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e. −18 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 33. Point charges of equal magnitudes (25 nC) and opposite signs are placed on (diagonally) opposite corners of a 60-cm × 80-cm rectangle. If point A is the corner of this rectangle nearest the positive charge and point B is located at the intersection of the diagonals of the rectangle, determine the potential difference, VB − VA. a. −47 V b. +94 V c. zero d. −94 V e. +47 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 34. Identical 2.0-μC charges are located on the vertices of a square with sides that are 2.0 m in length. Determine the electric potential (relative to zero at infinity) at the center of the square. a. 38 kV b. 51 kV c. 76 kV d. 64 kV e. 13 kV ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 35. A +4.0-μC charge is placed on the x axis at x = +3.0 m, and a −2.0-μC charge is located on the y axis at y = −1.0 m.

Point A is on the y axis at y = +4.0 m. Determine the electric potential at point A (relative to zero at the origin). a. 6.0 kV b. 8.4 kV c. 9.6 kV d. 4.8 kV e. 3.6 kV ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 36. Identical 4.0-μC charges are placed on the y axis at y = ±4.0 m. Point A is on the x axis at x = +3.0 m. Determine the electric potential of point A (relative to zero at the origin). a. −4.5 kV b. −2.7 kV Copyright Cengage Learning. Powered by Cognero.

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c. −1.8 kV d. −3.6 kV e. −14 kV ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 37. Four identical point charges (+6.0 nC) are placed at the corners of a rectangle which measures 6.0 m × 8.0 m. If the electric potential is taken to be zero at infinity, what is the potential at the geometric center of this rectangle? a. 58 V b. 63 V c. 43 V d. 84 V e. 11 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 38. Three identical point charges (+2.0 nC) are placed at the corners of an equilateral triangle with sides of 2.0-m length.

If the electric potential is taken to be zero at infinity, what is the potential at the midpoint of any one of the sides of the triangle? a. 16 V b. 10 V c. 70 V d. 46 V e. 44 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 39. A particle (charge = Q) is kept in a fixed position at point P, and a second particle (charge = q) is released from rest when it is a distance R from P. If Q = +2.0 mC, q = −1.5 mC, and R = 30 cm, what is the kinetic energy of the moving particle after it has moved a distance of 10 cm? a. 60 kJ b. 45 kJ c. 75 kJ d. 90 kJ e. 230 kJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 40. Particle A (mass = m, charge = Q) and B (mass = m, charge = 5 Q) are released from rest with the distance between Copyright Cengage Learning. Powered by Cognero.

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them equal to 1.0 m. If Q = 12 μC, what is the kinetic energy of particle B at the instant when the particles are 3.0 m apart? a. 8.6 J b. 3.8 J c. 6.0 J d. 2.2 J e. 4.3 J ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 41. A particle (charge = 40 μC) moves directly toward a second particle (charge = 80 μC) which is held in a fixed position. At an instant when the distance between the two particles is 2.0 m, the kinetic energy of the moving particle is 16 J. Determine the distance separating the two particles when the moving particle is momentarily stopped. a. 0.75 m b. 0.84 m c. 0.95 m d. 0.68 m e. 0.56 m ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 42. A particle (charge 7.5 μC) is released from rest at a point on the x axis, x = 10 cm. It begins to move due to the presence of a 2.0-μC charge which remains fixed at the origin. What is the kinetic energy of the particle at the instant it passes the point x = 1.0 m? a. 3.0 J b. 1.8 J c. 2.4 J d. 1.2 J e. 1.4 J ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 43. A particle (charge = 5.0 μC) is released from rest at a point x = 10 cm. If a 5.0-μC charge is held fixed at the origin, what is the kinetic energy of the particle after it has moved 90 cm? a. 1.6 J b. 2.0 J c. 2.4 J d. 1.2 J e. 1.8 J ANSWER: b POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 44. A 60-μC charge is held fixed at the origin and a −20-μC charge is held fixed on the x axis at a point x = 1.0 m. If a 10μC charge is released from rest at a point x = 40 cm, what is its kinetic energy the instant it passes the point x = 70 cm? a. 9.8 J b. 7.8 J c. 8.8 J d. 6.9 J e. 2.8 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 45. Two identical particles, each with a mass of 2.0 μg and a charge of 25 nC, are released simultaneously from rest when the two are 4.0 cm apart. What is the speed of either particle at the instant when the two are separated by 10 cm? a. 7.3 m/s b. 9.8 m/s c. 9.2 m/s d. 6.5 m/s e. 4.6 m/s ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 46. Two particles, each having a mass of 3.0 μg and having equal but opposite charges of magnitude 5.0 nC, are released simultaneously from rest when the two are 5.0 cm apart. What is the speed of either particle at the instant when the two are separated by 2.0 cm? a. 2.1 m/s b. 1.5 m/s c. 1.8 m/s d. 2.4 m/s e. 3.2 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 47. Two identical particles, each with a mass of 4.5 μg and a charge of 30 nC, are moving directly toward each other with equal speeds of 4.0 m/s at an instant when the distance separating the two is equal to 25 cm. How far apart will they be when closest to one another? a. 9.8 cm b. 12 cm c. 7.8 cm d. 15 cm Copyright Cengage Learning. Powered by Cognero.

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e. 20 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 48. Two particles, each having a mass of 3.0 μg and having equal but opposite charges of magnitude of 6.0 nC, are released simultaneously from rest when they are a very large distance apart. What distance separates the two at the instant when each has a speed of 5.0 m/s? a. 4.3 mm b. 8.6 mm c. 7.3 mm d. 5.6 mm e. 2.2 mm ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 49. A particle (q = +5.0 μC) is released from rest when it is 2.0 m from a charged particle which is held at rest. After the positively charged particle has moved 1.0 m toward the fixed particle, it has a kinetic energy of 50 mJ. What is the charge on the fixed particle? a. −2.2 μC b. +6.7 μC c. −2.7 μC d. +8.0 μC e. −1.1 μC ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 50. Four identical point charges (+4.0 μC) are placed at the corners of a square which has 20-cm sides. How much work is required to assemble this charge arrangement starting with each of the charges a very large distance from any of the other charges? a. +2.9 J b. +3.9 J c. +2.2 J d. +4.3 J e. +1.9 J ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 51. Identical 8.0-μC point charges are positioned on the x axis at x = ±1.0 m and released from rest simultaneously. What is the kinetic energy of either of the charges after it has moved 2.0 m?

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a. 84 mJ b. 54 mJ c. 96 mJ d. 63 mJ e. 48 mJ ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 52. Through what potential difference must an electron (starting from rest) be accelerated if it is to reach a speed of 3.0 × 7 10 m/s? a. 5.8 kV b. 2.6 kV c. 7.1 kV d. 8.6 kV e. 5.1 kV ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 53. Identical point charges (+50 μC) are placed at the corners of a square with sides of 2.0-m length. How much external energy is required to bring a fifth identical charge from infinity to the geometric center of the square? a. 41 J b. 16 J c. 64 J d. 10 J e. 80 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 54. A charge of +3.0 μC is distributed uniformly along the circumference of a circle with a radius of 20 cm. How much external energy is required to bring a charge of 25μC from infinity to the center of the circle? a. 5.4 J b. 3.4 J c. 4.3 J d. 2.7 J e. 6.8 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges Copyright Cengage Learning. Powered by Cognero.

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55. Identical point charges (+20 μC) are placed at the corners of an equilateral triangle with sides of 2.0-m length. How much external energy is required to bring a charge of 45 μC from infinity to the midpoint of one side of the triangle? a. 26 J b. 16 J c. 23 J d. 21 J e. 12 J ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 56. Identical point charges (+30 μC) are placed at the corners of a rectangle (4.0 m × 6.0 m). How much external energy is required to bring a charge of 55 μC from infinity to the midpoint of one of the 6.0-m long sides of the rectangle? a. 22 J b. 16 J c. 13 J d. 19 J e. 8.0 J ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 57. Two charges lie on the x axis, +3q at the origin, and −2q at x = 5.0 m. The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero) is a. 1.0 m. b. 2.0 m. c. 2.5 m. d. 3.0 m. e. 4.0 m.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 58. Two charges lie on the x axis, +2q at the origin, and −3q at x = 5.0 m. The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero) is a. 1.0 m. b. 2.0 m. c. 2.5 m. d. 3.0 m. e. 4.0 m.

ANSWER: b POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 59. A system consisting of a positively charged particle and an electric field a. loses potential difference and kinetic energy when the charged particle moves in the direction of the field. b. loses electric potential energy when the charged particle moves in the direction of the field. c. loses kinetic energy when the charged particle moves in the direction of the field. d. gains electric potential energy when the charged particle moves in the direction of the field. e. gains potential difference and electric potential energy when the charged particle moves in the direction of the field.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 60. A system consisting of a negatively charged particle and an electric field a. gains potential difference and kinetic energy when the charged particle moves in the direction of the field. b. loses electric potential energy when the charged particle moves in the direction of the field. c. gains kinetic energy when the charged particle moves in the direction of the field. d. gains electric potential energy when the charged particle moves in the direction of the field. e. gains potential difference and electric potential energy when the charged particle moves in the direction of the field.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 61. The Bohr model pictures a hydrogen atom in its ground state as a proton and an electron separated by the distance a0 = −10 0.529 × 10 m. The electric potential created by the proton at the position of the electron is a. −13.6 V. b. +13.6 V. c. −27.2 V. d. +27.2 V. e. +5.12 × 109 V. ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 62. The Bohr model pictures a hydrogen atom in its ground state as a proton and an electron separated by the distance a0 = −10 0.529 × 10 m. The electric potential created by the electron at the position of the proton is a. −13.6 V. b. +13.6 V. c. −27.2 V. d. +27.2 V. e. +5.12 × 109 V. Copyright Cengage Learning. Powered by Cognero.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.3 Electric Potential and Potential Energy Due to Point Charges 63. The electric field in a region of space is given by Ex = (3.0x) N/C, Ey = Ez = 0, where x is in m. Points A and B are on the x axis at xA = 3.0 m and xB = 5.0 m. Determine the potential difference VB − VA. a. −24 V b. +24 V c. −18 V d. +30 V e. −6.0 V ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential 64. Equipotentials are lines along which a. the electric field is constant in magnitude and direction. b. the electric charge is constant in magnitude and direction. c. maximum work against electrical forces is required to move a charge at constant speed. d. a charge may be moved at constant speed without work against electrical forces. e. charges move by themselves.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential 65. When a charged particle is moved along an electric field line, a. the electric field does no work on the charge. b. the electrical potential energy of the charge does not change. c. the electrical potential energy of the charge undergoes the maximum change in magnitude. d. the voltage changes, but there is no change in electrical potential energy. e. the electrical potential energy undergoes the maximum change, but there is no change in voltage.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential 66. When a positive charge is released and moves along an electric field line, it moves to a position of a. lower potential and lower potential energy. b. lower potential and higher potential energy. c. higher potential and lower potential energy. d. higher potential and higher potential energy. e. greater magnitude of the electric field.

ANSWER: a Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential 67. When a negative charge is released and moves along an electric field line, it moves to a position of a. lower potential and lower potential energy. b. lower potential and higher potential energy. c. higher potential and lower potential energy. d. higher potential and higher potential energy. e. decreasing magnitude of the electric field.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential 68. Which of the following represents the equipotential lines of a dipole? a.

b.

c.

d.

e.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential 69. Can the lines in the figure below be equipotential lines?

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a. No, because there are sharp corners. b. No, because they are isolated lines. c. Yes, because any lines within a charge distribution are equipotential lines. d. Yes, they might be boundary lines of the two surfaces of a conductor. e. It is not possible to say without further information.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential 70. When introduced into a region where an electric field is present, an electron with initial velocity move a. along an electric field line, in the positive direction of the line. b. along an electric field line, in the negative direction of the line. c. to a point of decreased potential. d. to a point of increased potential. e. as described in both (b) and (d).

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential

will eventually

71. When introduced into a region where an electric field is present, a proton with initial velocity a. along an electric field line, in the positive direction of the line. b. along an electric field line, in the negative direction of the line. c. to a point of decreased potential. d. to a point of decreased potential. e. as described in both (a) and (c).

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential

will eventually move

72. For the potential a.

, what is the corresponding electric field at the point (2,2,2)?

b. c. d.

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e. The correct answer is not given.

ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.4 Obtaining the Value of the Electric Field from the Electric Potential 2

73. A charge per unit length given by λ(x) = bx, where b = 12 nC/m , is distributed along the x axis from x = +9.0 cm to x = +16 cm. If the electric potential at infinity is taken to be zero, what is the electric potential at the point P on the y axis at y = 12 cm? a. 5.4 V b. 7.2 V c. 9.0 V d. 9.9 V e. 16 V ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 74. A charge Q is uniformly distributed along the x axis from x = a to x = b. If Q = 45 nC, a = −3.0 m, and b = 2.0 m, what is the electric potential (relative to zero at infinity) at the point x = 8.0 m on the x axis? a. 71 V b. 60 V c. 49 V d. 82 V e. 150 V ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 75. Charge of uniform density (3.5 nC/m) is distributed along the circular arc shown. Determine the electric potential (relative to zero at infinity) at point P.

a. 61 V b. 42 V c. 52 V d. 33 V e. 22 V Copyright Cengage Learning. Powered by Cognero.

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ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 76. A charge of uniform density (0.80 nC/m) is distributed along the x axis from the origin to the point x = 10 cm. What is the electric potential (relative to zero at infinity) at the point x = 18 cm on the x axis? a. 7.1 V b. 5.8 V c. 9.0 V d. 13 V e. 16 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 77. A charge of 20 nC is distributed uniformly along the x axis from x = −2.0 m to x = +2.0 m. What is the electric potential (relative to zero at infinity) at the point x = 5.0 m on the x axis? a. 57 V b. 48 V c. 38 V d. 67 V e. 100 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 78. Charge of uniform density 12 nC/m is distributed along the x axis from x = 2.0 m to x = 5.0 m. What is the electric potential (relative to zero at infinity) at the origin (x = 0)? a. 91 V b. 99 V c. 82 V d. 74 V e. 140 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 2

79. A linear charge of nonuniform density λ = bx, where b = 2.1 nC/m , is distributed along the x axis from x = 2.0 m to x = 3.0 m. Determine the electric potential (relative to zero at infinity) of the point y = 4.0 m on the y axis. a. 36 V b. 95 V c. 10 V Copyright Cengage Learning. Powered by Cognero.

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d. 17 V e. 15 V ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 80. A nonuniform linear charge distribution given by λ(x) = bx, where b is a constant, is distributed along the x axis from x 2 = 0 to x = +L. If b = 40 nC/m and L = 0.20 m, what is the electric potential (relative to a potential of zero at infinity) at the point y = 2L on the y axis? a. 19 V b. 17 V c. 21 V d. 23 V e. 14 V ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 81. A charge of 10 nC is distributed uniformly along the x axis from x = −2 m to x = +3 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +5 m on the x axis? a.

b.

c.

d.

e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 82. Charge of uniform linear density 3.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +4 m on the x axis? a.

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b.

c.

d.

e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 83. A charge of 4.0 nC is distributed uniformly along the x axis from x = +4 m to x = +6 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the origin? a.

b.

c.

d.

e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 84. A charge of 20 nC is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +3 m on the x axis? a.

b.

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c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 85. Charge of uniform linear density 6.0 nC/m is distributed along the x axis from x = 0 to x = +3 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point y = +4 m on the y axis? a.

b.

c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 86. A rod (length = 2.0 m) is uniformly charged and has a total charge of 5.0 nC. What is the electric potential (relative to zero at infinity) at a point which lies along the axis of the rod and is 3.0 m from the center of the rod? a. 22 V b. 19 V c. 16 V d. 25 V e. 12 V ANSWER: c POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 87. A charge of 18 nC is uniformly distributed along the y axis from y = 3 m to y = 5 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +2 m on the x axis? a.

b.

c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.5 Electric Potential Due to Continuous Charge Distributions 88. Two large parallel conducting plates are 8.0 cm apart and carry equal but opposite charges on their facing surfaces.

2 The magnitude of the surface charge density on either of the facing surfaces is 2.0 nC/m . Determine the magnitude of the electric potential difference between the plates. a. 36 V b. 27 V c. 18 V d. 45 V e. 16 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 89. A charge of 40 pC is distributed on an isolated spherical conductor that has a 4.0-cm radius. Point A is 1.0 cm from the center of the conductor and point B is 5.0 cm from the center of the conductor. Determine the electric potential difference VA − VB. a. +1.8 V b. +29 V c. +27 V d. +7.2 V e. +9.0 V Copyright Cengage Learning. Powered by Cognero.

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ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 90. A charge is placed on a spherical conductor of radius r1. This sphere is then connected to a distant sphere of radius r2 (not equal to r1) by a conducting wire. After the charges on the spheres are in equilibrium, a. the electric fields at the surfaces of the two spheres are equal. b. the amount of charge on each sphere is q/2. c. both spheres are at the same potential. d. the potentials are in the ratio . e. the potentials are in the ratio

.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 91. The electric potential inside a charged solid spherical conductor in equilibrium a. is always zero. b. is constant and equal to its value at the surface. c. decreases from its value at the surface to a value of zero at the center. d. increases from its value at the surface to a value at the center that is a multiple of the potential at the surface. e. is equal to the charge passing through the surface per unit time divided by the resistance.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 92. A series of n uncharged concentric shells surround a small central charge q. The charge distributed on the outside of the nth shell is a. −nq. b. −(ln n)q. c. +q. d. +(ln n)q. e. +nq.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 93. A series of 3 uncharged concentric shells surround a small central charge q. The charge distributed on the outside of the third shell is Copyright Cengage Learning. Powered by Cognero.

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a. −3q. b. −(ln 3)q. c. +q. d. +(ln 3)q. e. +3q.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 94. A series of n uncharged concentric spherical conducting shells surround a small central charge q. The potential at a point outside the nth shell, at distance r from the center, and relative to V = 0 at ∞, is a. . b. . c. . d. . e. .

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 95. A series of 3 uncharged concentric spherical conducting shells surround a small central charge q. The potential at a point outside the third shell, at distance r from the center, and relative to V = 0 at ∞, is a. . b. . c. . d. . e. .

ANSWER:

c

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 96. The electric potential at the surface of a charged conductor a. is always zero. b. is always independent of the magnitude of the charge on the surface. c. may be set equal to zero by adding an appropriate constant to the potential at all points of space. d. is always such that the potential is zero at all points inside the conductor. e. is always such that the potential is always zero within a hollow space inside the conductor.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 6

97. How much electrical charge is needed to raise an isolated metal sphere of radius 1.0 m to a potential of 1.0 × 10 V? −4 ANSWER: 1.1 × 10 C POINTS: 2 DIFFICULTY: Average REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 98. An uncharged spherical conducting shell surrounds a charge −q at the center of the shell. Then charge +3q is placed on the outside of the shell. When static equilibrium is reached, the charges on the inner and outer surfaces of the shell are, respectively, a. +q, −q. b. −q, +q. c. +q, +2q. d. +2q, +q. e. +3q, 0.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 99. An uncharged spherical conducting shell surrounds a charge −q at the center of the shell. The charges on the inner and outer surfaces of the shell are, respectively, a. −q, −q. b. −q, +q. c. +q, −q. d. +q, +q. e. +q, 0.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium Copyright Cengage Learning. Powered by Cognero.

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100. A positive point charge q is placed at the center of an uncharged metal sphere insulated from the ground. The outside of the sphere is then grounded as shown. Then the ground wire is removed. A is the inner surface and B is the outer surface. Which statement is correct?

a. The charge on A is −q; that on B is +q. b. The charge on B is −q; that on A is +q. c.

The charge is on A and on B. d. There is no charge on either A or B. e. The charge on A is −q; there is no charge on B. ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 101. A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown.

Where is the induced charge density greatest in magnitude and what is its sign?

a. A; negative. b. A; positive. c. B; negative. d. B; positive. e. C; negative.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium 102. An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station. Which statement is correct? a. The astronaut must abandon the chamber immediately to avoid being electrocuted. b. The astronaut will be safe only if she is wearing a spacesuit made of non-conducting materials. c. The astronaut does not need to worry: the charge will remain on the outside surface. d. The astronaut must abandon the chamber if the electric field on the outside surface becomes greater than the breakdown field of air. e. The astronaut must abandon the chamber immediately because the electric field inside the chamber is nonuniform.

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ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 24.6 Conductors in Electrostatic Equilibrium

1. Which of the following is not a capacitance? a.

b.

c.

d.

e.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.1 Definition of Capacitance 2. A parallel-plate capacitor is charged to voltage V and then disconnected from the battery. Leopold says that the voltage will decrease if the plates are pulled apart. Gerhardt says that the voltage will remain the same. Which one, if either, is correct, and why? a. Gerhardt, because the maximum voltage is determined by the battery. b. Gerhardt, because the charge per unit area on the plates does not change. c. Leopold, because charge is transferred from one plate to the other when the plates are separated. d. Leopold, because the force each plate exerts on the other decreases when the plates are pulled apart. e. Neither, because the voltage increases when the plates are pulled apart.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.2 Calculating Capacitance 3. A parallel-plate capacitor is connected to a battery and charged to voltage V. Leah says that the charge on the plates will decrease if the distance between the plates is increased while they are still connected to the battery. Gertie says that the charge will remain the same. Which one, if either, is correct, and why? a. Gertie, because the maximum voltage is determined by the battery. b. Gertie, because the capacitance of the capacitor does not change. c. Leah, because the capacitance decreases when the plate separation is increased. d. Leah, because the capacitance increases when the plate separation is increased. e. Neither, because the charge increases when the plate separation is increased.

ANSWER: c Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.2 Calculating Capacitance 4. Two spheres are made of conducting material. Sphere #2 has twice the radius of Sphere #1. What is the ratio of the capacitance of Sphere #2 to the capacitance of sphere #1? a. 1, since all conducting spheres have the same capacitance. b. 2 c. 4 d. 8 e. A single sphere has no capacitance since a second concentric spherical shell is necessary to make a spherical capacitor. Thus, none of the answers above is correct.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.2 Calculating Capacitance 5. Is it feasible to construct an air-filled parallel-plate capacitor that has its two plates separated by 0.10 mm and has a capacitance of 1.0 F? Why or why not?

7 2 ANSWER: No. Each plate would have an area of 1.1 × 10 m POINTS: 2 DIFFICULTY: Average REFERENCES: 25.2 Calculating Capacitance 6. Regarding the Earth and a cloud layer 800 m above the Earth as the "plates" of a capacitor, calculate the capacitance if 2 6 the cloud layer has an area of 1.0 km . If an electric field of 2.0 × 10 N/C makes the air break down and conduct electricity (lightning), what is the maximum charge the cloud can hold?

ANSWER: 11.1 nF, 17.7 C POINTS: 2 DIFFICULTY: Average REFERENCES: 25.2 Calculating Capacitance 7. Determine the equivalent capacitance of the combination shown when C = 12 pF.

a. 48 pF b. 12 pF c. 24 pF d. 6.0 pF e. 59 pF ANSWER: POINTS:

d 2

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DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 8. Determine the equivalent capacitance of the combination shown when C = 15 mF.

a. 20 mF b. 16 mF c. 12 mF d. 24 mF e. 75 mF ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 9. Determine the equivalent capacitance of the combination shown when C = 12 nF.

a. 34 nF b. 17 nF c. 51 nF d. 68 nF e. 21 nF ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 10. Determine the equivalent capacitance of the combination shown when C = 45 μF.

a. 36 μF b. 32 μF c. 34 μF Copyright Cengage Learning. Powered by Cognero.

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d. 30 μF e. 38 μF ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 11. If C = 10 μF, what is the equivalent capacitance for the combination shown?

a. 7.5 μF b. 6.5 μF c. 7.0 μF d. 5.8 μF e. 13 μF ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 12. What is the equivalent capacitance of the combination shown?

a. 29 μF b. 10 μF c. 40 μF d. 25 μF e. 6.0 μF ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 13. What is the equivalent capacitance of the combination shown?

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a. 20 μF b. 90 μF c. 22 μF d. 4.6 μF e. 67 μF ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 14. Determine the equivalent capacitance of the combination shown when C = 45 μF.

a. 28 μF b. 36 μF c. 52 μF d. 44 μF e. 23 μF ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 15. Determine the equivalent capacitance of the combination shown when C = 24 μF.

a. 20 μF b. 36 μF c. 16 μF d. 45 μF e. 27 μF Copyright Cengage Learning. Powered by Cognero.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 16. The equivalent capacitance of the circuit shown below is

a. 0.2 C. b. 0.4 C. c. 1 C. d. 4 C. e. 5 C. ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.3 Combinations of Capacitors 17. The equivalent capacitance of the circuit shown below is

a. 0.50 C. b. 1.0 C. c. 1.5 C. d. 2.0 C. e. 2.5 C. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.3 Combinations of Capacitors 18. Determine the energy stored in C2 when C1 = 15 μF, C2 = 10 μF, C3 = 20 μF, and V0 = 18 V.

a. 0.72 mJ b. 0.32 mJ c. 0.50 mJ d. 0.18 mJ Copyright Cengage Learning. Powered by Cognero.

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e. 1.60 mJ ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 25.4 Energy Stored in a Charged Capacitor 19. Determine the energy stored in C1 when C1 = 10 μF, C2 = 12 μF, C3 = 15 μF, and V0 = 70 V.

a. 6.5 mJ b. 5.1 mJ c. 3.9 mJ d. 8.0 mJ e. 9.8 mJ ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 20. Determine the energy stored by C4 when C1 = 20 μF, C2 = 10 μF, C3 = 14 μF, C4 = 30 μF, and V0 = 45 V.

a. 3.8 mJ b. 2.7 mJ c. 3.2 mJ d. 2.2 mJ e. 8.1 mJ ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 21. Determine the charge stored by C1 when C1 = 20 μF, C2 = 10 μF, C3 = 30 μF, and V0 = 18 V.

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a. 0.37 mC b. 0.24 mC c. 0.32 mC d. 0.40 mC e. 0.50 mC ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 22. What is the total energy stored by C3 when C1 = 50 μF, C2 = 30 μF, C3 = 36 μF, C4 = 12 μF, and V0 = 30 V?

a. 6.3 mJ b. 25 mJ c. 57 mJ d. 1.6 mJ e. 14 mJ ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 25.4 Energy Stored in a Charged Capacitor 23. How much energy is stored in the 50-μF capacitor when Va − Vb = 22 V?

a. 0.78 mJ b. 0.58 mJ Copyright Cengage Learning. Powered by Cognero.

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c. 0.68 mJ d. 0.48 mJ e. 0.22 mJ ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 24. What is the total energy stored in the group of capacitors shown if the charge on the 30-μF capacitor is 0.90 mC?

a. 29 mJ b. 61 mJ c. 21 mJ d. 66 mJ e. 32 mJ ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 25.4 Energy Stored in a Charged Capacitor 25. What is the potential difference across C2 when C1 = 5.0 μF, C2 = 15 μF, C3 = 30 μF, and V0 = 24 V?

a. 21 V b. 19 V c. 16 V d. 24 V e. 8.0 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor Copyright Cengage Learning. Powered by Cognero.

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26. What total energy is stored in the group of capacitors shown if the potential difference Vab is equal to 50 V?

a. 48 mJ b. 27 mJ c. 37 mJ d. 19 mJ e. 10 mJ ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 27. Determine the energy stored in the 60-μF capacitor.

a. 2.4 mJ b. 3.0 mJ c. 3.6 mJ d. 4.3 mJ e. 6.0 mJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 28. Determine the energy stored in the 40-μF capacitor.

a. 2.4 mJ Copyright Cengage Learning. Powered by Cognero.

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b. 1.6 mJ c. 2.0 mJ d. 2.9 mJ e. 4.0 mJ ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 29. If VA − VB = 50 V, how much energy is stored in the 36-μF capacitor?

a. 50 mJ b. 28 mJ c. 13 mJ d. 8.9 mJ e. 17 mJ ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 30. If VA − VB = 50 V, how much energy is stored in the 54-μF capacitor?

a. 50 mJ b. 13 mJ c. 28 mJ d. 8.9 mJ e. 17 mJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 31. A 3.0-μF capacitor charged to 40 V and a 5.0-μF capacitor charged to 18 V are connected to each other, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 3.0-μF capacitor?

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a. 11 μC b. 15 μC c. 19 μC d. 26 μC e. 79 μC ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 25.4 Energy Stored in a Charged Capacitor 32. A 6.0-μF capacitor charged to 50 V and a 4.0-μF capacitor charged to 34 V are connected to each other, with the two positive plates connected and the two negative plates connected. What is the total energy stored in the 6.0-μF capacitor at equilibrium? a. 6.1 mJ b. 5.7 mJ c. 6.6 mJ d. 7.0 mJ e. 3.8 mJ ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 25.4 Energy Stored in a Charged Capacitor 33. A 25-μF capacitor charged to 50 V and a capacitor C charged to 20 V are connected to each other, with the two positive plates connected and the two negative plates connected. The final potential difference across the 25-μF capacitor is 36 V. What is the value of the capacitance of C? a. 43 μF b. 29 μF c. 22 μF d. 58 μF e. 63 μF ANSWER: c POINTS: 2 DIFFICULTY: Challenging REFERENCES: 25.4 Energy Stored in a Charged Capacitor 34. A 4.0-mF capacitor initially charged to 50 V and a 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other. What is the final charge on the 6.0-mF capacitor? a. 20 mC b. 8.0 mC c. 10 mC d. 12 mC e. 230 mC ANSWER: d POINTS: 3 DIFFICULTY: Challenging Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 25.4 Energy Stored in a Charged Capacitor 35. When a capacitor has a charge of magnitude 80 μC on each plate the potential difference across the plates is 16 V. How much energy is stored in this capacitor when the potential difference across its plates is 42 V? a. 1.0 mJ b. 4.4 mJ c. 3.2 mJ d. 1.4 mJ e. 1.7 mJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 36. A 15-μF capacitor and a 30-μF capacitor are connected in series, and charged to a potential difference of 50 V. What is the resulting charge on the 30-μF capacitor? a. 0.70 mC b. 0.80 mC c. 0.50 mC d. 0.60 mC e. 0.40 mC ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 37. A 15-μF capacitor and a 25-μF capacitor are connected in parallel, and charged to a potential difference of 60 V. How much energy is then stored in this capacitor combination? a. 50 mJ b. 18 mJ c. 32 mJ d. 72 mJ e. 45 mJ ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 38. A 20-μF capacitor charged to 2.0 kV and a 40-μF capacitor charged to 3.0 kV are connected to each other, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 20-μF capacitor after the two are so connected? a. 53 mC b. 27 mC c. 40 mC d. 80 mC e. 39 mC ANSWER: b Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 39. A 15-μF capacitor is charged to 40 V and then connected across an initially uncharged 25-μF capacitor. What is the final potential difference across the 25-μF capacitor? a. 12 V b. 18 V c. 15 V d. 21 V e. 24 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 40. A 30-μF capacitor is charged to 40 V and then connected across an initially uncharged 20-μF capacitor. What is the final potential difference across the 30-μF capacitor? a. 15 V b. 24 V c. 18 V d. 21 V e. 40 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 41. A capacitor of unknown capacitance C is charged to 100 V and then connected across an initially uncharged 60-μF capacitor. If the final potential difference across the 60-μF capacitor is 40 V, determine C. a. 49 μF b. 32 μF c. 40 μF d. 90 μF e. 16 μF ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 42. A 30-μF capacitor is charged to 80 V and then connected across an initially uncharged capacitor of unknown capacitance C. If the final potential difference across the 30-μF capacitor is 20 V, determine C. a. 60 μF b. 75 μF c. 45 μF d. 90 μF e. 24 μF Copyright Cengage Learning. Powered by Cognero.

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ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 43. A 30-μF capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10-μF capacitor. If the final potential difference across the 10-μF capacitor is 20 V, determine V0. a. 13 V b. 27 V c. 20 V d. 29 V e. 60 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 44. A parallel-plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them. After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference between them are a.

Q0, V0. b.

Q0,

V0.

c. Q0, V0. d. Q0, 2V0. e. 2Q0, 2V0.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 45. A parallel-plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them. After the plates are 2d apart, the new capacitance and the potential difference between the plates are a.

C0, V0. b.

C0, V0. c.

C0, 2V0.

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d. C0, 2V0. e. 2C0, 2V0.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 46. A parallel-plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference between them are a.

Q0, V0. b.

Q0, V0. c. Q0, V0. d. 2Q0, V0. e. 2Q0, 2V0.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 47. A parallel-plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d apart, the capacitance of the capacitor and the magnitude of the charge on the plates are a.

C0, Q0. b.

C0, Q0. c. C0, Q0. d. 2C0, Q0. e. 2C0, 2Q0.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 48. A parallel-plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. While it is connected to the battery the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitude of the charge on the plates and the potential difference between them are Copyright Cengage Learning. Powered by Cognero.

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a.

Q0,

V0.

b.

Q0,

V0.

c. Q0, V0. d. 3Q0, V0. e. 3Q0, 3V0.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 49. An initially uncharged parallel-plate capacitor of capacitance C is charged to potential V by a battery. The battery is then disconnected. Which statement is correct? a. There is no charge on either plate of the capacitor. b. The capacitor can be discharged by grounding any one of its two plates. c. Charge is distributed evenly over both the inner and outer surfaces of the plates. d. The magnitude of the electric field outside the space between the plates is approximately zero. e. The capacitance increases when the distance between the plates increases.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.4 Energy Stored in a Charged Capacitor 50. A 0.120-pF parallel-plate capacitor is charged to a potential difference of 10.0 V and then disconnected from the 6 6 battery. A cosmic ray burst creates 1.00 × 10 electrons and 1.00 × 10 positive charges between the plates. If the charges do not recombine, but reach the oppositely charged plates, by how much is the potential difference between the capacitor plates reduced? a. 1.33 V b. 7.34 V c. 8.67 V d. 1,330 V e. 8,670 V ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 25.4 Energy Stored in a Charged Capacitor 51. A 0.16-pF parallel-plate capacitor is charged to 10 V. Then the battery is disconnected from the capacitor. When 1.00 7 × 10 electrons are now placed on the negative plate of the capacitor, the voltage between the plates changes by a. −5.0 V. b. −1.1 V. c. 0 V. d. +1.1 V. e. +5.0 V. Copyright Cengage Learning. Powered by Cognero.

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ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 25.4 Energy Stored in a Charged Capacitor 52. A 0.16-pF parallel-plate capacitor is charged to 10 V. Then the battery is disconnected from the capacitor. When 1.00 7 × 10 positive charges of magnitude |e| are now placed on the positive plate of the capacitor, the voltage between the plates changes by a. −5.0 V. b. −1.1 V. c. 0 V. d. +1.1 V. e. +5.0 V. ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 25.4 Energy Stored in a Charged Capacitor 53. An electron is released from rest at the negative plate of a parallel-plate capacitor. If the distance between the plates is 5 mm and the potential difference across the plates is 5 V, with what velocity does the electron hit the positive plate? (me −31 −19 = 9.1 × 10 kg, qe = 1.6 × 10 C.) 6 ANSWER: 1.33 × 10 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 25.4 Energy Stored in a Charged Capacitor 54. A parallel-plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. While it is connected to the battery, the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitude of the charge on the plates and the new capacitance are a.

Q0, C0. b.

Q0,

C0.

c. Q0, C0. d. 3Q0, C0. e. 3Q0, 3C0.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 25.5 Capacitors with Dielectrics 55. The equivalent capacitance of the circuit shown below is

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a. 0.2 C. b. 0.4 C. c. 1 C. d. 4 C. e. 5 C. ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.5 Capacitors with Dielectrics 56. A parallel-plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitudes of the charge on the plates and the potential difference between them are a.

Q0, V0. b.

Q0,

V0.

c. Q0, V0. d. Q0, 3V0. e. 3Q0, 3V0.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.5 Capacitors with Dielectrics 57. A parallel-plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitudes of the capacitance and the potential difference between the plates are a.

C0, V0. b.

C0,

V0.

c. C0, V0. d.

3C0,

V0.

e. 3C0, 3V0.

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ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.5 Capacitors with Dielectrics 58. Addition of a metal slab of thickness a between the plates of a parallel-plate capacitor of plate separation d is equivalent to introducing a dielectric with dielectric constant κ between the plates. The value of κ is a. . b. d. c. d − a. d. . e. .

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 25.5 Capacitors with Dielectrics 59. Which of the following statements is incorrect? a. Capacitance is always positive. b. The symbol for potential difference between the plates of a capacitor is

.

c. Water is a polar molecule. d. When a dielectric is placed in a capacitor it serves to reduce the electric field. e. Nonpolar molecules cannot be used for dielectric material in a capacitor.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.5 Capacitors with Dielectrics 60. Which of the following materials has the highest dielectric constant? a. air b. Mylar c. paper d. Pyrex glass e. water ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.5 Capacitors with Dielectrics 61. Into the gap between the plates of a parallel-plate capacitor of capacitance a slab of metal is inserted halfway between the plates filling one fourth of the gap between the plates. What is the resulting new capacitance?

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a. b. c. d. e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 25.5 Capacitors with Dielectrics 62. The plates of a parallel-plate capacitor of capacitance

are horizontal. Into the gap a slab of dielectric material with

is placed, filling the bottom half of the gap between the plates. What is the resulting new capacitance? a. b. c. d. e.

ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 25.5 Capacitors with Dielectrics 63. A 200-volt battery is connected to a 0.50-microfarad parallel-plate, air-filled capacitor. Now the battery is disconnected, with care taken not to discharge the plates. Some Pyrex glass is then inserted between the plates, completely filling up the space. What is the final potential difference between the plates? (The dielectric constant for Pyrex is κ = 5.6.)

ANSWER: 36 V POINTS: 2 DIFFICULTY: Average REFERENCES: 25.5 Capacitors with Dielectrics 64. An electric dipole having dipole moment of magnitude p is placed in a uniform electric field having magnitude E. What is the magnitude of the greatest change in potential energy that can happen for this dipole in this field? a. pE b. c. 4pE d.

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e. No answer given is correct.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 25.6 Electric Dipole in an Electric Field

28

3

-19

1. The electron density in copper is 8.49 × 10 electrons/m . The electron charge is e = −1.60 × 10 C. When a 1.00-A 2 current is present in a copper wire with a 0.40 cm cross-section, what is the electron drift velocity, in m/s? Use a sign convention where a positive velocity is defined to be in the same direction as the current density. a. −1.84 × 10-6 b. +1.84 × 10-6 c. −1.84 d. −5.43 × 105 e. +5.43 × 105 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 26.1 Electric Current 2. To increase the current density in a wire of length and diameter D, you can a. decrease the potential difference between the two ends of the wire. b. increase the potential difference between the two ends of the wire. c. decrease the magnitude of the electric field in the wire. d. heat the wire to a higher temperature. e. combine both (b) and (d).

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 26.1 Electric Current 2

3. An aluminum wire of cross-sectional area 4.0 mm is carrying a current of 8.0 A. The density of aluminum is 2.7 3 g/cm , and its molar mass is 27 g. Assuming one free electron per aluminum atom, what is the drift speed of the electrons in this wire?

ANSWER: POINTS: 2 DIFFICULTY: Average REFERENCES: 26.1 Electric Current 4. The diagram shown represents a portion of a wire in a circuit. A current is flowing in the wire in the direction shown.

Under the convention that it is positive charge that flows the electric field points in the direction of the current. How can the electric field change direction where the wire bends?

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a. There is an excess of negative charge in the center of the wire. b. There is an excess of positive charge at the bottom end of the wire. c. There is an excess of negative charge at the right end of the upper portion of the wire. d. There is an accumulation of positive charge on the surface, particularly at the bend, such that the sum of electric fields gives the new electric field. e. There is an accumulation of electrical potential as the current traverses the wire: The higher potential in the lower half is the source of the field.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 26.1 Electric Current 5. A rod of 2.0-m length and a square (2.0 mm × 2.0 mm) cross section is made of a material with a resistivity of 6.0 × −8 10 Ω ⋅ m. If a potential difference of 0.50 V is placed across the ends of the rod, at what rate is heat generated in the rod? a. 3.0 W b. 5.3 W c. 8.3 W d. 1.3 W e. 17 W ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 26.2 Resistance 6. An electric device, which heats water by immersing a resistance wire in the water, generates 50 cal of heat per second when an electric potential difference of 12 V is placed across its leads. What is the resistance of the heater wire? (Note: 1 cal = 4.186 J) a. 0.94 Ω b. 0.81 Ω c. 0.58 Ω d. 0.69 Ω e. 1.5 Ω ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 26.2 Resistance 7. A 4.0-Ω resistor has a current of 3.0 A in it for 5.0 min. How many electrons pass through the resistor during this time interval?

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a. 7.5 × 1021 b. 5.6 × 1021 c. 6.6 × 1021 d. 8.4 × 1021 e. 2.1 × 1021 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 26.2 Resistance 21

8. If 5.0 × 10 electrons pass through a 20-Ω resistor in 10 min, what is the potential difference across the resistor? a. 21 V b. 32 V c. 27 V d. 37 V e. 54 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 26.2 Resistance 9. How many electrons pass through a 20-Ω resistor in 10 min if there is a potential drop of 30 volts across it? a. 5.6 × 1021 b. 7.5 × 1021 c. 9.4 × 1021 d. 1.1 × 1021 e. 3.8 × 1021 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 26.2 Resistance 10. A wire (length = 2.0 m, diameter = 1.0 mm) has a resistance of 0.45 Ω. What is the resistivity of the material used to make the wire? a. 5.6 × 10-7 Ω ⋅ m b. 1.2 × 10-7 Ω ⋅ m c. 1.8 × 10-7 Ω ⋅ m d. 2.3 × 10-7 Ω ⋅ m e. 7.1 × 10-7 Ω ⋅ m ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 26.2 Resistance 11. What is the resistance of a wire made of a material with a resistivity of 3.2 × 10 diameter is 0.50 mm? a. 0.16 Ω b. 0.10 Ω c. 1.28 Ω d. 0.41 Ω e. 0.81 Ω ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 26.2 Resistance

−8

Ω ⋅ m if its length is 2.5 m and its

12. A rod (length = 80 cm) with a rectangular cross section (1.5 mm × 2.0 mm) has a resistance of 0.20 Ω. What is the resistivity of the material used to make the rod? a. 6.0 × 10-7 Ω ⋅ m b. 3.8 × 10-7 Ω ⋅ m c. 7.5 × 10-7 Ω ⋅ m d. 3.0 × 10-7 Ω ⋅ m e. 4.8 × 10-7 Ω ⋅ m ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 26.2 Resistance 13. Most telephone cables are made of copper wire of either 24 or 26 gauge. If the resistance of 24-gauge wire is 137 Ω/mile and the resistance of 26-gauge wire is 220 Ω/mile, what is the ratio of the diameter of 24-gauge wire to that of 26gauge wire? a. 1.6 b. 1.3 c. 0.62 d. 0.79 e. 0.88 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 26.2 Resistance -8

14. If a mile of 24-gauge copper wire has a resistance of 0.14 kΩ and the resistivity of copper is 1.7 × 10 Ω ⋅ m, what is the diameter of the wire? (1 mile = 1.6 km) a. 0.40 mm b. 0.50 mm c. 0.63 mm d. 0.80 mm Copyright Cengage Learning. Powered by Cognero.

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e. 0.25 mm ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 26.2 Resistance 15. A conductor of radius r, length , and resistivity ρ has resistance R. What is the new resistance if it is stretched to 4 times its original length? a.

R b.

R c. R d. 4R e. 16R ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 26.2 Resistance 16. A conductor of radius r, length , and resistivity ρ has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the length of the original conductor. What is the resistance of the new conductor? a.

R b.

R c. R d. 4R e. 16R ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 26.2 Resistance 17. Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why? a. Arnell, because the conductivity of the wire increases when it is heated. b. Arnell, because the conductivity of the wire decreases when it is heated. c. Jadeen, because the conductivity of a wire is directly proportional to its area and inversely proportional to its length. d. Jadeen, because the conductivity of a copper wire does not increase when it is hammered. e. Both are correct because (b) and (d) are both correct.

ANSWER: e POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 26.2 Resistance 18. A high-resistance material is used as an insulator between the conductors of a length of coaxial cable. The resistance material, which forms a hollow tube, has an inner radius a and an outer radius b, and the insulator provides a resistance R between the conductors. If a second insulator, made of the same material and having the same length, is made with double both the inner radius and the outer radius of the first, what resistance would it provide between the conductors? a. R b. 2 R c. 4 R d. (ln2)R e. R/(ln2) ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 26.2 Resistance 19. What is the resistance of 1 000 m of 4-mm diameter copper wire?

-8 (ρCu = 1.7 × 10 Ω ⋅ m) ANSWER: 1.35 ohm POINTS: 2 DIFFICULTY: Average REFERENCES: 26.2 Resistance 20. In the Drude model of electrical conduction, the current density is directly proportional to a. the average time interval between successive collisions. b. the number of charge carriers per unit volume. c. the square of the electron charge. d. the electric field present in the wire. e. the product of all four quantities listed above.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 26.3 A Model for Electrical Conduction 21. In the Drude model of electrical conduction, the current density is NOT directly proportional to a. the average time interval between successive collisions. b. the number of charge carriers per unit volume. c. the square of the electron charge. d. the electric field present in the wire. e. the resistivity of the wire.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 26.3 A Model for Electrical Conduction 22. A small bulb is rated at 7.50 W when operated at 125 V. The tungsten filament has a temperature coefficient of Copyright Cengage Learning. Powered by Cognero.

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-3

resistivity α = 4.50 × 10 / °C. When the filament is hot and glowing, its temperature is seven times room temperature (20 °C). What is the resistance of the filament (in ohms) at room temperature? a. 234 b. 1 350 c. 2 080 d. 4 530 e. 5 630 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 26.4 Resistance and Temperature -3

-3

23. The temperature coefficient of resistivity of iron is 5.0 × 10 /°C; that of carbon is −0.50 × 10 /°C. When an iron wire and a carbon rod, each having the same 10-Ω resistance at 20°C, are cooled from that temperature to −80°C, what is the new ratio of the resistance of the carbon rod to the resistance of the iron wire at the lower temperature? a. −0.10. b. +1.9. c. +2.1. d. −10. e. +10.

ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 26.4 Resistance and Temperature 24. A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance -8 -3 -6 when heated separately. (ρAl = 2.82 × 10 Ω ⋅ m; αAl = 3.9 × 10 /°C; ρnichrome = 1.50 × 10 Ω ⋅ m; αnichrome = 0.40 -3 × 10 /°C.) What is the ratio of the temperature change of the nichrome wire to the temperature change of the aluminum wire? a. 0.019. b. 0.10. c. 0.18. d. 9.8. e. 53.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 26.4 Resistance and Temperature 25. A light bulb is rated at 30 W when operated at 120 V. How much charge enters (and leaves) the light bulb in 1.0 min? a. 17 C b. 15 C c. 14 C d. 13 C e. 60 C ANSWER: b Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 26.6 Electrical Power 26. What maximum power can be generated from an 18-V emf using any combination of a 6.0-Ω resistor and a 9.0-Ω resistor? a. 54 W b. 71 W c. 90 W d. 80 W e. 22 W ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 26.6 Electrical Power 27. An electric heater is constructed by applying a potential difference of 110 V across a wire with a resistance of 5.0 Ω.

What is the power rating of the heater? a. 2.0 kW b. 2.4 kW c. 1.7 kW d. 1.5 kW e. 60 kW ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 26.6 Electrical Power 28. How much energy is dissipated as heat during a two-minute time interval by a 1.5-kΩ resistor which has a constant 20-V potential difference across its leads? a. 58 J b. 46 J c. 32 J d. 72 J e. 16 J ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 26.6 Electrical Power 29. A small bulb is rated at 7.5 W when operated at 125 V. Its resistance (in ohms) is a. 0.45. b. 7.5. c. 17. d. 940. e. 2 100.

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ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 26.6 Electrical Power 30. Light bulb A is rated at 60 W and light bulb B is rated at 100 W. Both are designed to operate at 110 V. Which statement is correct? a. The 60-W bulb has a greater resistance and greater current than the 100-W bulb. b. The 60-W bulb has a greater resistance and smaller current than the 100-W bulb. c. The 60-W bulb has a smaller resistance and smaller current than the 100-W bulb. d. The 60-W bulb has a smaller resistance and greater current than the 100-W bulb. e. We need to know the resistivities of the filaments to answer this question.

ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 26.6 Electrical Power 31. A cook plugs a 500-W crockpot and a 1 000-W kettle into a 240-V power supply, all operating on direct current.

When we compare the two, we find that a. Icrockpot < Ikettle and Rcrockpot < Rkettle. b. Icrockpot < Ikettle and Rcrockpot > Rkettle. c. Icrockpot = Ikettle and Rcrockpot = Rkettle. d. Icrockpot > Ikettle and Rcrockpot < Rkettle. e. Icrockpot > Ikettle and Rcrockpot > Rkettle.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 26.6 Electrical Power 32. A high-voltage transmission line carries 1 000 A at 700 kV for a distance of 100 miles. If the resistance per length in the wire is 0.5 Ω/mile, what is the power loss due to resistive losses?

ANSWER: 50 MW POINTS: 2 DIFFICULTY: Average REFERENCES: 26.6 Electrical Power 33. The heating coil of a hot water heater has a resistance of 20 ohms and operates at 210 V. If electrical energy costs 5.5 cents per kW-hr, what does it cost to raise the 200 kg of water in the tank from 15°C to 80°C? (The specific heat of water is 4 186 J/kg°C) ANSWER: 83 cents POINTS: 2 DIFFICULTY: Average REFERENCES: 26.6 Electrical Power 34. A copper cable is to be designed to carry a current of 300 A with a power loss of only 2.0 watts per meter. What is the −8 required radius of the copper cable? (The resistivity of copper is 1.7 × 10 Ω ⋅ m.)

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ANSWER: 1.6 cm POINTS: 2 DIFFICULTY: Average REFERENCES: 26.6 Electrical Power

1. If 480 C pass through a 4.0-Ω resistor in 10 min, what is the potential difference across the resistor? a. 3.6 V b. 2.8 V c. 2.4 V d. 3.2 V e. 5.0 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.1 Electromotive Force 2. A battery has an internal resistance of 4.0 Ω. Which of the following load resistors would have the most power delivered to it when connected across the battery? a. 1.4 Ω b. 2.0 Ω c. 4.0 Ω d. 8.0 Ω e. 16 Ω ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.1 Electromotive Force 3. At what rate is thermal energy being generated in the 2R-resistor when ε = 12 V and R = 3.0 Ω?

a. 12 W b. 24 W c. 6.0 W d. 3.0 W e. 1.5 W ANSWER: POINTS:

c 2

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DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 4. What is the magnitude of the potential difference across the 20-Ω resistor?

a. 3.2 V b. 7.8 V c. 11 V d. 5.0 V e. 8.6 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 5. What is the current in the 10-Ω resistor?

a. 0.60 A b. 3.0 A c. 1.2 A d. 2.4 A e. 0.30 A ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 6. At what rate is thermal energy generated in the 20-Ω resistor when ε = 20 V?

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a. 6.5 W b. 1.6 W c. 15 W d. 26 W e. 5.7 W ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 7. At what rate is thermal energy generated in the 5-Ω resistor when ε = 24 V?

a. 13 W b. 3.2 W c. 23 W d. 39 W e. 51 W ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 8. When a 20-V emf is placed across two resistors in series, a current of 2.0 A is present in each of the resistors. When the same emf is placed across the same two resistors in parallel, the current through the emf is 10 A. What is the magnitude of the greater of the two resistances? a. 7.2 Ω b. 7.6 Ω c. 6.9 Ω d. 8.0 Ω e. 2.8 Ω ANSWER: a POINTS: 3 DIFFICULTY: Challenging Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 27.2 Resistors in Series and Parallel 9. A resistor of unknown resistance and a 15-Ω resistor are connected across a 20-V emf in such a way that a 2.0-A current is observed in the emf. What is the value of the unknown resistance? a. 75 Ω b. 12 Ω c. 7.5 Ω d. 30 Ω e. 5.0 Ω ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 10. What is the current in the 15-Ω resistor when ε = 9.0 V?

a. 0.20 A b. 0.30 A c. 0.10 A d. 0.26 A e. 0.60 A ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 11. How much heat is produced in the 10-Ω resistor in 5.0 s when ε = 18 V?

a. 72 J b. 32 J c. 50 J d. 18 J e. 90 J ANSWER: POINTS:

d 2

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DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 12. Determine ε when I = 0.50 A and R = 12 Ω.

a. 12 V b. 24 V c. 30 V d. 15 V e. 6.0 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 13. What is the equivalent resistance between points a and b when R = 13 Ω?

a. 29 Ω b. 23 Ω c. 26 Ω d. 20 Ω e. 4.6 Ω ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 14. What is the equivalent resistance between points a and b when R = 30 Ω?

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a. 27 Ω b. 21 Ω c. 24 Ω d. 18 Ω e. 7.5 Ω ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 15. What is the equivalent resistance between points a and b when R = 12 Ω?

a. 20 Ω b. 16 Ω c. 24 Ω d. 28 Ω e. 6.0 Ω ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 16. What is the equivalent resistance between points a and b?

a. 14 Ω b. 8.0 Ω c. 6.0 Ω Copyright Cengage Learning. Powered by Cognero.

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d. 25 Ω e. 40 Ω ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 17. If R1 = 10 Ω, R2 = 15 Ω, R3 = 20 Ω, and I = 0.50 A, at what rate is heat being generated in these resistors?

a. 29 W b. 16 W c. 22 W d. 11 W e. 1.1 W ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 18. If R1 = 3.0 Ω, R2 = 6.0 Ω, R3 = 12 Ω, and I = 0.50 A, at what rate is heat being generated in R1?

a. 20 W b. 17 W c. 12 W d. 31 W e. 6.0 W ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 19. A certain brand of hot dog cooker applies a potential difference (120 V) to opposite ends of the hot dog and cooks by means of the joule heat produced. If 60 kJ is needed to cook each hot dog, what current is needed to cook four hot dogs simultaneously in 3.0 min? a. 11 A b. 2.8 A Copyright Cengage Learning. Powered by Cognero.

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c. 8.3 A d. 2.1 A e. 3.6 A ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 20. A 10-V battery is connected to a 15-Ω resistor and an unknown resistor R, as shown. The current in the circuit is 0.40 A. How much heat is produced in the 15-Ω resistor in 2.0 min?

a. 0.40 kJ b. 0.19 kJ c. 0.29 kJ d. 0.72 kJ e. 0.80 kJ ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 21. What is the equivalent resistance between points A and B in the figure when R = 20 Ω?

a. 77 Ω b. 63 Ω c. 70 Ω d. 84 Ω e. 140 Ω ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 27.2 Resistors in Series and Parallel 22. What is the equivalent resistance between points A and B in the figure when R = 18 Ω?

a. 48 Ω b. 64 Ω c. 80 Ω d. 96 Ω e. 110 Ω ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 23. What is the equivalent resistance between points A and B in the figure when R = 10 Ω?

a. 20 Ω b. 10 Ω c. 25 Ω d. 15 Ω e. 3.2 Ω ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 24. In a loop in a closed circuit, the sum of the currents entering a junction equals the sum of the currents leaving a junction because a. the potential of the nearest battery is the potential at the junction. b. there are no transformations of energy from one type to another in a circuit loop. c. capacitors tend to maintain current through them at a constant value. d. current is used up after it leaves a junction. e. charge is neither created nor destroyed at a junction.

ANSWER: e Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.2 Resistors in Series and Parallel 25. Which two circuits are exactly equivalent?

a. A and B b. B and C c. C and D d. D and E e. B and E ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.2 Resistors in Series and Parallel 26. A circuit consists of 2N resistors, all of resistance R, connected as shown below. A potential difference V is applied to one end, and the other end is at ground potential. The equivalent resistance of the circuit is

a. . b. R. c. . d. NR. e. 2NR. Copyright Cengage Learning. Powered by Cognero.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 27. A circuit consists of N resistors, all of resistance R, connected as shown below. A potential difference V is applied to the circuit. The equivalent resistance of the circuit is

a. . b. R. c. . d. NR. e. 4NR. ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 28. A circuit consists of N resistors, all of resistance R, connected as shown below. A potential difference V is applied to the circuit. The equivalent resistance of the circuit is

a. . b. . c. R. d. NR. e. 2NR. ANSWER: b POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 27.2 Resistors in Series and Parallel 29. The circuit below shows three resistors in parallel. R3 > R2 > R1. The resistors are all made of the same wire with the same diameter but have different lengths. Rank the magnitudes of the electric fields in the resistors from least to greatest.

a. E3 < E2 < E1. b. E2 < E1 = E3. c. E1 = E2 = E3. d. E1 = E3 < E2. e. E1 < E2 < E3.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 30. The circuit below shows three resistors in series. R3 > R2 > R1. The resistors are all made of the same wire with the same diameter but have different lengths. Rank the magnitudes of the electric fields in the resistors from least to greatest.

a. E3 < E2 < E1. b. E2 < E1 = E3. c. E1 = E2 = E3. d. E1 = E3 < E2. e. E1 < E2 < E3.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 31. A series circuit consists of a 100-V DC power source, a 100-Ω resistor, and a variable resistor of resistance R, which varies from 0 to 100 Ω. The current in the circuit is

a. directly proportional to R. Copyright Cengage Learning. Powered by Cognero.

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b. inversely proportional to R. c. directly proportional to (100 Ω + R). d. inversely proportional to (100 Ω + R). e. neither directly nor inversely proportional to R or to (100 Ω + R).

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.2 Resistors in Series and Parallel 32. A parallel circuit consists of a 100-V DC power source, a 100-Ω resistor, and a variable resistor of resistance R, which varies from 0 to 100 Ω. The current in the circuit is

a. directly proportional to R. b. inversely proportional to R. c. directly proportional to (100 Ω + R). d. inversely proportional to (100 Ω + R). e. neither directly nor inversely proportional to R or to (100 Ω + R).

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 27.2 Resistors in Series and Parallel 33. At what rate is thermal energy generated in the 30-Ω resistor?

a. 20 W b. 27 W c. 60 W d. 13 W e. 30 W ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.4 Kirchhoff’s Rules 34. Determine R when I = 0.20 A and ε = 18 V. Copyright Cengage Learning. Powered by Cognero.

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a. 50 Ω b. 8.0 Ω c. 10 Ω d. 20 Ω e. 30 Ω ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.4 Kirchhoff’s Rules 35. Determine the current in the 10-V emf.

a. 2.3 A b. 2.7 A c. 1.3 A d. 0.30 A e. 2.5 A ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.4 Kirchhoff’s Rules 36. What is the magnitude of the current in the 20-Ω resistor?

a. 0.75 A b. 0.00 A Copyright Cengage Learning. Powered by Cognero.

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c. 0.25 A d. 0.50 A e. 1.00 A ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.4 Kirchhoff’s Rules 37. Determine the potential difference Va − Vb shown in the circuit below.

a. −5.0 V b. +5.0 V c. −10 V d. +10 V e. 0 V ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.4 Kirchhoff’s Rules 38. What is the potential difference Vb − Va shown in the circuit below.

a. −8.0 V b. +8.0 V c. −18 V d. +18 V e. −12 V ANSWER:

a

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POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.4 Kirchhoff’s Rules 39. At what rate is power supplied by the 10-V emf shown below?

a. −10 W b. +10 W c. zero d. +20 W e. −20 W ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.4 Kirchhoff’s Rules 40. If ε = 8.0 V, at what rate is that emf providing energy to the circuit shown below?

a. 8.4 W b. 7.6 W c. 5.6 W d. 11 W e. 2.0 W ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.4 Kirchhoff’s Rules 41. Determine the magnitude and sense (direction) of the current in the 500-Ω resistor when I = 30 mA.

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a. 56 mA left to right b. 56 mA right to left c. 48 mA left to right d. 48 mA right to left e. 26 mA left to right ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 27.4 Kirchhoff’s Rules 42. Determine the magnitude and sense (direction) of the current in the 10-Ω resistor when I = 1.8 A.

a. 1.6 A right to left b. 1.6 A left to right c. 1.2 A right to left d. 1.2 A left to right e. 1.8 A left to right ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 27.4 Kirchhoff’s Rules 43. Determine the resistance R when I = 1.5 A.

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a. 40 Ω b. 8.0 Ω c. 85 Ω d. 28 Ω e. 32 Ω ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.4 Kirchhoff’s Rules 44. What is the potential difference VB − VA when I = 1.5 A in the circuit segment below?

a. +22 V b. −22 V c. −38 V d. +38 V e. +2.0 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.4 Kirchhoff’s Rules 45. What is the potential difference VB − VA when I = 0.50 A in the circuit segment shown below?

a. +28 V b. +2.0 V c. −28 V d. −2.0 V e. +18 V ANSWER: POINTS:

a 2

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DIFFICULTY: Average REFERENCES: 27.4 Kirchhoff’s Rules 46. If the current in the 4.0-Ω resistor is 1.4 A, what is the magnitude of the potential difference, VA − VB?

a. 69 V b. 55 V c. 62 V d. 48 V e. 31 V ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.4 Kirchhoff’s Rules 47. If I = 0.40 A in the circuit segment shown below, what is the potential difference Va − Vb?

a. 31 V b. 28 V c. 25 V d. 34 V e. 10 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.4 Kirchhoff’s Rules 48. If I = 2.0 A in the circuit segment shown below, what is the potential difference VB − VA?

a. +10 V b. −20 V c. −10 V Copyright Cengage Learning. Powered by Cognero.

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d. +20 V e. +30 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.4 Kirchhoff’s Rules 49. When a capacitor is fully charged, the current through the capacitor in a direct-current circuit is a. zero. b. at its maximum value. c. equal to the current in a resistive circuit in parallel with the capacitor circuit. d. greater than the current in a resistor that is farther from the battery than the capacitor. e. zero if it is the only capacitor, but maximum if there is another capacitor in series with it.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.4 Kirchhoff’s Rules 50. The circuit below contains three 100-W light bulbs. The emf ε = 110 V. Which light bulb(s) is(are) brightest?

a. A b. B c. C d. B and C e. All three are equally bright.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.4 Kirchhoff’s Rules 51. The circuit below contains three 100-watt light bulbs. The emf ε = 110 V. Which light bulb(s) is(are) the brightest?

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a. A b. B c. C d. B and C e. All three are equally bright.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.4 Kirchhoff’s Rules 52. The circuit below contains three resistors, A, B, and C, which all have equal resistances. The emf ε = 110V. Which resistor generates the most thermal energy after the switch is closed?

a. A b. B c. C d. A and B e. All three generate equal amounts of thermal energy.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.4 Kirchhoff’s Rules 53. The circuit below contains 4 100-W light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?

a. A b. B c. C d. D e. C and D ANSWER: b Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.4 Kirchhoff’s Rules 54. The circuit below contains 4 100-W light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?

a. A b. B c. C d. D e. C and D ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.4 Kirchhoff’s Rules 55. The circuit below contains 5 identical light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?

a. A: The one closest to the positive terminal of the battery. b. A and C: The bulbs closest to the positive terminal of the battery. c. A and B: Because they are closest to the terminals of the battery. d. C and D: Because they receive current from A and B and from E. e. E: Because the potential difference across E is that of the battery.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.4 Kirchhoff’s Rules 56. If R = 2.0 kΩ, C = 4.0 mF, ε = 8.0 V, Q = 20 mC, and I = 3.0 mA, what is the potential difference Vb − Va?

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a. +7.0 V b. +19 V c. +9.0 V d. −3.0 V e. −14 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 57. If R = 3.0 kΩ, C = 5.0 mF, ε = 6.0 V, Q = 15 mC, and I = 4.0 mA, what is the potential difference Vb − Va?

a. −3.0 V b. +9.0 V c. −15 V d. +21 V e. −6.0 V ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 58. If R = 4.0 kΩ, C = 3.0 mF, ε = 15 V, Q = 12 mC, and I = 2.0 mA, what is the potential difference Vb − Va?

a. +3.0 V b. −19 V c. −3.0 V d. +27 V e. +21 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 59. If R = 3.0 kΩ, C = 6.0 nF, ε 1 = 10.0 V, Q = 18 nC, ε 2 = 6.0 V, and I = 5.0 mA, what is the potential difference Vb − Va?

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a. −13 V b. +28 V c. +13 V d. −28 V e. +2.0 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 60. If ε 1 = 4.0 V, ε 2 = 12.0 V, R1 = 4 Ω, R2 = 12 Ω, C = 3 μF, Q = 18 μC, and I = 2.5 A, what is the potential difference Va − Vb?

a. −30 V b. 30 V c. 5.0 V d. −5.0 V e. −1.0 V ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 61. Determine the potential difference, VA − VB, in the circuit segment shown below when I = 2.0 mA and Q = 50 μC.

a. −40 V b. +40 V c. +20 V d. −20 V e. −10 V ANSWER: d POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 27.5 RC Circuits 62. If Q = 400 μC and the potential difference VA − VB = −10 V in the circuit segment shown below, what is the current in the resistor?

a. 1.0 mA right to left b. 1.0 mA left to right c. 3.5 mA right to left d. 3.5 mA left to right e. None of the above ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 63. If Q = 350 μC and I = 4.0 mA in the circuit segment shown below, determine the potential difference, VA − VB.

a. −30 V b. +80 V c. +40 V d. −40 V e. +10 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 64. In an RC circuit, how many time constants must elapse if an initially uncharged capacitor is to reach 80% of its final potential difference? a. 2.2 b. 1.9 c. 1.6 d. 3.0 e. 5.0 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 65. How many time constants must elapse if an initially charged capacitor is to discharge 55% of its stored energy through a resistor?

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a. 0.60 b. 0.46 c. 0.52 d. 0.40 e. 1.1 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.5 RC Circuits 66. In an RC circuit, what fraction of the final energy is stored in an initially uncharged capacitor after it has been charging for 3.0 time constants? a. 0.84 b. 0.90 c. 0.75 d. 0.60 e. 0.03 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 67. How long will it take a charged 80-μF capacitor to lose 20% of its initial energy when it is allowed to discharge through a 45-Ω resistor? a. 0.92 ms b. 0.64 ms c. 0.40 ms d. 0.19 ms e. 0.80 ms ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.5 RC Circuits 68. At t = 0 the switch S is closed with the capacitor uncharged. If C = 50 μF, ε = 20 V, and R = 4.0 kΩ, what is the charge on the capacitor when I = 2.0 mA?

a. 360 μC Copyright Cengage Learning. Powered by Cognero.

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b. 480 μC c. 240 μC d. 600 μC e. 400 μC ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.5 RC Circuits 69. At t = 0 the switch S is closed with the capacitor uncharged. If C = 30 μF, ε = 30 V, and R = 5.0 kΩ, at what rate is energy being stored in the capacitor when I = 2.0 mA?

a. 32 mW b. 40 mW c. 44 mW d. 36 mW e. 80 mW ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 70. At t = 0 the switch S is closed with the capacitor uncharged. If C = 40 μF, ε = 50 V, and R = 5.0 kΩ, how much energy is stored by the capacitor when I = 2.0 mA?

a. 20 mJ b. 28 mJ c. 32 mJ d. 36 mJ Copyright Cengage Learning. Powered by Cognero.

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e. 40 mJ ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 71. At t = 0 the switch S is closed with the capacitor uncharged. If C = 30 μF, ε = 50 V, and R = 10 kΩ, what is the potential difference across the capacitor when I = 2.0 mA?

a. 20 V b. 15 V c. 25 V d. 30 V e. 45 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 72. A capacitor in a single-loop RC circuit is charged to 85% of its final potential difference in 2.4 s. What is the time constant for this circuit? a. 1.5 s b. 1.3 s c. 1.7 s d. 1.9 s e. 2.9 s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 27.5 RC Circuits 73. The algebraic sum of the changes of potential around any closed circuit loop is a. zero. b. maximum. c. zero only if there are no sources of emf in the loop. d. maximum if there are no sources of emf in the loop. e. equal to the sum of the currents in the branches of the loop.

ANSWER: a Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.5 RC Circuits 74. The circuit below contains three 100-watt light bulbs and a capacitor. The emf ε = 110V. The capacitor is fully charged. Which light bulb(s) is(are) dimmest?

a. A b. B c. C d. A and B e. All three are equally bright (or dim).

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.5 RC Circuits 75. The circuit below contains three 100-W light bulbs and a capacitor. The emf ε = 110V. At the instant the switch S is closed, which light bulb is brightest?

a. A b. B c. C d. A and B e. All three are equally bright.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.5 RC Circuits 76. The circuit below contains three 100-W light bulbs and a capacitor. The emf is 110 V and the capacitor is fully Copyright Cengage Learning. Powered by Cognero.

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charged. Which light bulb(s) is(are) brightest?

a. A b. B c. C d. A and B e. A and C ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.5 RC Circuits 77. The circuit below contains 3 100-W light bulbs and a capacitor. The emf is 110 V. Which light bulb(s) is(are) brightest? (Assume the capacitor is fully charged.)

a. A b. B c. C d. A and B e. All three are equally bright.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.5 RC Circuits 78. Which of the identical light bulb(s) is(are) brightest when the capacitor has half its maximum charge?

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a. A b. B c. C d. A and B e. All three are equally bright.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.5 RC Circuits 79. The battery is disconnected from a series RC circuit after the capacitor is fully charged and is replaced by an open switch. When the switch is closed, a. the current through the resistor is always greater than the current through the capacitor. b. the current through the resistor is always less than the current through the capacitor. c. the current through the resistor is always equal to the current through the capacitor. d. the capacitor does not allow current to pass. e. the current stops in the resistor.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.5 RC Circuits 80. The capacitors are completely discharged in the circuit shown below.

The two resistors have the same resistance R and the two capacitors have the same capacitance C. After the switch is closed, the current a. is greatest in C1. b. is greatest in C2. c. is greatest in R1. d. is greatest in R2. e. is the same in C1, C2, R1 and R2.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 27.5 RC Circuits 81. A 5000-Ω resistor and a 50-μF capacitor are connected in series at t = 0 with a 6-V battery. The capacitor is initially Copyright Cengage Learning. Powered by Cognero.

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uncharged. What is the current in the circuit at t = 0? At t = 0.5 s? What is the maximum charge stored on the capacitor?

ANSWER: 1.2 mA, 0.162 mA, 300 μC POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.5 RC Circuits 82. An initially uncharged 10-μF capacitor is charged by a 10-V battery through a resistance R. The capacitor reaches a potential difference of 4 V in a period of 3 s after the charging began. Find the value of R. ANSWER: 587 kΩ POINTS: 3 DIFFICULTY: Challenging REFERENCES: 27.5 RC Circuits 83. What is the maximum number of 100-W lightbulbs you can connect in parallel in a 120-V home circuit without tripping the 20-A circuit breaker?

ANSWER: 23 POINTS: 2 DIFFICULTY: Average REFERENCES: 27.6 Household Wiring and Electrical Safety

6

1. An electron has a velocity of 6.0 × 10 m/s in the positive x direction at a point where the magnetic field has the components Bx = 3.0 T, By = 1.5 T, and Bz = 2.0 T. What is the magnitude of the acceleration of the electron at this point? a. 2.1 × 1018 m/s2 b. 1.6 × 1018 m/s2 c. 2.6 × 1018 m/s2 d. 3.2 × 1018 m/s2 e. 3.7 × 1018 m/s2 ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 2. A particle (q = 5.0 nC, m = 3.0 μg) moves in a region where the magnetic field has components Bx = 2.0 mT, By = 3.0 mT, and Bz = −4.0 mT. At an instant when the speed of the particle is 5.0 km/s and the direction of its velocity is 120° relative to the magnetic field, what is the magnitude of the acceleration of the particle? a. 33 m/s2 b. 17 m/s2 c. 39 m/s2 d. 25 m/s2 e. 45 m/s2 ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 3. A particle (q = −4.0 μC, m = 5.0 mg) moves in a uniform magnetic field with a velocity having a magnitude of 2.0 km/s and a direction that is 50° away from that of the magnetic field. The particle is observed to have an acceleration with a 2 magnitude of 5.8 m/s . What is the magnitude of the magnetic field? a. 5.3 mT b. 4.9 mT c. 5.1 mT d. 4.7 mT e. 3.6 mT ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 4. An electron moving in the positive x direction experiences a magnetic force in the positive z direction. If Bx = 0, what is the direction of the magnetic field? a. negative y direction b. positive y direction c. negative z direction d. positive z direction e. negative x direction ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 5. A 2.0-C charge moves with a velocity of (

) m/s and experiences a magnetic force of (

) N. The x component of the magnetic field is equal to zero. Determine the y component of the magnetic field. a. −3.0 T b. +3.0 T c. +5.0 T d. −5.0 T e. +6.0 T ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 6. A 2.0-C charge moves with a velocity of (

) m/s and experiences a magnetic force of (

) N. The x component of the magnetic field is equal to zero. Determine the z component of the magnetic field. a. −3.0 T b. +3.0 T Copyright Cengage Learning. Powered by Cognero.

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c. +5.0 T d. −5.0 T e. +6.0 T ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 7. A particle (mass = 2.0 mg, charge = −6.0 μC) moves in the positive direction along the x axis with a velocity of 3.0 km/s. It enters a magnetic field of ( 2 a.

(36 − 27 ) m/s b. c.

(−36 + 27 ) m/s (−24 + 18 ) m/s

d.

(24 − 18 ) m/s

2

e.

(24 − 27 ) m/s

2

) mT. What is the acceleration of the particle?

2 2

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 8. A particle (mass = 6.0 mg) moves with a speed of 4.0 km/s in a direction that makes an angle of 37° above the positive 2

x axis in the xy plane. At the instant it enters a magnetic field of (5.0 ) mT it experiences an acceleration of (8.0 ) m/s .

What is the charge of the particle? a. −4.8 μC b. 4.0 μC c. −4.0 μC d. 4.8 μC e. −5.0 μC ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 9. A positively charged particle has a velocity in the negative z direction at point P. The magnetic force on the particle at this point is in the negative y direction. Which one of the following statements about the magnetic field at point P can be determined from this data? a. Bx is positive. b. Bz is positive. c. By is negative. d. By is positive. e. Bx is negative.

ANSWER:

a

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 10. A charged particle (mass = 4.0 μg, charge = 5.0 μC) moves in a region where the only force on it is magnetic. What is the magnitude of the acceleration of the particle at a point where the speed of the particle is 5.0 km/s, the magnitude of the magnetic field is 8.0 mT, and the angle between the direction of the magnetic field and the velocity of the particle is 60°? a. 39 km/s2 b. 43 km/s2 c. 48 km/s2 d. 52 km/s2 e. 25 km/s2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 11. A charged particle (mass = M, charge = Q > 0) moves in a region of space where the magnetic field has a constant magnitude of B and a downward direction. What is the magnetic force on the particle at an instant when it is moving horizontally toward the north with speed v? a. QvB toward the east b. Zero c. QvB toward the west d. QvB upward e. QvB toward the south ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 12. What is the magnitude of the magnetic force on a charged particle (Q = 5.0 μC) moving with a speed of 80 km/s in the positive x direction at a point where Bx = 5.0 T, By = −4.0 T, and Bz = 3.0 T? a. 2.8 N b. 1.6 N c. 1.2 N d. 2.0 N e. 0.4 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 13. A charged particle (m = 5.0 g, q = −70 μC) moves horizontally at a constant speed of 30 km/s in a region where the 2 free-fall gravitational acceleration is 9.8 m/s downward, the electric field is 700 N/C upward, and the magnetic field is perpendicular to the velocity of the particle. What is the magnitude of the magnetic field in this region? a. 47 mT Copyright Cengage Learning. Powered by Cognero.

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b. zero c. 23 mT d. 35 mT e. 12 mT ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 4

14. Equal charges, one at rest, the other having a velocity of 10 m/s, are released in a uniform magnetic field. Which charge has the largest force exerted on it by the magnetic field? a. The charge that is at rest. b. The charge that is moving, if its velocity is parallel to the magnetic field direction when it is released. c. The charge that is moving, if its velocity makes an angle of 45o with the direction of the magnetic field when it is released. d. The charge that is moving, if its velocity is perpendicular to the magnetic field direction when it is released. e. All the charges above experience equal forces when released in the same magnetic field.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 15. One reason why we know that magnetic fields are not the same as electric fields is because the force exerted on a charge +q a. is in opposite directions in electric and magnetic fields. b. is in the same direction in electric and magnetic fields. c. is parallel to a magnetic field and perpendicular to an electric field. d. is parallel to an electric field and perpendicular to a magnetic field. e. is zero in both if the charge is not moving.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 16. You stand near the Earth's equator. A positively charged particle that starts moving parallel to the surface of the Earth in a straight line directed east is initially deflected upwards. If you know there are no electric fields in the vicinity, a possible reason why the particle does not initially acquire a downward component of velocity is because near the equator the magnetic field lines of the Earth are directed a. upward. b. downward. c. from south to north. d. from north to south. e. from east to west.

ANSWER: c POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 17. The diagram below shows the position of a long, straight wire perpendicular to the page and a set of directions labeled A through H.

When the current in the wire is directed out of the page, the direction of the magnetic field at point P is a. A. b. B. c. C. d. D. e. E. ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 18. The diagram below shows the position of a long, straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed out of the page, the direction of the magnetic field at point P is

a. D. b. E. c. F. d. G. e. H. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 19. The diagram below shows the position of a long, straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed out of the page, the direction of the magnetic field at point P is

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a. E. b. F. c. G. d. H. e. A. ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 20. The diagram below shows the position of a long, straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed out of the page, the direction of the magnetic field at point P is

a. E. b. F. c. G. d. H. e. A. ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 21. The point P lies along the perpendicular bisector of the line connecting two long, straight wires S and T that are perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed up out of the page, the direction of the magnetic field at P is closest to the direction of

a. E. b. F. Copyright Cengage Learning. Powered by Cognero.

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c. G. d. H. e. A ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 22. The point P lies along the perpendicular bisector of the line connecting two long, straight wires S and T perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed out of the page, the direction of the magnetic field at P is closest to the direction of

a. E. b. F. c. G. d. H. e. A. ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 23. The point P lies along the perpendicular bisector of the line connecting two long, straight wires S and T perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed into the page, the direction of the magnetic field at P is closest to the direction of

a. E. b. F. c. G. d. H. e. A. ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) Copyright Cengage Learning. Powered by Cognero.

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24. The point P lies along the perpendicular bisector of the line connecting two long, straight wires S and T perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed into the page, the direction of the magnetic field at P is closest to the direction of

a. A b. B. c. C. d. D. e. E. ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 25. An explorer walks into a lab in a science building. She has a compass in her hand and finds that the south pole of her compass points toward the room's east wall when she is nearer that wall and toward the west wall when she is nearer that wall. You could explain this if magnetized metal had been installed in the east and west walls with north poles pointing into the room. If no magnetic material was installed in the north or South walls of the room, she would expect that a. the south pole of the compass would tend to point toward those walls. b. the north pole of the compass would tend to point toward those walls. c. the compass needle would not point in any particular direction. d. the north pole of the compass needle would tend to point toward the centers of those walls, but the south pole would tend to point toward the sides of those walls. e. the south pole of the compass needle would tend to point toward the centers of those walls, but the north pole would tend to point toward the sides of those walls.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) 26. The reason the north pole of a bar magnet free to rotate points north is because a. the south geographic pole of the earth is the earth's magnetic north pole. b. the south geographic pole of the earth is the earth's magnetic south pole. c. there is a net accumulation of negative magnetic charge at the earth's south geographic pole. d. there is a net accumulation of positive magnetic charge at the earth's north geographic pole. e. the north geographic pole of the earth is the earth's magnetic north pole.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.1 Analysis Model: Particle in a Field (Magnetic) Copyright Cengage Learning. Powered by Cognero.

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27. A uniform magnetic field of 0.50 T is directed along the positive x axis. A proton moving with a speed of 60 km/s enters this field. The helical path followed by the proton shown has a pitch of 5.0 mm. Determine the angle between the magnetic field and the velocity of the proton.

a. 39° b. 51° c. 44° d. 34° e. 71° ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 28. A deuteron is accelerated from rest through a 10-kV potential difference and then moves perpendicularly to a uniform -27 magnetic field with B = 1.6 T. What is the radius of the resulting circular path? (deuteron: m = 3.3 × 10 kg, q = 1.6 × -19 10 C) a. 19 mm b. 13 mm c. 20 mm d. 10 mm e. 9.0 mm ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 29. A particle (m = 3.0 μg, q = 5.0 μC) moves in a uniform magnetic field given by ( particle is equal to (

) mT. At t = 0 the velocity of the

) m/s. The subsequent path of the particle is

a. circular with a 50-cm radius. b. helical with a 6.3-cm pitch. c. circular with a period of 31 ms. d. helical with a 40-cm radius. e. none of the above ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field Copyright Cengage Learning. Powered by Cognero.

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30. A 500-eV electron and a 300-eV electron trapped in a uniform magnetic field move in circular paths in a plane perpendicular to the magnetic field. What is the ratio of the radii of their orbits? a. 2.8 b. 1.7 c. 1.3 d. 4.0 e. 1.0 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 31. The boundary shown is that of a uniform magnetic field directed in the positive z direction. An electron enters the magnetic field with a velocity pointing along the x axis and exits 0.63 μs later at point A. What is the magnitude of the magnetic field?

a. 18 μT b. 14 μT c. 28 μT d. 34 μT e. 227 μT ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 32. A proton moves around a circular path (radius = 2.0 mm) in a uniform 0.25-T magnetic field. What total distance does -27 -19 this proton travel during a 1.0-s time interval? (m = 1.67 × 10 kg, q = 1.6 × 10 C) a. 82 km b. 59 km c. 71 km d. 48 km e. 7.5 km ANSWER: d POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 33. A charged particle (m = 2.0 g, q = −50 μC) moves in a region of uniform field along a helical path (radius = 4.0 cm, pitch = 8.0 cm) as shown. What is the angle between the velocity of the particle and the magnetic field?

a. 27° b. 72° c. 63° d. 18° e. 58° ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 34. A charged particle moves in a region of uniform magnetic field along a helical path (radius = 5.0 cm, pitch = 12 cm, period = 5.0 ms). What is the speed of this particle as it moves along this path? a. 67 m/s b. 26 m/s c. 63 m/s d. 24 m/s e. 87 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 35. Two single charged ions moving perpendicularly to a uniform magnetic field (B = 0.40 T) with speeds of 5 000 km/s follow circular paths that differ in diameter by 5.0 cm. What is the difference in the mass of these two ions? a. 2.6 × 10-28 kg b. 6.4 × 10-28 kg c. 3.2 × 10-28 kg d. 5.1 × 10-28 kg e. 1.1 × 10-28 kg ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field Copyright Cengage Learning. Powered by Cognero.

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36. A charged particle moves in a region of uniform magnetic field along a helical path (radius = 4.0 cm, pitch = 20 cm, period = 2.0 ms). What is the speed of the particle as it moves along this path? a. 0.13 km/s b. 0.10 km/s c. 0.16 km/s d. 0.23 km/s e. 0.06 km/s ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 37. What is the radius of curvature of the path of a 3.0-keV proton in a perpendicular magnetic field of magnitude 0.80 T? a. 9.9 mm b. 1.1 cm c. 1.3 cm d. 1.4 cm e. 7.6 mm ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 38. An electron moves in a region where the magnetic field is uniform and has a magnitude of 80 μT. The electron follows a helical path which has a pitch of 9.0 mm and a radius of 2.0 mm. What is the speed of this electron as it moves in this region? a. 48 km/s b. 28 km/s c. 20 km/s d. 35 km/s e. 8.0 km/s ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 39. An electron moves in a region where the magnetic field is uniform, has a magnitude of 60 μT, and points in the positive x direction. At t = 0 the electron has a velocity that has an x component of 30 km/s, a y component of 40 km/s, and a z component of zero. What is the radius of the resulting helical path? a. 4.7 mm b. 18 mm c. 3.8 mm d. 2.8 mm e. 5.7 mm ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 40. An electron follows a circular path (radius = 15 cm) in a uniform magnetic field (magnitude = 3.0 G). What is the period of this motion? a. 0.12 μs b. 1.2 ms c. 0.18 μs d. 1.8 ms e. 1.8 μs ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 41. A proton with a kinetic energy of 0.20 keV follows a circular path in a region where the magnetic field is uniform and has a magnitude of 60 mT. What is the radius of this path? a. 4.1 cm b. 2.9 cm c. 3.4 cm d. 5.1 cm e. 2.4 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 42. A proton is accelerated from rest through a potential difference of 150 V. It then enters a region of uniform magnetic field and moves in a circular path (radius = 12 cm). What is the magnitude of the magnetic field in this region? a. 18 mT b. 12 mT c. 15 mT d. 22 mT e. 10 mT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 43. A proton is accelerated from rest through a potential difference of 2.5 kV and then moves perpendicularly through a uniform 0.60-T magnetic field. What is the radius of the resulting path? a. 15 mm b. 12 mm c. 18 mm d. 24 mm e. 8.5 mm ANSWER: b POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 44. An electron moves in a region where the magnetic field is uniform, has a magnitude of 60 μT, and points in the positive x direction. At t = 0 the electron has a velocity that has an x component of 30 km/s, a y component of 40 km/s, and a z component of zero. What is the pitch of the resulting helical path? a. 13 mm b. 32 mm c. 24 mm d. 18 mm e. 3.8 mm ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 45. Three particles of equal charge, X, Y, and Z, enter a uniform magnetic field B. X has velocity of magnitude v parallel to the field. Y has velocity of magnitude v perpendicular to the field. Z has equal velocity components v parallel and perpendicular to the field. Rank the radii of their orbits from least to greatest. a. Rx = Ry < Rz. b. Rx < Ry < Rz. c. Rx = Ry = Rz. d. Rx > Ry > Rz. e.

Rx < Ry =

.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 46. A magnetic field is directed out of the page. Two charged particles enter from the top and take the paths shown in the figure. Which statement is correct?

a. Particle 1 has a positive charge and particle 2 has a negative charge. b. Both particles are positively charged. c. Both particles are negatively charged. d. Particle one has a negative charge and particle 2 has a positive charge. e. The direction of the paths depends on the magnitude of the velocity, not on the sign of the charge.

ANSWER: a POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field -27

47. A physicist claims that she has found a new particle with a mass 200 000 times the mass of the proton (1.67 × 10 -19 kg) and a charge of 3.20 × 10 C. If she is correct, such a particle traveling in a circle in a uniform, 5.00-T magnetic field at a velocity of 2 500 m/s will have a radius of a. 0.261 m. b. 0.522 m. c. 1.04 m. d. 3.27 m. e. 3.13 × 1026 m.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 48. Bert says that a charged particle in a vacuum can travel in a helix only if a uniform electric field and a uniform magnetic field are both present and both parallel to the axis of the helix. Stuart says that only a magnetic field with a component parallel to the axis of the helix is needed. Which one, if either, is correct, and why? a. Bert, because the charged particle's velocity can have a vertical component only if an electric field in the vertical direction is present. b. Stuart, because a component of velocity in the vertical direction is not changed by a vertical component of a magnetic field. c. Bert, because a component of velocity in the vertical direction is changed by a vertical component of a magnetic field. d. Stuart, because an electric field in the vertical direction would cause the particle to come to a complete stop. e. Neither, because particles cannot move in helical paths in the presence of magnetic and electric fields.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field

49. A magnetic field of 2.00 T is applied to a bubble chamber to make the tracks of protons and other charged particles identifiable by the radius of the circles they move in. If a high-energy proton moves along an arc of a 3.30-m circle, what -19 -27 is the momentum of the proton? [q = 1.60 × 10 C, m = 1.67 × 10 kg] -18 ANSWER: 1.06 × 10 kg ⋅ m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field 50. At what speed would a proton need to circle the Earth at a height of 1 000 km above the equator if the Earth's -8 magnetic field is horizontal and directed north-south, with an intensity of 4.00 × 10 T? (The radius of the Earth is 6 400 -19 -27 km and the charge and mass of the proton are q = 1.60 × 10 C and mp = 1.67 × 10 kg. Ignore relativistic corrections.)

7 ANSWER: 2.84 × 10 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 28.2 Motion of a Charged Particle in a Uniform Magnetic Field Copyright Cengage Learning. Powered by Cognero.

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51. What is the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E = 4.0 kV/m and B = 8.0 mT? a. 0.65 eV b. 0.71 eV c. 0.84 eV d. 0.54 eV e. 1.4 eV ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.3 Applications Involving Charged Particles Moving in a Magnetic Field 52. What value of B should be used in a velocity selector to separate out 2.0-keV protons if E is fixed at 80 kV/m? a. 0.18 T b. 0.11 T c. 0.15 T d. 0.13 T e. 0.23 T ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.3 Applications Involving Charged Particles Moving in a Magnetic Field 53. A velocity selector uses a fixed electric field of magnitude E and the magnetic field is varied to select particles of various energies. If a magnetic field of magnitude B is used to select a particle of a certain energy and mass, what magnitude of magnetic field is needed to select a particle of equal mass but twice the energy? a. 0.50 B b. 1.4 B c. 2.0 B d. 0.71 B e. 1.7 B ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.3 Applications Involving Charged Particles Moving in a Magnetic Field 54. A stream of electrons passes through a velocity filter where the crossed magnetic and electric fields are 0.020 T and 4 5.00 × 10 V/m, respectively. Find the kinetic energy (in electron volts) of the electrons passing through the filter. [1 eV = -19 1.60 × 10 J] ANSWER: 17.8 eV POINTS: 2 DIFFICULTY: Average REFERENCES: 28.3 Applications Involving Charged Particles Moving in a Magnetic Field 55. A 2.0-m wire carries a current of 15 A directed along the positive x axis in a region where the magnetic field is uniform and given by B = (30 − 40 ) mT. What is the resulting magnetic force on the wire?

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a. b. c. d.

(+1.2 ) N (−1.2 ) N (−1.5 ) N (+1.5 ) N

e.

(+0.90 ) N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 56. A straight wire carries a current of 40 A in a uniform magnetic field (magnitude = 80 mT). If the force per unit length on this wire is 2.0 N/m, determine the angle between the wire and the magnetic field. a. either 39° or 141° b. either 25° or 155° c. either 70° or 110° d. either 42° or 138° e. either 65° or 115° ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 57. A segment of wire carries a current of 25 A along the x axis from x = −2.0 m to x = 0 and then along the y axis from y = 0 to y = 3.0 m. In this region of space, the magnetic field is equal to 40 mT in the positive z direction. What is the magnitude of the force on this segment of wire? a. 2.0 N b. 5.0 N c. 1.0 N d. 3.6 N e. 3.0 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 58. A segment of wire carries a current of 25 A along the x axis from x = −2.0 m to x = 0, and then along the z axis from z = 0 to z = 3.0 m. In this region of space, the magnetic field is equal to 40 mT in the positive z direction. What is the magnitude of the force on this segment of wire? a. 1.0 N b. 5.0 N c. 2.0 N d. 3.6 N e. 3.0 N ANSWER: c POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 59. A straight wire of length 70 cm carries a current of 50 A and makes an angle of 60° with a uniform magnetic field. If the force on the wire is 1.0 N, what is the magnitude of B? a. 41 mT b. 33 mT c. 55 mT d. 87 mT e. 57 mT ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 60. A straight wire of length L carries a current I in the positive z direction in a region where the magnetic field is uniform and specified by Bx = 3B, By = −2B, and Bz = B, where B is a constant. What is the magnitude of the magnetic force on the wire? a. 3.2 ILB b. 5.0 ILB c. 4.2 ILB d. 3.6 ILB e. 1.0 ILB ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 61. A straight wire is bent into the shape shown. Determine the net magnetic force on the wire when the current I travels in the direction shown in the magnetic field

.

a. 2IBL in the −z direction b. 2IBL in the +z direction c. 4IBL in the +z direction d. 4IBL in the −z direction e. zero ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor Copyright Cengage Learning. Powered by Cognero.

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62. A straight wire is bent into the shape shown. Determine the net magnetic force on the wire.

a. Zero b. IBL in the +z direction c. IBL in the −z direction d. 1.7 IBL in the +z direction e. 1.4 IBL in the −z direction ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 63. What is the magnetic force on a 2.0-m length of (straight) wire carrying a current of 30 A in a region where a uniform magnetic field has a magnitude of 55 mT and is directed at an angle of 20° away from the wire? a. 1.5 N b. 1.3 N c. 1.1 N d. 1.7 N e. 3.1 N ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 64. The figure shows the orientation of a rectangular loop consisting of 80 closely wrapped turns each carrying a current I. The magnetic field in the region is ( ) mT. The loop can turn about the y axis. If θ = 30°, a = 0.40 m, b = 0.30 m, and I = 8.0 A, what is the magnitude of the torque exerted on the loop?

a. 2.5 N ⋅ m Copyright Cengage Learning. Powered by Cognero.

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b. 1.5 N ⋅ m c. 3.1 N ⋅ m d. 2.7 N ⋅ m e. 0.34 N ⋅ m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 65. A straight 10-cm wire bent at its midpoint so as to form an angle of 90° carries a current of 10 A. It lies in the xy plane in a region where the magnetic field is in the positive z direction and has a constant magnitude of 3.0 mT. What is the magnitude of the magnetic force on this wire? a. 3.2 mN b. 2.1 mN c. 5.3 mN d. 4.2 mN e. 6.0 mN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 66. A wire (mass = 50 g, length = 40 cm) is suspended horizontally by two vertical wires which conduct a current I = 8.0 A, as shown in the figure. The magnetic field in the region is into the paper and has a magnitude of 60 mT. What is the tension in either wire?

a. 0.15 N b. 0.68 N c. 0.30 N d. 0.34 N e. 0.10 N ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 67. A coaxial cable has an inner cylindrical conductor surrounded by cylindrical insulation and an outer cylindrical conducting shell. The outer shell carries the same current but in the opposite direction from that in the inner conductor as shown. If the coaxial cable sits in a uniform magnetic field directed upwards with respect to the cable, the effect of the field on the cable is

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a. a net force to the left. b. a net force to the right. c. a net force upwards. d. no net force but a slight shift of the inner conductor to the left and the outer conductor to the right. e. no net force but a slight shift of the inner conductor to the right and the outer conductor to the left.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 68. An unusual lightning strike has a vertical portion with a positive current of +400 A upwards. The Earth's magnetic field at that location is parallel to the ground and has a magnitude of 30 μT. In N, the force exerted by the Earth's magnetic field on the 25-m-long current is a. 0. b. 0.012 N, East. c. 0.012 N, West. d. 0.30 N, West. e. 300 N, East.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 69. An unusual lightning strike has a vertical portion with a current of −400 A downwards. The Earth's magnetic field at that location is parallel to the ground and has a magnitude of 30 μT. In N, the force exerted by the Earth's magnetic field on the 25-m-long current is a. 0. b. 0.012 N, East. c. 0.012 N, West. d. 0.30 N, West. e. 300 N, East.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.4 Magnetic Force Acting on a Current-Carrying Conductor 70. A current of 4.0 A is maintained in a single circular loop having a circumference of 80 cm. An external magnetic field of 2.0 T is directed so that the angle between the field and the plane of the loop is 20°. Determine the magnitude of the torque exerted on the loop by the magnetic forces acting upon it.

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a. 0.41 N ⋅ m b. 0.14 N ⋅ m c. 0.38 N ⋅ m d. 0.27 N ⋅ m e. 0.77 N ⋅ m ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.5 Torque on a Current Loop in a Uniform Magnetic Field 71. The figure shows the orientation of a flat circular loop consisting of 50 closely wrapped turns each carrying a current I. The magnetic field in the region is directed in the positive z direction and has a magnitude of 50 mT. The loop can turn about the y axis. If θ = 20°, R = 0.50 m, and I = 12A, what is the magnitude of the torque exerted on the loop?

a. 8.1 N ⋅ m b. 24 N ⋅ m c. 22 N ⋅ m d. 13 N ⋅ m e. 16 N ⋅ m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 28.5 Torque on a Current Loop in a Uniform Magnetic Field 72. What current must be maintained in a square loop (50 cm on a side) to create a torque of 1.0 N ⋅ m about an axis through its center and parallel to one of its sides when a magnetic field of magnitude 70 mT is directed at 40° to the plane of the loop? a. 66 A b. 89 A c. 61 A d. 75 A e. 37 A ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.5 Torque on a Current Loop in a Uniform Magnetic Field 73. A circular loop (radius = 0.50 m) carries a current of 3.0 A and has unit normal vector of ( Copyright Cengage Learning. Powered by Cognero.

)/3. What is the Page 578

x component of the torque on this loop when it is placed in a uniform magnetic field of ( a. 4.7 N ⋅ m b. 3.1 N ⋅ m c. 19 N ⋅ m d. 9.4 N ⋅ m e. 12 N ⋅ m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 28.5 Torque on a Current Loop in a Uniform Magnetic Field

)T?

74. A square loop (L = 0.20 m) consists of 50 closely wrapped turns, each carrying a current of 0.50 A. The loop is oriented as shown in a uniform magnetic field of 0.40 T directed in the positive y direction. What is the magnitude of the torque on the loop?

a. 0.21 N ⋅ m b. 0.20 N ⋅ m c. 0.35 N ⋅ m d. 0.12 N ⋅ m e. 1.73 N ⋅ m ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.5 Torque on a Current Loop in a Uniform Magnetic Field 75. A rectangular coil (0.20 m × 0.80 m) has 200 turns and is in a uniform magnetic field of 0.30 T. When the orientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is 0.080 N ⋅ m.

What is the current in the coil? a. 5.0 mA b. 1.7 A c. 8.3 mA d. 1.0 A e. 42 mA ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 28.5 Torque on a Current Loop in a Uniform Magnetic Field 76. A circular coil (radius = 0.40 m) has 160 turns and is in a uniform magnetic field. When the orientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is 0.16 N ⋅ m when the current in the coil is 4.0 mA. What is the magnitude of the magnetic field? a. 0.37 T b. 1.6 T c. 0.50 T d. 1.2 T e. 2.5 T ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 28.5 Torque on a Current Loop in a Uniform Magnetic Field 77. A current loop is oriented in three different positions relative to a uniform magnetic field. In position 1 the plane of the loop is perpendicular to the field lines. In position 2 and 3 the plane of the loop is parallel to the field as shown. The torque on the loop is maximum in

a. position 1. b. position 2. c. position 3 d. positions 2 and 3. e. all three positions.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.5 Torque on a Current Loop in a Uniform Magnetic Field 78. The magnetic field in a region of space is parallel to the surface of a long, flat table. Imagine that this page is lying flat on the table. When current is present in the coil, which is lying on the table, the coil tends to rotate so that the left side moves up and the right side moves down. The magnetic field is

a. directed parallel to the page and downwards. b. directed parallel to the page and upwards. c. directed parallel to the page and to the right.

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d. directed parallel to the page and to the left. e. in a direction that cannot be determined in this experiment ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 28.5 Torque on a Current Loop in a Uniform Magnetic Field 79. A thin ribbon of a silver alloy 2.00 cm wide and 0.015 0 mm thick carries a current of 6.98 A perpendicular to a -4 magnetic field. The Hall voltage is found to be 1.24 × 10 V when the magnetic field is 2.50 T. Calculate n, the number of charge carriers per cubic meter.

28 3 ANSWER: 5.86 × 10 /m POINTS: 2 DIFFICULTY: Average REFERENCES: 28.6 The Hall Effect

1. One long wire carries a current of 30 A along the entire x axis. A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0, 4, 0) m. What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis? a. 4.0 μT b. 5.0 μT c. 3.0 μT d. 7.0 μT e. 1.0 μT ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 2. Two long, parallel wires each carry a current of 5.0 A directed to the east. The two wires are separated by 8.0 cm. What is the magnitude of the magnetic field at a point that is 5.0 cm from each of the wires? a. 72 μT b. 48 μT c. 24 μT d. 96 μT e. 32 μT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 3. A 2.0-cm length of wire centered on the origin carries a 20-A current directed in the positive y direction. Determine the magnetic field at the point x = 5.0 m on the x-axis. a. 1.6 nT in the negative z direction b. 1.6 nT in the positive z direction c. 2.4 nT in the negative z direction d. 2.4 nT in the negative z direction Copyright Cengage Learning. Powered by Cognero.

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e. None of the above ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.1 The Biot–Savart Law 4. A long, straight wire carries a current of 40 A in a region where a uniform external magnetic field has a 30-μT magnitude and is parallel to the current. What is the magnitude of the resultant magnetic field at a point that is 20 cm from the wire? a. 70 μT b. 40 μT c. 10 μT d. 50 μT e. 36 μT ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 5. A segment of wire of total length 3.0 m carries a 15-A current and is formed into a semicircle. Determine the magnitude of the magnetic field at the center of the circle along which the wire is placed. a. 1.6 μT b. 4.9 μT c. 1.0 μT d. 9.8 μT e. 15 μT ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 6. A segment of wire of total length 2.0 m is formed into a circular loop having 5.0 turns. If the wire carries a 1.2-A current, determine the magnitude of the magnetic field at the center of the loop. a. 79 μT b. 69 μT c. 59 μT d. 89 μT e. 9.4 μT ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.1 The Biot–Savart Law 7. If a = 2.0 cm, b = 5.0 cm, and I = 20 A, what is the magnitude of the magnetic field at the point P?

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a. 4.5 μT b. 7.5 μT c. 9.0 μT d. 6.0 μT e. 3.6 μT ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 8. If a = 1.0 cm, b = 3.0 cm, and I = 30 A, what is the magnitude of the magnetic field at point P?

a. 0.62 mT b. 0.59 mT c. 0.35 mT d. 0.31 mT e. 0.10 mT ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 9. A straight wire (length = 8.0 m) is bent to form a square. If the wire carries a current of 20 A, what is the magnitude of the magnetic field at the center of the square? a. 17 μT b. 14 μT c. 11 μT d. 20 μT e. 36 μT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law Copyright Cengage Learning. Powered by Cognero.

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10. In the figure, if a = 2.0 cm, b = 4.0 cm, and I = 2.0 A, what is the magnitude of the magnetic field at point P?

a. 49 μT b. 39 μT c. 50 μT d. 69 μT e. 13 μT ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 11. The segment of wire (total length = 6R, including the incoming and outgoing portions of the wire) is formed into the shape shown and carries a current I. What is the magnitude of the resulting magnetic field at the point P?

a.

b.

c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 29.1 The Biot–Savart Law 12. The segment of wire (total length including portions of incoming and outgoing wire = 6R) is formed into the shape shown and carries a current I. What is the magnitude of the resulting magnetic field at the point P?

a.

b.

c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 13. What is the magnitude of the magnetic field at point P if a = R and b = 2R?

a.

b.

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c.

d.

e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 14. What is the magnitude of the magnetic field at point P if a = R and b = 2R?

a.

b.

c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 15. What is the magnitude of the magnetic field at point P if a = R and b = 2R?

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a.

b.

c.

d.

e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 16. What is the magnitude of the magnetic field at point P in the figure if a = 2.0 cm, b = 4.5 cm, and I = 5.0 A?

a. 87 μT, into the paper b. 87 μT, out of the paper c. 0.23 mT, out of the paper d. 0.23 mT, into the paper e. 23 μT, into the paper ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 17. A single circular (radius = R) loop of wire is located in the y-z plane with its center at the origin. The loop has a clockwise current as seen from the point (+R, 0, 0). The direction of the magnetic field at the point Copyright Cengage Learning. Powered by Cognero.

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a. (0, 0, 0) is −i and at the point (+R, 0, 0) is −i. b. (0, 0, 0) is −i and at the point (0, +2R, 0) is −i. c. (0, 0, 0) is +i and at the point (+R, 0, 0) is +i. d. (0, 0, 0) is +i and at the point (0, +2R, 0) is +i. e. None of the above ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 18. A current element (length = 1.0 cm) lies along the x axis with its center at x = 0 and carries a 20-A current in the positive x direction. Consider only the field of this current element and decide which combination of the following statements is correct.

1.

2.

3.

4.

The field at (0, 0, 1.0 m) is in the positive z direction.

The field at (0, 1.0 m, 0) is in the negative y direction.

The field at (1.0 m, 0, 0) is zero.

The field at (0, 0, 1.0 m) is in the negative y direction. a. 3 and 4 b. 1 and 3 c. 2 and 4 d. 1 and 2 e. None of these ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 19. Which diagram correctly shows the magnetic field lines created by a circular current loop in which current flows in the direction shown? a.

b.

c.

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d.

e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 20. By using a compass to measure the magnetic field direction at various points adjacent to a long straight wire, you can show that the wire's magnetic field lines are a. straight lines in space that go from one magnetic charge to another. b. straight lines in space that are parallel to the wire. c. straight lines in space that are perpendicular to the wire. d. circles that have their centers on the wire and lie in planes perpendicular to the wire. e. circles that have the wire lying along a diameter of the circle.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 21. At a point in space where the magnetic field is measured, the magnetic field produced by a current element a. points radially away in the direction from the current element to the point in space. b. points radially in the direction from the point in space towards the current element. c. points in a direction parallel to the current element. d. points in a direction parallel to but opposite in direction to the current element. e. points in a direction that is perpendicular to the current element and perpendicular to the radial direction.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 22. A long wire lies in a tangle on the surface of a table, as shown below. When a current is run through the wire as shown, the largest component of the magnetic field at X points

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a. into the table. b. out of the table. c. parallel to the nearest segment of wire. d. antiparallel to the nearest segment of wire. e. along a circle which has its center at the center of the overall loop.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 23. Equal currents of magnitude I travel out of the page in wires M and N. Eight directions are indicated by letters A through H.

What is the direction of the magnetic field at point P? a. E. b. F. c. G. d. H. e. A. ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 24. Equal currents of magnitude I travel out of the page in wire M and into the page in wire N. Eight directions are indicated by letters A through H.

What is the direction of the magnetic field at point P? a. A Copyright Cengage Learning. Powered by Cognero.

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b. B c. C d. D e. E ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 25. Equal currents of magnitude I travel into the page in wire M and out of the page in wire N. Eight directions are indicated by letters A through H.

What is the direction of the magnetic field at point P? a. C b. E c. F d. G e. H ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 26. Equal currents of magnitude I travel into the page in wires M and N. Eight directions are indicated by letters A through H.

What is the direction of the magnetic field at point P? a. B b. C c. D d. E e. F ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 27. If you were to travel parallel to an infinitely long straight wire with current I at the same velocity as the electrons in Copyright Cengage Learning. Powered by Cognero.

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the wire at a distance a from the wire, what would be the magnitude of the magnetic field, according to your measuring instruments? a. 0 b.

c.

d.

e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 28. Two parallel and coaxial current loops of radius a are placed a distance 2L apart. The current in each ring circulates in the same direction. At a point on the axis halfway between the loops, what is the magnitude of the magnetic field? a. 0 b.

c.

d.

e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 29. Two parallel and coaxial current loops of radius a are placed a distance 2L apart. When you look along the axis at the loops, the current in one is clockwise, and counterclockwise in the other. At a point on the axis halfway between the loops, what is the magnitude of the magnetic field? a. 0 b.

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c.

d.

e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.1 The Biot–Savart Law 30. Two current loops are coaxial and coplanar. One has radius a and the other has radius 2a. Current 2I in the outer loop is parallel to current I in the inner loop. What is the magnitude of the magnetic field at the center of the two loops? a. 0 b.

c.

d.

e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 31. Two current loops are coaxial and coplanar. One has radius a and the other has radius 2a. Current 2I in the outer loop is antiparallel to current I in the inner loop. What is the magnitude of the magnetic field at the center of the two loops? a. 0 b.

c.

d.

e.

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ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 32. We find that N current loops are coplanar and coaxial. The first has radius a and current I. The second has radius 2a and current 2I, and the pattern is repeated up to the Nth, which has radius Na and current NI. The current in each loop is counterclockwise as seen from above. What is the magnitude of the magnetic field at the center of the loops? a.

b.

c.

d.

e.

ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.1 The Biot–Savart Law 33. We find that 2N current loops are coplanar and coaxial. The first has radius a and current I. The second has radius 2a and current 2I, and the pattern is repeated up to the Nth, which has radius Na and current NI. The current in the loops alternates in direction from loop to loop as seen from above. Thus, the current in the first loop is counterclockwise, in the next clockwise, up to the last loop where it is again clockwise. What is the magnitude of the magnetic field at the center of the loops? a. 0 b.

c.

d.

e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law Copyright Cengage Learning. Powered by Cognero.

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4

34. A superconducting wire carries a current of 1.0 × 10 A. Find the magnetic field at a distance of 1.0 m from the wire.

-3 ANSWER: 2.0 × 10 T POINTS: 2 DIFFICULTY: Average REFERENCES: 29.1 The Biot–Savart Law 35. The planetary model of the hydrogen atom consists of an electron in a circular orbit about a proton. The motion of the -19 -11 electron of charge 1.60 × 10 C creates an electric current. The radius of the electron orbit is 5.30 × 10 m and the 6 electron's velocity is 2.20 × 10 m/s. What is the magnetic field strength at the location of the proton?

ANSWER: 12.5 T POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.1 The Biot–Savart Law 36. Three long wires parallel to the x axis carry currents as shown. If I = 20 A, what is the magnitude of the magnetic field at the origin?

a. 37 μT b. 28 μT c. 19 μT d. 47 μT e. 58 μT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 37. Each of two long, straight, parallel wires separated by a distance of 16 cm carries a current of 20 A in the same direction. What is the magnitude of the resulting magnetic field at a point that is 10 cm from each wire? a. 57 μT b. 80 μT c. 64 μT d. 48 μT e. 40 μT ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors Copyright Cengage Learning. Powered by Cognero.

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38. Two long, straight, parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in opposite directions. What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the 30-A current and 25 cm from the other wire? a. 51 μT b. 33 μT c. 72 μT d. 64 μT e. 46 μT ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 39. Two long, parallel wires carry unequal currents in the same direction. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 μT. What is the larger of the two currents? a. 5.3 A b. 3.8 A c. 4.5 A d. 3.0 A e. 0.5 A ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 40. Two long, straight wires carry currents perpendicular to the xy plane. One carries a current of 50 A and passes through the point x = 5.0 cm on the x axis. The second wire has a current of 80 A and passes through the point y = 4.0 cm on the y axis. What is the magnitude of the resulting magnetic field at the origin? a. 200 μT b. 600 μT c. 450 μT d. 300 μT e. 400 μT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 41. Two very long, parallel wires carry currents in the positive x direction. One wire (current = 15 A) is coincident with the x axis. The other wire (current = 50 A) passes through the point (0, 4.0 mm, 0). What is the magnitude of the magnetic field at the point (0, 0, 3.0 mm)? a. 3.8 mT b. 2.7 mT c. 2.9 mT d. 3.0 mT e. 0.6 mT Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 42. Each of two parallel wires separated by 8.0 mm carries a 20-A current. These two currents are oppositely directed.

Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires. a. 2.0 mT b. 1.6 mT c. 1.3 mT d. 1.8 mT e. 1.0 mT ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 43. Each of two parallel wires separated by 6.0 mm carries a 40-A current. These two currents are in the same direction.

Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires. a. 2.6 mT b. zero c. 1.9 mT d. 1.6 mT e. 3.2 mT ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 44. Two long, parallel wires separated by 5.0 mm each carry a current of 60 A. These two currents are oppositely directed.

What is the magnitude of the magnetic field at a point that is between the two wires and 2.0 mm from one of the two wires? a. 2.0 mT b. 10 mT c. 8.0 mT d. 1.6 mT e. 7.2 mT ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 45. Two long, parallel wires separated by 4.0 mm each carry a current of 24 A. These two currents are in the same direction. What is the magnitude of the magnetic field at a point that is between the two wires and 1.0 mm from one of the two wires? a. 4.8 mT b. 6.4 mT Copyright Cengage Learning. Powered by Cognero.

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c. 3.2 mT d. 9.6 mT e. 5.3 mT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 46. Two long, parallel wires carry unequal currents in opposite directions. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 μT. What is the larger of the two currents? a. 0.5 A b. 1.0 A c. 1.5 A d. 2.0 A e. 3.0 A ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 47. Three long, straight, parallel wires each carry a current of 10 A in the positive x direction. If the distance between each wire and the other two is 10 cm, what is the magnitude of the magnetic force on a 20-cm length of either of the wires? a. 57 μN b. 40 μN c. 69 μN d. 50 μN e. 20 μN ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 48. Two long, parallel wires are separated by 6.0 mm. The current in one of the wires is twice the other current. If the magnitude of the force on a 3.0-m length of one of the wires is equal to 8.0 μN, what is the greater of the two currents? a. 0.20 A b. 0.40 A c. 40 mA d. 20 mA e. 0.63 A ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 49. Two long, parallel wires are separated by 2.0 cm. The current in one of the wires is three times the other current. If the magnitude of the force on a 2.0-m length of one of the wires is equal to 60 μN, what is the greater of the two currents?

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a. 2.0 A b. 1.0 A c. 3.0 A d. 9.0 A e. 1.5 A ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 50. Three long, straight, parallel wires all lie in the yz plane and each carries a current of 20 A in the positive z direction.

The two outer wires are each 4.0 cm from the center wire. What is the magnitude of the magnetic force on a 50-cm length of either of the outer wires? a. 1.0 mN b. 0.50 mN c. 1.1 mN d. 1.5 mN e. 2.0 mN ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 51. Two long, parallel wires are separated by 4.0 cm. One of the wires carries a current of 20 A and the other carries a 30A current. Determine the magnitude of the magnetic force on a 2.0-m length of the wire carrying the greater current. a. 7.0 mN b. 6.0 mN c. 8.0 mN d. 9.0 mN e. 4.0 mN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 52. The figure shows a cross section of three parallel wires each carrying a current of 5.0 A out of the paper. If the distance R = 6.0 mm, what is the magnitude of the magnetic force on a 2.0-m length of any one of the wires?

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a. 2.5 mN b. 3.3 mN c. 2.2 mN d. 2.9 mN e. 1.7 mN ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 53. The figure shows a cross section of three parallel wires each carrying a current of 20 A. The currents in wires A and B are out of the paper, while that in wire C is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 2.0-m length of wire A?

a. 23 mN b. 64 mN c. 32 mN d. 46 mN e. 55 mN ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 54. The figure shows a cross section of three parallel wires each carrying a current of 15 A. The currents in wires A and C are out of the paper, while that in wire B is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force Copyright Cengage Learning. Powered by Cognero.

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on a 4.0-m length of wire C?

a. 90 mN b. 54 mN c. 30 mN d. 18 mN e. 36 mN ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 55. The figure shows a cross section of three parallel wires each carrying a current of 24 A. The currents in wires B and C are out of the paper, while that in wire A is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 4.0-m length of wire A?

a. 15 mN b. 77 mN c. 59 mN d. 12 mN e. 32 mN ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 56. Two long, parallel wires lie in the x-z plane. One wire passes through the point (−2 m, 0, 0) and the other through the point (+2 m, 0, 0). The wires carry equal currents in the positive z direction.

1.

2.

3.

4.

The magnetic field at (−3 m, 0, 0) is in the negative y direction.

The magnetic field at (−1 m, 0, 0) is in the positive y direction.

The magnetic field at (+1 m, 0, 0) is in the positive y direction.

The magnetic field at (+3 m, 0, 0) is in the negative y direction. a. 1 and 2 are correct. b. 1 and 4 are correct. c. 2 and 3 are correct. d. 3 and 4 are correct. e. None of the above are correct.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors Copyright Cengage Learning. Powered by Cognero.

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57. When a microwave filter consisting of vertical parallel metal rods is in the absorbing position, oscillating currents are set up in the rods. At any one instant, the current in each rod has the same magnitude and direction. Which of the following best describes the behavior of the rods? a. The rods will try to move apart horizontally. b. The rods will try to move together horizontally. c. The rods will try to shift vertically upwards. d. The rods will try to shift vertically downwards. e. The rods will not be affected.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 58. Three coplanar, parallel, straight wires carry equal currents I to the right as shown below. Each pair of wires is a distance a apart. What is the direction of the magnetic force on the middle wire?

a. Out of the plane of the wires b. Into the plane of the wires c. In the plane of the wires, directed upwards d. In the plane of the wires, directed downwards e. The direction cannot be defined, because there is no magnetic force on the middle wire.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 59. Three coplanar, parallel, straight wires carry equal currents I as shown below. The current in the outer wires is directed to the right, and that in the middle wire is directed to the left. Each pair of wires is a distance a apart. What is the direction of the magnetic force on the middle wire?

a. Out of the plane of the wires b. Into the plane of the wires c. In the plane of the wires, directed upwards d. In the plane of the wires, directed downwards e. The direction cannot be defined, because there is no magnetic force on the middle wire.

ANSWER: e POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 60. Three coplanar, parallel, straight wires carry equal currents I to the right as shown below. The current in the upper two wires is directed to the right, but the current in the bottom wire is directed to the left. Each pair of wires is a distance a apart. What is the direction of the magnetic force on the middle wire?

a. Out of the plane of the wires b. Into the plane of the wires c. In the plane of the wires, directed upwards d. In the plane of the wires, directed downwards e. The direction cannot be defined, because there is no magnetic force on the middle wire.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors -4

61. Two wires, each having a weight per unit length of 1.0 × 10 N/m, are strung parallel, one 0.10 m above the other. If the wires carry the same current, though in opposite directions, how great must the current in each wire be for the magnetic field of the lower conductor to balance the weight of the upper conductor?

ANSWER: 7.1 A POINTS: 2 DIFFICULTY: Average REFERENCES: 29.2 The Magnetic Force Between Two Parallel Conductors 62. A long, cylindrical wire (radius = 2.0 cm) carries a current of 40 A that is uniformly distributed over a cross section of the wire. What is the magnitude of the magnetic field at a point which is 1.5 cm from the axis of the wire? a. 0.53 mT b. 28 mT c. 0.30 mT d. 40 mT e. 1.9 mT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 63. A long, straight wire (diameter = 2.0 mm) carries a current of 25 A. What is the magnitude of the magnetic field 0.50 mm from the axis of the wire? a. 5.0 mT b. 10 mT c. 0.63 mT d. 2.5 mT Copyright Cengage Learning. Powered by Cognero.

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e. 0.01 mT ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 64. A long, straight wire (diameter = 2.0 mm) carries a current of 40 A. What is the magnitude of the magnetic field 1.5 mm from the axis of the wire? a. 3.0 mT b. 12 mT c. 5.3 mT d. 7.4 mT e. 8.0 mT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 65. A hollow cylindrical (inner radius = 1.0 mm, outer radius = 3.0 mm) conductor carries a current of 80 A parallel to its axis. This current is uniformly distributed over a cross section of the conductor. Determine the magnitude of the magnetic field at a point that is 2.0 mm from the axis of the conductor. a. 8.0 mT b. 3.0 mT c. 5.3 mT d. 16 mT e. 1.2 mT ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 66. A hollow cylindrical (inner radius = 2.0 mm, outer radius = 4.0 mm) conductor carries a current of 24 A parallel to its axis. This current is uniformly distributed over a cross section of the conductor. Determine the magnitude of the magnetic field at a point that is 5.0 mm from the axis of the conductor. a. 0.96 mT b. 1.7 mT c. 0.55 mT d. 1.2 mT e. 0.40 mT ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 67. A long, straight wire (diameter = 2.0 mm) carries a current of 30 A. What is the magnitude of the magnetic field 2.5 mm from the axis of the wire? a. 3.2 mT Copyright Cengage Learning. Powered by Cognero.

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b. 2.8 mT c. 2.4 mT d. 3.6 mT e. 3.0 mT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 68. A long, hollow, cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 24 A distributed uniformly across its cross section. A long wire which is coaxial with the cylinder carries an equal current in the opposite direction. What is the magnitude of the magnetic field 3.0 mm from the axis? a. 0.82 mT b. 0.93 mT c. 0.70 mT d. 0.58 mT e. 0.40 mT ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 69. A long, hollow, cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 12 A distributed uniformly across its cross section. A long wire which is coaxial with the cylinder carries an equal current in the same direction. What is the magnitude of the magnetic field 3.0 mm from the axis? a. 1.1 mT b. 1.4 mT c. 1.7 mT d. 2.0 mT e. 0.2 mT ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 70. A long, straight wire (radius = 2.0 mm) carries a current of 2.0 A distributed uniformly over a cross section perpendicular to the axis of the wire. What is the magnitude of the magnetic field at a distance of 1.0 mm from the axis of the wire? a. 0.40 mT b. 0.80 mT c. 0.10 mT d. 0.20 mT e. 0.75 mT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law Copyright Cengage Learning. Powered by Cognero.

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71. A long wire is known to have a radius greater than 4.0 mm and to carry a current uniformly distributed over its cross section. If the magnitude of the magnetic field is 0.285 mT at a point 4.0 mm from the axis of the wire and 0.200 mT at a point 10 mm from the axis, what is the radius of the wire? a. 4.6 mm b. 7.1 mm c. 5.3 mm d. 12 mm e. 10 mm ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.3 Ampère’s Law 72. A conducting hollow cylinder (inner radius = a, outer radius = b) carries a current of 40 A that is uniformly distributed over the cross section of the conductor. If a = 3.0 mm and b = 6.0 mm, what is the magnitude of the (line) integral around a circular path (radius = 5.0 mm) centered on the axis of the cylinder and in a plane perpendicular to that axis? a. 50 μT ⋅ m b. 30 μT ⋅ m c. 22 μT ⋅ m d. 37 μT ⋅ m e. 47 μT ⋅ m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 73. A conducting rod with a square cross section (3.0 cm × 3.0 cm) carries a current of 60 A that is uniformly distributed across the cross section. What is the magnitude of the (line) integral

around a square path (1.5 cm × 1.5 cm) if

the path is centered on the center of the rod and lies in a plane perpendicular to the axis of the rod? a. 14 μT ⋅ m b. 75 μT ⋅ m c. 19 μT ⋅ m d. 57 μT ⋅ m e. 38 μT ⋅ m ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 74. A toroid is made of 2 000 turns of wire of radius 2.00 cm formed into a donut shape of inner radius 10.0 cm and outer radius 14.0 cm. When a 30.0-A current is present in the toroid, what is the magnetic field at a distance of 11.0 cm from the center of the toroid? a. 0.0857 T b. 0.109 T Copyright Cengage Learning. Powered by Cognero.

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c. 0.120 T d. 0.600 T e. 0.685 T ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.3 Ampère’s Law 75. A thin, infinitely large current sheet lies in the y-z plane. Current of magnitude Js per unit length along the z axis travels in the y-axis direction, which is up out of the page. Which diagram below correctly represents the direction of the magnetic field on either side of the sheet? a.

b.

c.

d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.3 Ampère’s Law 76. A long wire carries a current of 3.0 A along the axis of a long solenoid (radius = 3.0 cm, n = 900 turns/m, current = 30 mA). What is the magnitude of the magnetic field at a point 2.0 cm from the axis of the solenoid? Neglect any end effects. a. 34 μT b. 64 μT c. 30 μT d. 45 μT e. 4.0 μT ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 29.4 The Magnetic Field of a Solenoid

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77. A long solenoid (diameter = 5.0 cm) is wound with 960 turns per meter of thin wire through which a current of 300 mA is maintained. A wire carrying 12 A is inserted along the axis of the solenoid. What is the magnitude of the magnetic field at a point 2.0 cm from the axis? a. 0.41 mT b. 0.48 mT c. 0.38 mT d. 0.56 mT e. 0.24 mT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.4 The Magnetic Field of a Solenoid 78. A current-carrying 2.0-cm long segment of wire is inside a long solenoid (radius = 4.0 cm, n = 800 turns/m, current = 50 mA). The wire segment is oriented perpendicularly to the axis of the solenoid. If the current in the wire segment is 12 A, what is the magnitude of the magnetic force on this segment? a. 22 μN b. 16 μN c. 18 μN d. 12 μN e. 0 μN ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 29.4 The Magnetic Field of a Solenoid 79. A long solenoid (n = 1200 turns/m, radius = 2.0 cm) has a current of a 0.30 A in its winding. A long wire carrying a current of 20 A is parallel to and 1.0 cm from the axis of the solenoid. What is the magnitude of the resulting magnetic field at a point on the axis of the solenoid? a. 0.60 mT b. 0.85 mT c. 52 μT d. 0.40 mT e. 0.75 mT ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 29.4 The Magnetic Field of a Solenoid 80. A long solenoid (1500 turns/m) carries a current of 20 mA and has an inside diameter of 4.0 cm. A long wire carries a current of 2.0 A along the axis of the solenoid. What is the magnitude of the magnetic field at a point that is inside the solenoid and 1.0 cm from the wire? a. 78 μT b. 55 μT c. 48 μT d. 68 μT e. 2.0 μT Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.4 The Magnetic Field of a Solenoid 81. A long solenoid (1000 turns/m) carries a current of 25 mA and has an inside radius of 2.0 cm. A long wire which is parallel to and 4.0 cm from the axis of the solenoid carries a current of 6.0 A. What is the magnitude of the magnetic field at a point on the axis of the solenoid? a. 51 μT b. 61 μT c. 43 μT d. 81 μT e. 1.4 μT ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.4 The Magnetic Field of a Solenoid 82. When the number of turns in a solenoid and its length are both doubled, the ratio of the magnitude of the new magnetic field inside to the magnitude of the original magnetic field inside is what? a. 0.25 b. 0.50 c. 1 d. 2 e. 4 ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.4 The Magnetic Field of a Solenoid 83. A solenoid consists of 100 circular turns of copper wire. Parts of three turns, A, B and C, are shown below.

When a current flows through the coil, a. both A and C are repelled by B. b. A is attracted to B; C is repelled by B. c. neither A nor C is attracted to or repelled by B. d. A is repelled by B; C is attracted to B. e. both A and C are attracted to B. ANSWER: e POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 29.4 The Magnetic Field of a Solenoid 84. Two solenoids are each made of 2 000 turns of copper wire per meter. Solenoid I is 2 m long, while solenoid II is 1 m long. When equal currents are present in the two solenoids, what is the ratio of the magnetic field BI along the axis of solenoid I to the magnetic field BII along the axis of solenoid II, BI/BII? a. 1/4 b. 1/2 c. 1 d. 2 e. 4 ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.4 The Magnetic Field of a Solenoid 85. A 0.50-m long solenoid consists of 1 000 turns of copper wire wound with a 4.0 cm radius. When the current in the solenoid is 18 A, what is the magnetic field at a point 1.0 cm from the central axis of the solenoid? a. 0.090 mT b. 0.36 mT c. 23 mT d. 36 mT e. 45 mT ANSWER: e POINTS: 1 DIFFICULTY: Average REFERENCES: 29.4 The Magnetic Field of a Solenoid 86. Two solenoids of equal length are each made of 2 000 turns of copper wire per meter. Solenoid I has a 5.00-cm radius; solenoid II a 10.0-cm radius. When equal currents are present in the two solenoids, the ratio of the magnitude of the magnetic field BI along the axis of solenoid I to the magnitude of the magnetic field BII along the axis of solenoid II, BI/BII, is which of the following? a. 1/4 b. 1/2 c. 1 d. 2 e. 4 ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.4 The Magnetic Field of a Solenoid 87. A long solenoid (n = 80 turns/cm) carries a current of 70 mA. Determine the magnitude of the magnetic field inside the solenoid.

ANSWER: 7.0 gauss POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 29.4 The Magnetic Field of a Solenoid 88. What current in a solenoid 15.0 cm long wound with 100 turns would produce a magnetic field equal to that of the -5 Earth, 5.00 × 10 T? ANSWER: 59.7 mA POINTS: 2 DIFFICULTY: Average REFERENCES: 29.4 The Magnetic Field of a Solenoid 89. A solenoid 4.0 cm in radius and 4.0 m in length has 8 000 uniformly spaced turns and carries a current of 5.0 A. Consider a plane circular surface (radius = 2.0 cm) located at the center of the solenoid with its axis coincident with the 2 axis of the solenoid. What is the magnetic flux through this surface? (1 Wb = 1 T ⋅ m ) a. 63 μWb b. 16 μWb c. 0.25 mWb d. 10 μWb e. 5.0 μWb ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 29.5 Gauss’s Law in Magnetism 90. Gauss's law states that the net electric flux, enclosed:

, through any closed surface is proportional to the charge

. What is the analogous formula for magnetic fields?

a. b.

c.

d.

e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.5 Gauss’s Law in Magnetism 91. An ideal solenoid of radius a has n turns per unit length and current I. Find the magnetic flux ΦB through any circular area of radius a inside the solenoid, centered on and perpendicular to the solenoid axis.

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a.

b. c. μ0πa2nI d. 2μ0πa2nI e. 0.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.5 Gauss’s Law in Magnetism 92. An ideal solenoid of radius a has n turns per unit length and current I. Find the magnetic flux ΦB through any area completely inside the solenoid, centered on the solenoid axis but at a 45° angle to the axis, so that it touches the inside of the solenoid, as shown below.

a.

b. c. μ0πa2nI d. 2μ0πa2nI e. 0.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 29.5 Gauss’s Law in Magnetism 93. The following statements all refer to the human brain when mental activity is occurring. Which statement is correct? a. In order to detect electric currents in the brain, you must open the skull and make direct electrical contact with the brain. b. The electric currents in the brain can be detected outside the brain by detecting the magnetic fields they produce. c. The electric currents in the brain can be mapped by shaving a person's head and dropping iron filings on the head. d. The electric currents in the brain produce an aura that can be detected visually. e. The electric currents in the brain cannot be detected by any means.

ANSWER: b POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 29.6 Magnetism in Matter 94. The magnetic moment of an electron (charge = −e; mass = me) moving in a circular orbit of radius r with speed v about a nucleus of mass mN is proportional to which of the following? a. r b. v c. vr d. evr e. mNvr ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.6 Magnetism in Matter 95. On the average, in a ferromagnetic domain, permanent atomic magnetic moments are aligned ____ to one another. a. antiparallel b. parallel c. perpendicular d. alternately parallel and antiparallel e. randomly relative ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.6 Magnetism in Matter 96. Which of the following type(s) of materials is(are) repelled when a magnet is brought near by? a. paramagnetic b. diamagnetic c. ferromagnetic d. paramagnetic and ferromagnetic e. paramagnetic, ferromagnetic, and diamagnetic ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 29.6 Magnetism in Matter 97. When a ferromagnetic material that has been magnetized is brought to a temperature greater than the Curie temperature, what happens to its residual magnetism. a. Nothing happens to the residual magnetism. b. The residual magnetism disappears. c. The residual magnetism reaches it’s highest value. d. All the magnetic domains causing magnetism become a single domain. e. 0.

ANSWER: b POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 29.6 Magnetism in Matter

1. A coil is wrapped with 300 turns of wire on the perimeter of a circular frame (radius = 8.0 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic field is turned on perpendicular to the plane of the coil. This field changes at a constant rate from 20 to 80 mT in a time of 20 ms. What is the magnitude of the induced emf in the coil at the instant the magnetic field has a magnitude of 50 mT? a. 24 V b. 18 V c. 15 V d. 10 V e. 30 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 2

2. A flat coil of wire consisting of 20 turns, each with an area of 50 cm , is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 2.0 T to 6.0 T in 2.0 s. If the coil has a total resistance of 0.40 Ω, what is the magnitude of the induced current? a. 0.70 A b. 0.60 A c. 0.50 A d. 0.80 A e. 0.20 A ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 3. A 40-turn circular coil (radius = 4.0 cm, total resistance = 0.20 Ω) is placed in a uniform magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies with time as given by B = 50 sin(10 πt) mT, where t is measured in s. What is the magnitude of the induced current in the coil at 0.10 s? a. 50 mA b. 1.6 A c. 0.32 A d. zero e. 0.80 A ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.1 Faraday’s Law of Induction 4. A 400-turn circular coil (radius = 1.0 cm) is oriented with its plane perpendicular to a uniform magnetic field which has a magnitude that varies sinusoidally with a frequency of 90 Hz. If the maximum value of the induced emf in the coil is observed to be 4.2 V, what is the maximum value of the magnitude of the varying magnetic field?

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a. 59 mT b. 62 mT c. 65 mT d. 68 mT e. 31 mT ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.1 Faraday’s Law of Induction 5. A square loop (length along one side = 20 cm) rotates in a constant magnetic field which has a magnitude of 2.0 T. At an instant when the angle between the field and the normal to the plane of the loop is equal to 20° and increasing at the rate of 10°/s, what is the magnitude of the induced emf in the loop? a. 13 mV b. 0.27 V c. 4.8 mV d. 14 mV e. 2.2 mV ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 6. A loop of wire (resistance = 2.0 mΩ) is positioned as shown with respect to a long wire which carries a current. If d = 1.0 cm, D = 6.0 cm, and L = 1.5 m, what current is induced in the loop at an instant when the current in the wire is increasing at a rate of 100 A/s?

a. 34 mA b. 30 mA c. 27 mA d. 38 mA e. 0.50 mA ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.1 Faraday’s Law of Induction 7. A rectangular wire loop (length = 60 cm, width = 40 cm) lies completely within a perpendicular and uniform magnetic field of magnitude of 0.5 T. If the length of the loop starts increasing at a rate of 20 mm/s at time t = 0, while the width is decreasing at the same rate, what is the magnitude of the induced emf at time t = 4.0 s? a. 6.8 mV Copyright Cengage Learning. Powered by Cognero.

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b. 5.2 mV c. 3.6 mV d. 8.4 mV e. 10 mV ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.1 Faraday’s Law of Induction 8. A coil is wrapped with 300 turns of wire on the perimeter of a square frame (side length = 20 cm). Each turn has the same area as the frame, and the total resistance of the coil is 1.5 Ω. A uniform magnetic field perpendicular to the plane of the coil changes in magnitude at a constant rate from 0.50 T to 0.90 T in 2.0 s. What is the magnitude of the induced emf in the coil while the field is changing? a. 2.4 V b. 1.6 V c. 3.2 V d. 4.0 V e. 8.4 V ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 2

9. A planar loop consisting of four turns of wire, each of which encloses 200 cm , is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms. What is the resulting induced current in the coil if the resistance of the coil is 5.0 Ω? a. 60 mA b. 12 mA c. 0.24 mA d. 48 mA e. 6.0 mA ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 10. A 5-turn square loop (10 cm along a side, resistance = 4.0 Ω) is placed in a magnetic field that makes an angle of 30° 2 with the plane of the loop. The magnitude of this field varies with time according to B = 0.50t , where t is measured in s and B in T. What is the induced current in the coil at t = 4.0 s? a. 25 mA b. 5.0 mA c. 13 mA d. 43 mA e. 50 mA ANSWER: a POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 11. A square coil (length of side = 24 cm) of wire consisting of two turns is placed in a uniform magnetic field that makes an angle of 60° with the plane of the coil. If the magnitude of this field increases by 6.0 mT every 10 ms, what is the magnitude of the emf induced in the coil? a. 55 mV b. 46 mV c. 50 mV d. 60 mV e. 35 mV ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 12. A 50-turn circular coil (radius = 15 cm) with a total resistance of 4.0 Ω is placed in a uniform magnetic field directed perpendicularly to the plane of the coil. The magnitude of this field varies with time according to B = A sin (αt), where A = 80 μT and α = 50π rad/s. What is the magnitude of the current induced in the coil at t = 20 ms? a. 11 mA b. 18 mA c. 14 mA d. 22 mA e. zero ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 13. A long, straight wire is parallel to one edge and is in the plane of a single-turn rectangular loop as shown. If the loop is changing width so that the distance x changes at a constant rate of 4.0 cm/s, what is the magnitude of the emf induced in the loop at an instant when x = 6.0 cm? Let a = 2.0 cm, b = 1.2 m, and I = 30 A.

a. 5.3 μV b. 2.4 μV c. 4.8 μV d. 2.6 μV e. 1.3 μV ANSWER: c POINTS: 3 DIFFICULTY: Challenging Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 30.1 Faraday’s Law of Induction 2

2

14. A long solenoid (n = 1 500 turns/m) has a cross-sectional area of 0.40 m and a current given by I = (4.0 + 3.0t ) A, 2 where t is in seconds. A flat circular coil (N = 300 turns) with a cross-sectional area of 0.15 m is inside and coaxial with the solenoid. What is the magnitude of the emf induced in the coil at t = 2.0 s? a. 2.7 V b. 1.0 V c. 6.8 V d. 0.68 V e. 1.4 V ANSWER: b POINTS: 2 DIFFICULTY: Challenging REFERENCES: 30.1 Faraday’s Law of Induction 2

15. The coil shown in the figure has 2 turns, a cross-sectional area of 0.20 m , and a field (parallel to the axis of the coil) 2 with a magnitude given by B = (4.0 + 3.0t ) T, where t is in s. What is the potential difference, VA − VC, at t = 3.0 s?

a. −7.2 V b. +7.2 V c. −4.8 V d. +4.8 V e. −12 V ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 2

16. A rectangular loop (area = 0.15 m ) turns in a uniform magnetic field with B = 0.20 T. At an instant when the angle between the magnetic field and the normal to the plane of the loop is (π/2) rad and increasing at the rate of 0.60 rad/s, what is the magnitude of the emf induced in the loop? a. 24 mV b. zero c. 18 mV d. 20 mV e. 6.0 mV ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction Copyright Cengage Learning. Powered by Cognero.

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2

17. A circular loop (area = 0.20 m ) turns in a uniform magnetic field with B = 0.13 T. At an instant when the angle between the magnetic field and the normal to the plane of the loop is (π) rads and is decreasing at the rate of 0.50 rad/s, what is the magnitude of the emf induced in the loop? a. zero b. 13 mV c. 26 mV d. 20 mV e. 18 mV ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction 18. A conducting rectangular loop of mass M, resistance R, and dimensions a × b is allowed to fall from rest through a uniform magnetic field which is perpendicular to the plane of the loop. The loop accelerates until it reaches a terminal speed (before the upper end enters the magnetic field). If a = 2.0 m, B = 6.0 T, R = 40 Ω, and M = 0.60 kg, what is the terminal speed?

a. 1.6 m/s b. 20 m/s c. 2.2 m/s d. 26 m/s e. 5.3 m/s ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.1 Faraday’s Law of Induction 19. The magnetic flux through a loop perpendicular to a uniform magnetic field will change a. if the loop is replaced by two loops, each of which has half of the area of the original loop. b. if the loop moves at constant velocity while remaining perpendicular to and within the uniform magnetic field. c. if the loop moves at constant velocity in a direction parallel to the axis of the loop while remaining in the uniform magnetic field. d. if the loop is rotated through 180 degrees about an axis through its center and in the plane of the loop. e. in none of the above cases.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction Copyright Cengage Learning. Powered by Cognero.

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20. A current may be induced in a coil by a. moving one end of a bar magnet through the coil. b. moving the coil toward one end of the bar magnet. c. holding the coil near a second coil while the electric current in the second coil is increasing. d. all of the above. e. none of the above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction 21. Coil 1, connected to a 100-Ω resistor, sits inside coil 2. Coil 1 is connected to a source of 60 cycle per second AC current. Which statement about coil 2 is correct? a. No current will be induced in coil 2. b. DC current (current flow in only one direction) will be induced in coil 2. c. AC current (current flow in alternating directions) will be induced in coil 2. d. DC current will be induced in coil 2, but its direction will depend on the initial direction of flow of current in coil 1. e. Both AC and DC current will be induced in coil 2.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction 22. An induced emf is produced in a. a closed loop of wire when it remains at rest in a nonuniform static magnetic field. b. a closed loop of wire when it remains at rest in a uniform static magnetic field. c. a closed loop of wire moving at constant velocity in a nonuniform static magnetic field. d. all of the above. e. only (b) and (c) above.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction 23. A bar magnet is dropped from above and falls through the loop of wire shown below. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct?

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a. The current in the loop always flows in a clockwise direction. b. The current in the loop always flows in a counterclockwise direction. c. The current in the loop flows first in a clockwise, then in a counterclockwise direction. d. The current in the loop flows first in a counterclockwise, then in a clockwise direction. e. No current flows in the loop because both ends of the magnet move through the loop.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction 24. Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is closed,

a. bulb 1 glows more brightly. b. bulb 2 glows more brightly. c. both bulbs continue to glow with the same brightness. d. bulb 1 goes out. e. bulb 2 goes out.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction 25. Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is closed,

a. bulb 1 glows more brightly. b. bulb 2 glows more brightly. c. both bulbs glow equally brightly. d. bulb 1 goes out.

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e. bulb 2 goes out.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction 26. Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is open,

a. bulb 1 is glowing; bulb 2 is dark. b. bulb 2 is glowing; bulb 1 is dark. c. both bulbs glow equally brightly. d. both bulbs glow one half as brightly as they do with the switch closed. e. both bulbs are dark.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction 27. As shown below, a square loop of wire of side a moves through a uniform magnetic field of magnitude B perpendicular to the page at constant velocity directed to the right. Judd says that the emf induced in the loop is zero.

Roger claims that it has magnitude B . Which one, if either, is correct, and why?

a. Judd, because the magnetic flux through the loop is constant. b. Roger, because the magnetic flux through the loop is constant. c. Judd, because the magnetic flux through the loop is not constant if d. Roger, because the magnetic flux through the loop is not constant if

. .

e. Roger, because the magnetic flux through the loop is ΦB = 0.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.1 Faraday’s Law of Induction 2

28. In a demonstration, a 4.00 cm square coil with 10 000 turns enters a larger square region with a uniform 1.50 T magnetic field at a speed of 100 m/s. The plane of the coil is perpendicular to the field lines. If the breakdown voltage of air is 4 000 V/cm on that day, the largest gap you can have between the two wires connected to the ends of the coil and still get a spark is Copyright Cengage Learning. Powered by Cognero.

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a. 7.5 × 10-3 cm. b. 0.015 cm. c. 7.5 cm. d. 13 cm. e. 15 cm.

ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.1 Faraday’s Law of Induction 29. A rectangular coil of 100 turns measures 40.0 cm by 20.0 cm. This coil is placed next to an electromagnet which is switched on, increasing the magnetic field through the coil from zero to 0.800 T in 50.0 ms. If the resistance of the coil is 2.0 ohms, what are the induced voltage and current in the coil?

ANSWER: 128 V, 64 A POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 30. A bolt of lightning strikes the ground 200 m from a 100-turn coil oriented vertically and with the plane of the coil pointing toward the lightning strike. The radius of the coil is 0.800 m and the current in the lightning bolt falls from 6.02 × 6 10 A to zero in 10.5 μs. What is the voltage induced in the coil over this time period? [A question for future electrical engineers: is there any way to get lightning to strike repeatedly at the same point?]

ANSWER: 115000 V POINTS: 2 DIFFICULTY: Average REFERENCES: 30.1 Faraday’s Law of Induction 31. A conducting rod (length = 80 cm) rotates at a constant angular rate of 15 revolutions per second about a pivot at one end. A uniform field (B = 60 mT) is directed perpendicularly to the plane of rotation. What is the magnitude of the emf induced between the ends of the rod? a. 2.7 V b. 2.1 V c. 2.4 V d. 1.8 V e. 3.3 V ANSWER: d POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 30.2 Motional emf 32. A metal blade spins at a constant rate of 5.0 revolutions per second about a pivot through one end of the blade. This rotation occurs in a region where the component of the Earth's magnetic field perpendicular to the blade is 30 μT. If the blade is 60 cm in length, what is the magnitude of the potential difference between its ends? a. 0.24 mV b. 0.20 mV c. 0.17 mV d. 0.27 mV e. 0.34 mV ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 33. A 20-cm length of wire is held along an east-west direction and moved horizontally to the north with a speed of 3.0 m/s in a region where the magnetic field of the earth is 60 μT directed 30° below the horizontal. What is the magnitude of the potential difference between the ends of the wire? a. 36 μV b. 18 μV c. 31 μV d. 24 μV e. 21 μV ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 34. In the arrangement shown, a conducting bar of negligible resistance slides along horizontal, parallel, frictionless conducting rails connected as shown to a 2.0-Ω resistor. A uniform 1.5-T magnetic field is perpendicular to the plane of the paper. If L = 60 cm, at what rate is thermal energy being generated in the resistor at the instant the speed of the bar is equal to 4.2 m/s?

a. 8.6 W b. 7.8 W c. 7.1 W d. 9.3 W e. 1.8 W ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 35. A rod (length = 10 cm) moves on two horizontal frictionless conducting rails, as shown. The magnetic field in the Copyright Cengage Learning. Powered by Cognero.

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region is directed perpendicularly to the plane of the rails and is uniform and constant. If a constant force of 0.60 N moves the bar at a constant velocity of 2.0 m/s, what is the current through the 12-Ω load resistor?

a. 0.32 A b. 0.34 A c. 0.37 A d. 0.39 A e. 0.43 A ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 36. A metal blade (length = 80 cm) spins at a constant rate of 10 radians/s about a pivot at one end. A uniform magnetic field of 2.0 mT is directed at an angle of 30° with the plane of the rotation. What is the magnitude of the potential difference between the two ends of the blade? a. 5.5 mV b. 6.4 mV c. 3.2 mV d. 11 mV e. 13 mV ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 37. A conducting rod (length = 2.0 m) spins at a constant rate of 2.0 revolutions per second about an axis that is perpendicular to the rod and through its center. A uniform magnetic field (magnitude = 8.0 mT) is directed perpendicularly to the plane of rotation. What is the magnitude of the potential difference between the center of the rod and either of its ends? a. 16 mV b. 50 mV c. 8.0 mV d. 0.10 mV e. 100 mV ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 38. A long, straight wire is parallel to one edge and is in the plane of a single-turn rectangular loop as shown. If the loop is moving in the plane shown so that the distance x changes at a constant rate of 20 cm/s, what is the magnitude of the emf induced in the loop at the instant x = 5.0 cm? Let I = 50 A, a = 50 cm, b = 6.0 cm.

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a. 11 μV b. 22 μV c. 27 μV d. 16 μV e. 34 μV ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.2 Motional emf 39. In a region of space where the magnetic field of the Earth has a magnitude of 80 μT and is directed 30° below the horizontal, a 50-cm length of wire oriented horizontally along an east-west direction is moved horizontally to the south with a speed of 20 m/s. What is the magnitude of the induced potential difference between the ends of this wire? a. 0.45 mV b. 0.35 mV c. 0.30 mV d. 0.40 mV e. 0.69 mV ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 40. A small airplane with a wing span of 12 m flies horizontally and due north at a speed of 60 m/s in a region where the magnetic field of the earth is 60 μT directed 60° below the horizontal. What is the magnitude of the induced emf between the ends of the wing? a. 50 mV b. 31 mV c. 37 mV d. 44 mV e. 22 mV ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 41. A conducting bar moves as shown near a long wire carrying a constant 80-A current. If a = 1.0 mm, b = 20 mm, and v = 5.0 m/s, what is the potential difference, Va − Vb?

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a. −0.24 mV b. +0.24 mV c. −0.19 mV d. +0.19 mV e. −0.76 mV ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.2 Motional emf 42. A conducting bar moves as shown near a long wire carrying a constant 50-A current. If a = 4.0 mm, L = 50 cm, and v = 12 m/s, what is the potential difference, VA − VB?

a. +15 mV b. −15 mV c. +20 mV d. −20 mV e. +10 mV ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 43. A bar (L = 80 cm) moves on two frictionless rails, as shown, in a region where the magnetic field is uniform (B = 0.30 T) and into the paper. If v = 50 cm/s and R = 60 mΩ, what is the magnetic force on the moving bar?

a. 0.48 N to the right b. 0.48 N to the left c. 0.32 N to the left d. 0.32 N to the right e. None of the above ANSWER: b Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 44. A conducting bar of length L rotates in a counterclockwise direction with a constant angular speed of +2.0 rad/s about a pivot P at one end, as shown. A uniform magnetic field (magnitude = 0.20 T) is directed into the paper. If L = 0.40 m, what is the potential difference, VA − VB?

a. +24 mV b. −24 mV c. +16 mV d. −16 mV e. +32 mV ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 45. A conducting bar of length L rotates with a constant angular speed of +2.0 rad/s about a pivot P at one end, as shown.

A uniform magnetic field (magnitude = 0.20 T) is directed into the paper. If L = 0.40 m, what is the potential difference, VA − VP?

a. −12 mV b. +8.0 mV c. −8.0 mV d. +12 mV e. −16 mV ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 46. A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity ω. While it rotates, which point(s) is(are) at the highest potential?

a. A b. B c. C d. D Copyright Cengage Learning. Powered by Cognero.

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e. A and E ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.2 Motional emf 47. A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity ω. While it rotates, which point(s) is(are) at the lowest potential?

a. A b. B c. C d. D e. A and E ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.2 Motional emf 48. A metal rod of length L in a region of space where a constant magnetic field points into the page rotates about an axis through its center at constant angular velocity ω. The ends, A and E, make contact with a split ring that connects to an external circuit. What is the magnitude of the current in the external circuit of resistance R?

a. 0 b.

c.

d.

e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.2 Motional emf -5

49. A car with a radio antenna 1.0 m long travels at 80 km/h in a locality where the Earth's magnetic field is 5.0 × 10 T. What is the maximum possible emf induced in the antenna as a result of moving through the Earth's magnetic field?

ANSWER: 1.1 mV Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 30.2 Motional emf 50. As shown below, a square loop of wire of side a moves through a uniform magnetic field of magnitude B perpendicular to the page at constant velocity directed to the right. Which statement regarding the electric field induced in the wires is correct for the wires at the left and right sides of the loop?

a. b. c.

The electric field

is directed upwards in both the right and left sides of the loop.

The electric field

is directed upwards in the right side and downwards in the left side of the loop.

The electric field

is directed upwards in the left side and downwards in the right side of the loop.

d.

The electric field is directed downwards in both the right and left sides of the loop. e. There is no electric field present in any side of the loop.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.3 Lenz’s Law 51. Starting outside the region with the magnetic field, a single square coil of wire moves across the region with a uniform magnetic field perpendicular to the page. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. Roger claims that the graph shown below represents the induced emf.

Martin says he's wrong. In which direction did the loop move over the plane of the page, or is Martin correct?

a. Roger is correct: the loop moved from bottom to top. b. Roger is correct: the loop moved from top to bottom. c. Roger is correct: the loop moved from left to right. d. Roger is correct: the loop moved from right to left. e. Martin is correct: none of these directions of motion will produce the graph of emf vs t.

ANSWER: e Copyright Cengage Learning. Powered by Cognero.

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.3 Lenz’s Law 52. Starting outside the region with the magnetic field, a single square coil of wire enters, moves across, and then leaves the region with a uniform magnetic field perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. In which direction did the loop move over the plane of the page?

a. The loop moved from bottom to top. b. The loop moved from top to bottom. c. The loop moved from left to right. d. The loop moved from right to left. e. All of these directions of motion will produce the graph of emf vs t.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.3 Lenz’s Law 53. Starting outside the region with the magnetic field, a single square coil of wire enters, moves across, and then leaves the region with a uniform magnetic field perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. In which direction did the loop move over the plane of the page?

a. The loop moved from bottom to top.

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b. The loop moved from top to bottom. c. The loop moved from left to right. d. The loop moved from right to left. e. All of these directions of motion will produce the graph of emf vs t.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.3 Lenz’s Law 54. A long solenoid (radius = 3.0 cm, 2 500 turns per meter) carries a current given by I = 0.30 sin(200πt) A, where t is measured in s. When t = 5.0 ms, what is the magnitude of the induced electric field at a point which is 2.0 cm from the axis of the solenoid? a. 7.3 × 10-3 V/m b. 6.4 × 10-3 V/m c. 6.9 × 10-3 V/m d. 5.9 × 10-3 V/m e. 8.9 × 10-3 V/m ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.4 The General Form of Faraday's Law 55. A long solenoid (radius = 3.0 cm, 2 500 turns per meter) carries a current given by I = 0.30 sin(200 t) A, where t is measured in s. When t = 2.5 ms, what is the magnitude of the induced electric field at a point which is 4.0 cm from the axis of the solenoid? a. 9.3 × 10-3 V/m b. 8.0 × 10-3 V/m c. 6.7 × 10-3 V/m d. 5.3 × 10-3 V/m e. 1.9 × 10-3 V/m ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 30.4 The General Form of Faraday's Law 56. A long solenoid has a radius of 4.0 cm and has 800 turns/m. If the current in the solenoid is increasing at the rate of 3.0 A/s, what is the magnitude of the induced electric field at a point 2.2 cm from the axis of the solenoid? a. 3.3 × 10-5 V/m b. 3.6 × 10-5 V/m c. 3.9 × 10-5 V/m d. 4.2 × 10-5 V/m e. 6.0 × 10-5 V/m ANSWER:

a

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POINTS: 2 DIFFICULTY: Average REFERENCES: 30.4 The General Form of Faraday's Law 57. An electric field of 4.0 μV/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm, 800 turns/m). At what rate is the current in the solenoid changing at this instant? a. 0.50 A/s b. 0.40 A/s c. 0.60 A/s d. 0.70 A/s e. 0.27 A/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 30.4 The General Form of Faraday's Law 58. A long solenoid has a radius of 2.0 cm and has 700 turns/m. If the current in the solenoid is decreasing at the rate of 8.0 A/s, what is the magnitude of the induced electric field at a point 2.5 cm from the axis of the solenoid? a. 56 μV/m b. 8.8 μV/m c. 88 μV/m d. 69 μV/m e. 44 μV/m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 30.4 The General Form of Faraday's Law 2

59. An AC generator consists of 6 turns of wire. Each turn has an area of 0.040 m . The loop rotates in a uniform field (B = 0.20 T) at a constant frequency of 50 Hz. What is the maximum induced emf? a. 13 V b. 2.4 V c. 3.0 V d. 15 V e. 4.8 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 30.5 Generators and Motors 2

60. At what frequency should a 200-turn, flat coil of cross sectional area of 300 cm be rotated in a uniform 30-mT magnetic field to have a maximum value of the induced emf equal to 8.0 V? a. 7.5 Hz b. 7.1 Hz c. 8.0 Hz d. 8.4 Hz Copyright Cengage Learning. Powered by Cognero.

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e. 16 Hz ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 30.5 Generators and Motors 61. The difference between a DC and an AC generator is that a. the DC generator has one unbroken slip ring. b. the AC generator has one unbroken slip ring. c. the DC generator has one slip ring split in two halves. d. the AC generator has one slip ring split in two halves. e. the DC generator has two unbroken slip rings.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 30.5 Generators and Motors 62. A 500-turn circular loop 15.0 cm in diameter is initially aligned so that its axis is parallel to the Earth's magnetic field.

In 2.77 ms the coil is flipped so that its axis is perpendicular to the Earth's field. If a voltage of 0.166 V is induced in the coil, what is the value of the Earth's magnetic field?

-5 ANSWER: 5.20 × 10 T POINTS: 2 DIFFICULTY: Average REFERENCES: 30.5 Generators and Motors

1. What is the inductance of a series RL circuit in which R = 1.0 kΩ if the current increases to one-third of its final value in 30 μs? a. 74 mH b. 99 mH c. 49 mH d. 62 mH e. none of the above ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 31.1 Self-Induction and Inductance 2. Which of the following are the units of a henry and a farad, respectively? a. J ⋅ s2/C2 and C2/J b. V ⋅ s/A and V/C c. V/(A ⋅ s) and C/V d. N ⋅ m/A2 and 1/J e. None of the above ANSWER: a POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 31.1 Self-Induction and Inductance 3. A circuit contains two inductors of 6.0-mH inductance in series placed in parallel with an inductor of 8.0-mH inductance. After one of the 6.0-mH inductors burns out, the repair person wants to replace all three inductors with one inductor of equivalent inductance. Assuming inductors combine in series and parallel the same way resistors do, what inductance should she use? a. 3.0 mH b. 3.4 mH c. 4.8 mH d. 11 mH e. 20 mH ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 31.1 Self-Induction and Inductance 4. An inductor produces a back emf in a DC series RL circuit when a switch connecting the battery to the circuit is closed.

We can explain this by a. Lenz's law. b. increasing magnetic flux within the coils of the inductor. c. increasing current in the coils of the inductor. d. all of the above. e. only (a) and (c) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 31.1 Self-Induction and Inductance 5. Coaxial Cable A has twice the length, twice the radius of the inner solid conductor, and twice the radius of the outer cylindrical conducting shell of coaxial Cable B. What is the ratio of the inductance of Cable A to that of Cable B? a. b. c. 2 d. e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 31.2 Mutual Inductance 6. Before the switch is closed in the figure, the potential across the capacitor is 200 V. At some instant after the switch is closed, the instantaneous current is 0.70 A. What is the energy in the capacitor at this instant?

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a. 49 mJ b. 31 mJ c. 80 mJ d. 0.13 J e. 62 mJ ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 31.3 Energy in a Magnetic Field 7. The magnetic field in a superconducting solenoid is 3.0 T. How much energy per unit volume is stored in the solenoid, 3 -7 in J/m ? μ0 = 4π × 10 T ⋅ A/m 6 3 ANSWER: 3.6 × 10 J/m POINTS: 2 DIFFICULTY: Average REFERENCES: 31.3 Energy in a Magnetic Field 8. Find the magnetic energy stored in the air gap between two very large magnetic pole pieces, one north, one nouth, each 2 with an area of 100 cm . Assume the 0.05-T magnetic field is uniform within the 2-cm gap.

ANSWER: 0.2 J POINTS: 2 DIFFICULTY: Average REFERENCES: 31.3 Energy in a Magnetic Field 9. For the circuit shown, what is the rate of change of the current in the inductor when the current in the battery is 0.50 A?

a. 600 A/s b. 400 A/s c. 200 A/s d. 800 A/s e. 500 A/s ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 31.5 RL Circuits 10. The switch in the figure is closed at t = 0 when the current I is zero. When I = 15 mA, what is the potential difference across the inductor?

a. 240 V b. 60 V c. 0 d. 180 V e. 190 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 31.5 RL Circuits 11. There is no current in the circuit shown in the figure below until the switch is closed. The current through the 20-Ω resistor the instant after the switch is closed is either [1] 15 A or [2] 5.0 A, and the current through the 20-Ω resistor after the switch has been closed a long time is either [3] 5.0 A or [4] 15 A. Which combination of the above choices is correct?

a. [1] and [3] b. [1] and [4] c. [2] and [3] d. [2] and [4] e. None of these ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 31.5 RL Circuits 12. The figure shows an LR circuit with a switch and a 240-volt battery. At the instant the switch is closed, the current in the circuit and the potential difference between points a and b, Vab, are

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a. 0 A, 0 V b. 0 A, −240 V c. 0 A, +240 V d. 0.024 A, 0 V e. 0.024 A, +240 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 31.5 RL Circuits 13. When a switch is closed, completing an LR series circuit, the time needed for the current to reach one half its maximum value is ____ time constants. a. 0.250 b. 0.500 c. 0.693 d. 1.00 e. 1.44 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 31.5 RL Circuits 14. When a switch is closed, completing an LR series circuit, the time needed for the current to reach three-quarters its maximum value is ____ time constants. a. 0.500 b. 0.693 c. 0.725 d. 1.33 e. 1.39 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 31.5 RL Circuits 15. When a switch is closed to complete a DC series RL circuit, a. the electric field in the wires increases to a maximum value. b. the magnetic field outside the wires increases to a maximum value. c. the rate of change of the electric and magnetic fields is greatest at the instant when the switch is closed. d. all of the above are true.

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e. only (a) and (c) above are true.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 31.5 RL Circuits 16. After a switch is thrown to remove the battery from a DC LR circuit, but the circuit is still left complete, the time constant represents a. the time rate of change of the current in the circuit. b. the time rate of change of the induced emf in the circuit. c. the magnitude of the ratio of the current to the time rate of change of the current. d. all of the above. e. only (a) and (b) above.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 31.5 RL Circuits 17. A 10-mH inductor is connected in series with a 10-ohm resistor, a switch, and a 6-volt battery. What is the time constant of the circuit? How long after the switch is closed will the current reach 99 percent of its final value?

ANSWER: 1.0 ms, 4.6 ms POINTS: 2 DIFFICULTY: Average REFERENCES: 31.5 RL Circuits 18. A series LC circuit contains a 100-mH inductor, a 36.0-mF capacitor and a 12-V battery. The angular frequency of the electromagnetic oscillations in the circuit is a. 36.0 × 10-4 rad/s. b. 6.00 × 10-2 rad/s. c. 2.78 rad/s. d. 16.7 rad/s. e. 277 rad/s.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 31.6 LC Circuits 19. A series LC circuit contains a 100-mH inductor, a 36.0-mF capacitor and a 12-V battery. The frequency of the electromagnetic oscillations in the circuit is a. 5.73 × 10-4 Hz. b. 9.55 × 10-3 Hz. c. 0.442 Hz. d. 2.65 Hz. e. 44.0 Hz. ANSWER: d POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 31.6 LC Circuits 20. A series LC circuit contains a 100-mH inductor, a 36.0-mF capacitor and a 12-V battery. The period of the electromagnetic oscillations in the circuit is a. 0.0227 s. b. 0.377 s. c. 2.26 s. d. 105 s. e. 1750 s.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 31.6 LC Circuits 21. If we wished to construct a "tank circuit", where electric charge originally stored on a capacitor flows through an inductor, then back again, what value of inductance should we place in series with a fully-charged 100-μF capacitor to get the circuit to resonate at 60.0 Hz? ANSWER: 70.4 mH POINTS: 2 DIFFICULTY: Average REFERENCES: 31.5 Oscillations in an LC Circuit 22. An RLC circuit has L = 250 mH, C = 0.200 μF, and R = 2.00 kΩ. What is the angular frequency of its damped oscillations?

ANSWER: POINTS: 2 DIFFICULTY: Average REFERENCES: 31.7 RLC Circuits

1. An AC generator with peak voltage 100 volts is placed across a 10-Ω resistor. What is the average power dissipated? a. 100 W b. 150 W c. 500 W d. 1 000 W e. 2 000 W ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 32.1 AC Sources 2. An electric heater draws an average power of 1 100 watts when plugged into a 110-V rms outlet. Calculate the resistance of the heater and the rms current. a. 11 Ω, 10 A (rms) b. 110 Ω, 10 A (rms) c. 10 Ω, 11 A (rms) Copyright Cengage Learning. Powered by Cognero.

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d. 10 Ω, 110 A (rms) e. 0.09 Ω, 11 A (rms) ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 32.2 Resistors in an AC Circuit 3. An incandescent lightbulb is rated at 100 watts when plugged into a 110-V rms household outlet. Calculate the resistance of the filament and the rms current. a. 12.2 Ω, 0.91 A (rms) b. 10 Ω, 1.0 A (rms) c. 110 Ω, 1.0 A (rms) d. 121 Ω, 0.91 A (rms) e. 11 Ω, 1.1 A (rms) ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.2 Resistors in an AC Circuit 4. A high-voltage powerline operates at 500 000-V rms and carries an rms current of 500 A. If the resistance of the cable is 0.050 Ω/km, what is the resistive power loss in 200 km of the powerline? a. 250 kW b. 500 kW c. 1 Megawatt d. 2.5 Megawatts e. 250 Megawatts ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.2 Resistors in an AC Circuit 5. A 230 000-V rms powerline carries an average power Pavg = 250 MW a distance of 200 km. If the total resistance of the cables is 10 ohms, what is the resistive power loss? a. 1.0 MW b. 2.5 MW c. 5.4 MW d. 12 MW e. 10 kW ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.2 Resistors in an AC Circuit 6. Inductive reactance XL is given by which of the following? a. Lω b. L/ω Copyright Cengage Learning. Powered by Cognero.

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c. 1/Lω d. ω/L e. ω2L ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.2 Resistors in an AC Circuit 7. The graphs below show a voltage phasor at different instances of time. Which graph of the voltage phasor shows the instantaneous value of the voltage with the largest magnitude? a.

b.

c.

d.

e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.2 Resistors in an AC Circuit 8. At what frequency will a 50.0-mH inductor have a reactance XL = 700 Ω? a. 352 Hz b. 777 Hz c. 1.25 kHz d. 2.23 kHz e. 14 kHz ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.3 Inductors in an AC Circuit Copyright Cengage Learning. Powered by Cognero.

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9. A 0.500-H inductor is connected into a 110-V rms, 60.0-Hz voltage source, with an ammeter in series. What is the rms value of the current through the inductor? a. 0.189 A (rms) b. 0.292 A (rms) c. 0.584 A (rms) d. 1.19 A (rms) e. 0.093 A (rms) ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 32.3 Inductors in an AC Circuit 10. Capacitive reactance XC is given by which of the following? a. 1/ωC b. ωC c. ω/C d. C/ω e. 1/ω2C ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.4 Capacitors in an AC Circuit 11. At what frequency will a 12-μF capacitor have a reactance XC = 300 Ω? a. 44 Hz b. 88 Hz c. 180 Hz d. 350 Hz e. 280 Hz ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 32.4 Capacitors in an AC Circuit 12. A 10.0-μF capacitor is plugged into a 110- V rms, 60.0-Hz voltage source, with an ammeter in series. What is the rms value of the current through the capacitor? a. 0.202 A (rms) b. 0.415 A (rms) c. 0.626 A (rms) d. 0.838 A (rms) e. 0.066 A (rms) ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 32.4 Capacitors in an AC Circuit Copyright Cengage Learning. Powered by Cognero.

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13. The total impedance Z of an RLC circuit driven by an AC voltage source at angular frequency ω is what? a. b. c.

d. e.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 14. A 2.0-μF capacitor in series with a 2.0-kΩ resistor is connected to a 60-Hz ac source. Calculate the impedance of the circuit. a. 1 500 ohms b. 1 800 ohms c. 2 100 ohms d. 2 400 ohms e. 8 600 ohms ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 15. The voltage 8.00 sin (400t) is applied to a series RLC circuit, with R = 200 Ω, L = 0.100 H, and C = 1.00 μF. What are the impedance Z and the phase angle θ? a. 200 Ω, −37.0° b. 566 Ω, +87.0° c. 2 470 Ω, −85.4° d. 2 540 Ω, −88.8° e. 393 Ω, −63.0° ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 32.5 The RLC Series Circuit 16. If an R = 1.0-kΩ resistor, a C = 1.0-μF capacitor, and an L = 0.20-H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source? a. 0.007 0 A b. 27 mA c. 54 mA Copyright Cengage Learning. Powered by Cognero.

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d. 0.31 A e. 0.34 A ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 17. If the input to an RLC series circuit is V = Vm cos ωt, then the current in the circuit is what? a. cos ωt b.

c.

d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 18. An RLC series circuit has R = 100 ohms, C = 25 μF, and L = 0.16 H. For what angular frequency of an AC voltage is the current flow maximum? a. 251 rad/s b. 500 rad/s c. 757 rad/s d. 884 rad/s e. 79.6 rad/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 19. Determine the rms voltage for the circuit.

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a. 99 V (rms) b. 140 V (rms) c. 196 V (rms) d. 70 V (rms) e. 110 V (rms) ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 20. Determine the impedance for the circuit.

a. 600 Ω b. 1200 Ω c. 1800 Ω d. 2300 Ω e. 1100 Ω ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 21. Determine the rms current for the circuit.

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a. 55 mA b. 77 mA c. 99 mA d. 0.19 A e. 61 mA ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 22. Determine the resonant frequency of the circuit.

a. 159 Hz b. 32 Hz c. 5 Hz d. 500 Hz e. 79.5 Hz ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 23. Determine the rms voltage drop across the resistor in the circuit.

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a. 55 V b. 77 V c. 9.9 V d. 5.5 V e. 61 V ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 24. Determine the rms voltage drop across the inductor in the circuit.

a. 11 V b. 27.5 V c. 33 V d. 38.5 V e. 30.5 V ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 25. Determine the rms voltage drop across the capacitor in the circuit.

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a. 55 V b. 77 V c. 110 V d. 154 V e. 198 V ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 26. Calculate Vout/Vin for the circuit if R = 2.0 kΩ, C = 0.020 μF, and V = 140 V sin(50 000t).

a. 0.02 b. 0.45 c. 0.80 d. 0.98 e. 2.2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 27. The impedance of the parallel RLC circuit shown is given by what?

a. b.

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c.

d.

e.

ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 32.5 The RLC Series Circuit 28. The phase angle between V and I is what?

a.

b.

c.

d.

e.

ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 32.5 The RLC Series Circuit 29. For driving voltage V = Vm sin ωt, the current through the resistor is what?

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a. Vm sin (ωt + υ) b. Vm cos (ωt + υ) c. sin (ωt + υ) d. sin (ωt + υ) e. sin ωt ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 30. An alternating current circuit has resistance R, inductance L, and capacitance C in series with a voltage source. Which statement is correct? a. The voltage across the capacitor leads the voltage across the inductor by 90°. b. The voltage across the inductor leads the voltage across the capacitor by 90°. c. The voltage across the inductor leads the voltage across the resistor by 180°. d. The voltage across the inductor is out of phase with the voltage across the capacitor by 180°. e. Both voltages lead the voltage across the resistor by 90°.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 31. Whenever the alternating current frequency in a series RLC circuit is halved, a. the inductive reactance is doubled and the capacitive reactance is halved. b. the inductive reactance is doubled and the capacitive reactance is doubled. c. the inductive reactance is halved and the capacitive reactance is halved. d. the inductive reactance is halved and the capacitive reactance is doubled. e. the reactance of the circuit remains the same.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 32. A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 Ω and C = 300 μF. What is the peak current in the circuit? a. 8.24 A b. 8.84 A c. 11.0 A d. 12.4 A e. 23.5 A ANSWER: a Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 33. A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 Ω and C = 300 μF. What is the impedance? a. 4.68 Ω b. 8.84 Ω c. 10.0 Ω d. 13.4 Ω e. 18.8 Ω ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 34. A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 Ω and C = 300 μF. What is the power factor, cos υ? a. −1.00 b. −0.749 c. +0.749 d. +0.834 e. +1.00 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 35. A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 Ω and L = 10.0 mH. What is the peak current in the circuit? a. 0.963 A b. 10.3 A c. 11.0 A d. 11.9 A e. 29.2 A ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 36. A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 Ω and L = 10.0 mH. What is the impedance? a. 3.77 Ω b. 9.26 Ω c. 10.0 Ω d. 10.7 Ω e. 13.8 Ω Copyright Cengage Learning. Powered by Cognero.

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ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 37. A 10-μF capacitor in an LC circuit made entirely of superconducting materials (R = 0 Ω) is charged to 100 μC. Then a superconducting switch is closed. At t = 0 s, plate 1 is positively charged and plate 2 is negatively charged. At a later time, Vab = +10 V. At that time, what is Vdc?

a. 0 V b. 3.54 V c. 5.0 V d. 7.07 V e. 10 V ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 32.5 The RLC Series Circuit 38. The graphs below represent current and voltage phasors at one instant of time. The solid arrows represent the voltage phasors, ΔV, and the dashed arrows represent the current phasors, Imax. Which graph shows the correct relationship between current and voltage phasors for an inductor in an RL circuit? a.

b.

c.

d.

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e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 39. The graphs below represent current and voltage phasors at one instant of time. The solid arrows represent the voltage phasors, ΔVmax, and the dashed arrows represent the current phasors, Imax. Which graph shows the correct relationship between current and voltage phasors for a capacitor in an RC circuit? a.

b.

c.

d.

e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 40. The graphs below show the phasors ΔVmax and Imax for five RLC series circuits. The solid arrows represent the voltage phasors, ΔV, and the dashed arrows represent the current phasors, Imax. Which graph represents a circuit where the inductive reactance is greater than the capacitive reactance? a.

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b.

c.

d.

e.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 41. The graphs below show the phasors ΔVmax and Imax for five RLC series circuits. The solid arrows represent the voltage phasors, ΔV, and the dashed arrows represent the current phasors, Imax. The graph which represents a circuit where the capacitive reactance is greater than the inductive reactance is a.

b.

c.

d.

e.

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ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 42. In a parallel RLC circuit, where IR = IR, max sin(ωt), the current through the capacitor, IC, is which of the following? a. IC = −IC, max sin(ωt) b. IC = IC, max sin(ωt) c. IC = −IC, max cos(ωt) d. IC = IC, max cos(ωt) e. IC = IC, max tan(ωt) ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 43. In a parallel RLC circuit, where IR = IR, max sin(ωt), the current through the inductor, IL, is which of the following? a. IL = −IL, max sin(ωt) b. IL = IL, max sin(ωt) c. IL = −IL, max cos(ωt) d. IL = IL, max cos(ωt) e. IL = IL, max tan(ωt) ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.5 The RLC Series Circuit 44. A 10.0-Ω resistor, 10.0-mH inductor, and 10.0-μF capacitor are connected in series with a 10.0-kHz voltage source.

The rms current through the circuit is 0.200 A. Find the rms voltage drop across each of the 3 elements.

ANSWER: 2.00 V, 126 V, 0.318 V POINTS: 3 DIFFICULTY: Challenging REFERENCES: 32.5 The RLC Series Circuit 45. A current I = 3 sin (400 t) amperes flows in a series RL circuit in which L = 1 mH and R = 100Ω. What is the average power loss? a. 225 W b. 450 W c. 980 W d. 1.12 kW e. 900 W ANSWER: b POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 32.6 Power in an AC Circuit 46. What is the average power dissipation in a series RC circuit if R = 5.00 kΩ, C = 2.00 μF, and V = 170 cos (300t)? a. 0.930 W b. 2.60 W c. 28.2 W d. 157 W e. 5.20 W ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 32.6 Power in an AC Circuit 47. What is the average power dissipation in an RLC series circuit with R = 10 Ω, L = 0.1 H, C = 10 μF when driven at resonance by a 100-V rms source? a. 100 W b. 500 W c. 1000 W d. 2 kW e. 700 W ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 32.6 Power in an AC Circuit 48. A series RLC circuit has an impedance of 120 Ω and a resistance of 64 Ω. What average power is delivered to this circuit when Vrms = 90 volts? a. 36 W b. 100 W c. 192 W d. 360 W e. 12 W ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 32.6 Power in an AC Circuit 49. The average power input to a series alternating current circuit is minimum when a. there are only a resistor and capacitor in the circuit. b. there are only a resistor and inductor in the circuit. c. there is only a resistor in the circuit. d. XL = XC and the circuit contains a resistor, an inductor, and a capacitor. e. there is only a capacitor in the circuit.

ANSWER: e POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 32.6 Power in an AC Circuit 50. A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 Ω and L = 10.0 mH. What is the power factor, cos υ? a. −1.00 b. −0.936 c. +0.943 d. +0.936 e. +1.00 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.6 Power in an AC Circuit 51. An LC circuit is to have resonant oscillations at 5.0 MHz. Find the value of a capacitor which will work with a 1.0-mH inductor. a. 2.0 mF b. 1.0 μF c. 0.020 μF d. 1.0 pF e. 40 pF ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.7 Resonance in a Series RLC Circuit 52. The inductance of a tuning circuit of an AM radio is 4.00 mH. Find the capacitance of the circuit required for reception at 1 200 kHz. a. 2.10 pF b. 4.40 pF c. 21.2 pF d. 43.4 pF e. 27.6 pF ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 32.7 Resonance in a Series RLC Circuit 53. Find the resonant frequency for a series RLC circuit where R = 10 Ω, C = 5.00 μF, and L = 2.00 mH. a. 998 Hz b. 1.59 kHz c. 2.45 kHz d. 11.3 kHz e. 2.53 kHz ANSWER: b POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 32.7 Resonance in a Series RLC Circuit 54. All three circuits shown below have R = 100 Ω, L = 0.1 H, and emf ε = (5.0 V) sin (377 t). Which statement regarding the angular resonance frequencies ωA, ωB, and ωC is correct?

a. ωC > ωA = ωB b. ωC < ωA = ωB c. ωA = ωB = ωC d. ωB < ωA = ωC e. ωB > ωA = ωC ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.7 Resonance in a Series RLC Circuit 55. All three circuits below have R = 100 Ω, C = 1.0 mF, and emf ε = (5.0 V) sin (377 t). The inductors in (B) and (C) are placed sufficiently far apart so that they do not alter one another's inductance. Such inductors add combine like resistors.

Which statement regarding the angular resonance frequencies ωA, ωB, and ωC is correct?

a. ωC > ωA = ωB b. ωC < ωA = ωB c. ωA = ωB = ωC d. ωB < ωA = ωC e. ωB > ωA = ωC ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 32.7 Resonance in a Series RLC Circuit Copyright Cengage Learning. Powered by Cognero.

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56. Suppose the circuit parameters in a series RLC circuit are: L = 1.00 μH, C = 10.0 nF, R = 100 Ω, and the source voltage is 220 V. Determine the resonant frequency of the circuit and the amplitude of the current at resonance.

ANSWER: 1.59 MHz, 2.20 A POINTS: 2 DIFFICULTY: Average REFERENCES: 32.7 Resonance in a Series RLC Circuit 57. A transformer is to be designed to increase the 30-kV rms output of a generator to the transmission-line voltage of 345-kV rms. If the primary winding has 80 turns, how many turns must the secondary have? a. 6 b. 70 c. 920 d. 9200 e. 12 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 32.8 The Transformer and Power Transmission 58. The primary winding of an electric train transformer has 400 turns and the secondary has 50. If the input voltage is 120 V (rms) what is the output voltage? a. 15 V (rms) b. 30 V (rms) c. 60 V (rms) d. 2.4 V (rms) e. 960 V (rms) ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 32.8 The Transformer and Power Transmission 59. A step-up transformer has an input voltage of 110 V (rms). There are 100 turns on the primary and 1 500 on the secondary. What is the output voltage? a. 1 600 V (max) b. 1 650 V (rms) c. 3 260 V (max) d. 165 kV (rms) e. 7.3 V (rms) ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 32.8 The Transformer and Power Transmission 60. A primary current of 6.0 A exists in an ideal iron-core transformer at a primary voltage of 100 volts. If the current in the secondary is 0.75 A, calculate the output voltage. a. 12.5 V Copyright Cengage Learning. Powered by Cognero.

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b. 40 V c. 400 V d. 800 V e. 200 V ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.8 The Transformer and Power Transmission 61. An ideal step-down transformer has 200 primary turns and 50 secondary turns. If 440 volts (rms) is placed across the primary, what is the current in the secondary when the load resistance is 7.00 ohms? a. 3.6 A (rms) b. 7.3 A (rms) c. 11.4 A (rms) d. 15.7 A (rms) e. 12.4 A (rms) ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.8 The Transformer and Power Transmission 62. The power output, Pout, of an ideal step-up transformer that receives power input, Pin, and which has N1 turns in the primary and N2 turns in the secondary coil is given by which of the following? a. Pout = Pin b.

Pout =

Pin

Pout =

Pin

c.

d.

Pout =

Pin

Pout =

Pin

e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 32.8 The Transformer and Power Transmission 63. In a typical transmission line, the current I is very small and the voltage V is very large. A unit length of line has resistance R. For a power line that supplies power to 10 000 households, which of the following is true? a. IV = I2R b. I = V/R c. IV < I2R d. IV > I2R Copyright Cengage Learning. Powered by Cognero.

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e. I2R = 0 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 32.8 The Transformer and Power Transmission 64. An ac power generator produces 50 A (rms) at 3600 V. The voltage is stepped up to 100 000 V by an ideal transformer and the energy is transmitted through a long-distance power line which has a resistance of 100 ohms. What percentage of the power delivered by the generator is dissipated as heat in the long-distance power line?

ANSWER: 0.18% POINTS: 2 DIFFICULTY: Average REFERENCES: 32.8 The Transformer and Power Transmission

1. An open circuit consists of a 12-μF parallel-plate capacitor charged to 200 V and a 10-Ω resistor. At the instant when a switch closes the circuit (with no battery in it), what is the displacement current between the plates of the capacitor? a. 1.2 μA b. 2.4 × 10-4 A c. 2.4 mA d. 10 A e. 20 A ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 33.1 Displacement Current and the General Form of Ampère’s Law 2. Which of the following is the correct form of Ampere's law for circuits with gaps in them? a. b. c. d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.1 Displacement Current and the General Form of Ampère’s Law 2

3. A plane parallel-plate capacitor has plates of 10 cm area that are 1.0 mm apart. At an instant when charge is being accumulated on the plates at a rate of 12 nC/s, the displacement current between the plates is Copyright Cengage Learning. Powered by Cognero.

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a. 1.06 × 10-16 A. b. 1.2 × 10-8 A. c. 8.85 × 10-9 A. d. 1.00 A. e. 1.36 A. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.1 Displacement Current and the General Form of Ampère’s Law 4. Magnetic fields are produced by a. constant electric currents. b. electric currents that vary sinusoidally with time. c. time-varying electric fields. d. all of the above. e. only (a) and (b) above.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 33.2 Maxwell’s Equations and Hertz’s Discoveries 5. Find the frequency of X-rays of wavelength 1 Å = 10 a. 3 × 1018 Hz

-10

m.

b. 3 × 1010 MHz c. 6 × 109 Hz d. 3 × 108 Hz e. 3 × 1020 Hz ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 33.3 Plane Electromagnetic Waves -7

6. Green light has a wavelength of 5.4 × 10 m. What is the frequency of this EM wave in air? a. 5.55 × 1014 Hz b. 6.00 × 1011 Hz c. 9.00 × 108 Hz d. 3.00 × 1010 MHz e. 1.80 × 1015 Hz ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 33.3 Plane Electromagnetic Waves Copyright Cengage Learning. Powered by Cognero.

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7. An FM radio station broadcasts at 98.6 MHz. What is the wavelength of the radiowaves? a. 60.8 m b. 6.08 m c. 3.04 m d. 0.314 m e. 0.33 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 33.3 Plane Electromagnetic Waves 8. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. What is the maximum E-field? a. 1 000 V/m b. 180 V/m c. 81 V/m d. 360 V/m e. 0.40 V/m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 33.3 Plane Electromagnetic Waves 9. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. What is the frequency of the wave? a. 500 MHz b. 250 kHz c. 1.25 MHz d. 10 mHz e. 300 MHz ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 33.3 Plane Electromagnetic Waves 10. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. What is the wavelength of the EM wave? a. 120 m Copyright Cengage Learning. Powered by Cognero.

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b. 240 m c. 60 m d. 100 m e. 360 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 33.3 Plane Electromagnetic Waves 11. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. What is the speed of the EM wave? a. 3 × 108 m/s b. 100 m/s c. 106 m/s d. 2 × 107 m/s e. 2 × 108 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 33.3 Plane Electromagnetic Waves 12. In an electromagnetic wave, 1) how are the electric and magnetic field directions related; and 2) how is the direction of travel determined from their directions? ( is the velocity of the light wave.) a. . b. . c. . d. . e. .

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.3 Plane Electromagnetic Waves Copyright Cengage Learning. Powered by Cognero.

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13. Which of the following gives the value of the speed of light? a. ε0μ0 b. c.

d.

e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.3 Plane Electromagnetic Waves 14. If E is the electric field amplitude and c is the speed of light, which of the following gives the magnetic field amplitude B for an electromagnetic wave in vacuum? a. . b. . c. E. d.

.

e. cE. ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.3 Plane Electromagnetic Waves -12

15. If E is the electric field magnitude and ε0 = 8.85 × 10 a. .

2

2

2

C / N ⋅ m , which of the following gives the units of ε0E

b. . c. . d. .

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e. .

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 33.3 Plane Electromagnetic Waves 16. At every instant the ratio of the magnitude of the electric to the magnetic field in an electromagnetic wave in vacuum is equal to a. the speed of radio waves. b. the speed of light. c. the speed of gamma rays. d. all of the above. e. only (a) and (b) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.3 Plane Electromagnetic Waves 11

2

17. The Earth is 1.49 × 10 meters from the Sun. If the solar radiation at the top of the Earth's atmosphere is 1 340 W/m , what is the total power output of the Sun? a. 7.10 × 1027 W b. 2.20 × 1030 W c. 6.62 × 1026 W d. 3.74 × 1026 W e. 2.98 × 1025 W ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 2

18. If the radiant energy from the Sun comes in as a plane EM wave of intensity 1 340 W/m , calculate the peak values of E and B. a. 300 V/m, 10-4 T b. 1 000 V/m, 3.35 × 10-6 T c. 225 V/m, 1.60× 10-3 T d. 111 V/m, 3.00 × 10-5 T e. 711 V/m, 2.37 × 10-6 T ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves Copyright Cengage Learning. Powered by Cognero.

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19. If the maximum E-component of an electromagnetic wave is 600 V/m, what is the maximum B-component? a. 1.4 T b. 1.8 × 10-5 T c. 2.0 × 10-6 T d. 1.0 × 10-3 T e. 1.6 × 10-10 T ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 20. What is the average value of the magnitude of the Poynting vector all directions? a. 1 W/m2

at 1 meter from a 100-watt lightbulb radiating in

b. 4 W/m2 c. 2 W/m2 d. 8 W/m2 e. 12 W/m2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 21. A 100-kW radio station emits EM waves in all directions from an antenna on top of a mountain. What is the intensity of the signal at a distance of 10 km? a. 8 × 10-5 W/m2 b. 8 × 10-6 W/m2 c. 3 × 10-3 W/m2 d. 0.8 W/m2 e. 2.5 × 10-5 W/m2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 22. How much electromagnetic energy is contained in each cubic meter near the Earth's surface if the intensity of sunlight 2 under clear skies is 1 000 W/m ? a. 3.3 × 10-6 J b. 3.3 J c. 0.003 J d. 10-4 J e. 3.0 × 105 J Copyright Cengage Learning. Powered by Cognero.

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ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 23. At a distance of 10 km from a radio transmitter, the amplitude of the E-field is 0.20 volts/meter. What is the total power emitted by the radio transmitter? a. 10 kW b. 67 kW c. 140 kW d. 245 kW e. 21 kW ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 24. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. Find the average power per square meter carried by the EM wave. a. 720 W b. 172 W c. 500 W d. 2 × 107 W e. 86 W ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 2

25. A solar cell has a light-gathering area of 10 cm and produces 0.2 A at 0.8 V (DC) when illuminated with S = 1 000 2 W/m sunlight. What is the efficiency of the solar cell? a. 16% b. 7% c. 23% d. 4% e. 32% ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 2

6

26. The intensity of radiation reaching the Earth from the Sun is 1 350 W/m . The Earth's radius is 6.4 × 10 m. How big a Copyright Cengage Learning. Powered by Cognero.

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force does this radiation exert on the Earth? (Assume it is all absorbed.) a. 5.8 × 108 N b. 1.2 × 109 N c. 2.3 × 109 N d. 4.6 × 109 N e. 1.7 × 1017 N ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 27. If E and B are the amplitudes of the electric and magnetic fields, respectively, in an electromagnetic wave in vacuum, which of the following gives the total average energy density in the wave? a. b. c. ε0E2 d.

e.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.4 Energy Carried by Electromagnetic Waves -4

3

28. Near the surface of the planet, the Earth's magnetic field is about 0.50 × 10 T. How much energy is stored in 1.0 m of the atmosphere because of this field? −4 ANSWER: 9.9 × 10 J POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 26

8

29. The Sun radiates energy at a rate of 3.86 × 10 W. Its radius is 7.0 × 10 m. If the distance from the Earth to the Sun 11 is 1.5 × 10 m, what is the intensity of solar radiation at the top of the Earth's atmosphere?

2 ANSWER: W/m POINTS: 2 DIFFICULTY: Average REFERENCES: 33.4 Energy Carried by Electromagnetic Waves 30. Find the force exerted by reflecting sunlight off a reflecting aluminum sheet in space if the area normal to the sunlight Copyright Cengage Learning. Powered by Cognero.

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2

2

is 10 000 m and the solar intensity is 1 350 W/m . a. 0.72 N b. 0.09 N c. 9 N d. 45 N e. 0.18 N ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 33.5 Momentum and Radiation Pressure 2

31. What is the maximum radiation pressure exerted by sunlight in space (S = 1 350 W/m ) on a flat black surface? a. 2.25 × 10-5 Pa b. 0.06 Pa c. 7 × 10-4 Pa d. 4.5 × 10-6 Pa e. 9.0 × 10-6 Pa ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 33.5 Momentum and Radiation Pressure 2

32. What is the maximum radiation pressure exerted by sunlight in space (S = 1 350 W/m ) on a highly polished silver surface? a. 1.4 × 10-2 Pa b. 0.12 Pa c. 9.0 × 10-6 Pa d. 4.5 × 10-5 Pa e. 2.3 × 10-6 Pa ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 33.5 Momentum and Radiation Pressure 33. Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1) and 2R (sphere 2) from the Sun, respectively. What is the ratio of the pressure of solar radiation on sphere 2 to that on sphere 1? a. 0.25 b. 0.50 c. 1.0 d. 2.0 e. 4.0 ANSWER: a POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 33.5 Momentum and Radiation Pressure 34. Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1) and 2R (sphere 2) from the Sun, respectively. The ratio of the gravitational force exerted by the Sun on sphere 1 to the pressure of solar radiation on sphere 1 is T1; the ratio for sphere 2 is T2. What is the ratio of T2 to T1? a. 0.25 b. 0.50 c. 1.0 d. 2.0 e. 4.0 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 33.5 Momentum and Radiation Pressure

35. A spherical particle of density 11

the Earth. RSE = 1.5 × 10

and 2.00-mm radius is located at the same distance from the Sun as

m.

. Assume the

particle absorbs 100 percent of the sunlight reaching it. What is the ratio of the force exerted by the solar radiation to the force of gravity exerted on the particle by the Sun? a. 5.8 × 10-5 b. 0.58 c. 1.0 d. 1.7 e. 1.7 × 104 ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 33.5 Momentum and Radiation Pressure 36. A possible means of space flight is to place a perfectly reflecting aluminized sheet into Earth orbit and use the light 5 2 from the Sun to push this solar sail. If a huge sail of area 6.00 × 10 m and mass 6 000 kg were placed into orbit and 2 turned toward the Sun, what would be the force exerted on the sail? (Assume a solar intensity of 1 380 W/m .)

ANSWER: 5.52 N POINTS: 2 DIFFICULTY: Average REFERENCES: 33.5 Momentum and Radiation Pressure 37. What should be the height of a dipole antenna (of dimensions 1/4 wavelength) if it is to transmit 1 200-kHz radio waves? a. 11.4 m b. 60 cm c. 1.12 m Copyright Cengage Learning. Powered by Cognero.

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d. 62.5 m e. 250 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 33.6 Production of Electromagnetic Waves by an Antenna 38. High-frequency alternating current is passed through a solenoid that contains a solid copper core insulated from the coils of the solenoid. Which statement is correct? a. A copper core remains cool no matter what the frequency of the current in the solenoid is. b. The copper core remains cool because the induced emf is parallel to the solenoid axis and fluctuates rapidly. c. The copper core heats up because an emf parallel to the solenoid axis is induced in the core. d. The copper core heats up because circular currents around its axis are induced in the core. e. The copper core heats up because the electric field induced in the copper is parallel to the magnetic field produced by the solenoid.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.6 Production of Electromagnetic Waves by an Antenna 39. Which of the following types of electromagnetic waves has the shortest wavelength? a. microwaves b. infrared waves c. ultraviolet waves d. X-rays e. gamma rays ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.7 The Spectrum of Electromagnetic Waves 40. You can raise the temperature of an object with a. microwaves. b. infrared waves. c. ultraviolet rays. d. all of the above. e. only (a) and (b) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 33.7 The Spectrum of Electromagnetic Waves

1. According to Einstein's theory, the energy of a photon is a. proportional to its wavelength. b. proportional to its frequency.

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c. constant, since the speed of light is a constant. d. quantized, since it always appears in bundles of size, 1.6 × 10-19 C. e. proportional to the square of the frequency.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.1 The Nature of Light 2. Light behaves like a. a wave at times, and a particle at other times. b. a wave. c. a particle. d. both a wave and a particle, because of its dual nature.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.1 The Nature of Light 3. The first successful measurement of the speed of light was made by a. Rene Descartes. b. Armand Fizeau. c. Christian Huygens. d. Ole Roemer. e. James Maxwell.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.1 The Nature of Light 4. An experiment to measure the speed of light uses an apparatus similar to Fizeau's. The distance between the light source and the mirror is 10 m, and the wheel has 800 notches. If the wheel rotates at 9 000 rev/s when the light from the source is extinguished, what is the experimental value for c (in m/s)? a. 2.94 × 108 b. 2.92 × 108 c. 2.88 × 108 d. 2.98 × 108 e. 3.01 × 108 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 34.1 The Nature of Light 5. Light can exhibit the characteristics of a. a particle with energy E = hf.

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b. a wave with wavelength

.

c. a particle or wave that travels at speed

in all materials.

d. all of the above. e. only (a) or (b) above.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.1 The Nature of Light -7

8

6. The wavelength of light visible to the human eye is on the order of 5 × 10 m. If the speed of light in air is 3 × 10 m/s, find the frequency of the light wave. a. 3 × 107 Hz b. 4 × 109 Hz c. 5 × 1011 Hz d. 6 × 1014 Hz e. 4 × 1015 Hz ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 34.1 The Nature of Light 7. A light ray is incident on the surface of water (n = 1.33) at an angle of 60° relative to the normal to the surface. What is the angle of the reflected wave relative to the normal? a. 80°. b. 40°. c. 20°. d. 60°. e. 30°.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.3 Analysis Model: Wave Under Reflection 8. Two mirrors are at right angles to one another. A light ray is incident on the first at an angle of 30° with respect to the normal to the surface. What is the angle of reflection from the second surface? a. 30° b. 60° c. 45° d. 53° e. 75° ANSWER: b POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 34.3 Analysis Model: Wave Under Reflection 9. Two mirrors are at right angles to one another. If an object is placed near the mirrors, what is the largest number of images that would be seen in the mirrors? a. 3 b. 2 c. 4 d. 5 e. 6 ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.3 Analysis Model: Wave Under Reflection 10. When light scatters from a rough surface, the law a. does not hold. b. holds on average, with reflected light from the surface leaving in the average direction of reflection. c. applies to each small relatively flat area of surface individually. d. applies only when the particle aspect of light predominates. e. applies only when the wavelength of light is greater than 800 nm but less than 2000 nm.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.3 Analysis Model: Wave Under Reflection 11. Two flat, rectangular mirrors are set edge to edge and placed perpendicular to a flat, nonreflecting surface. A light ray that reflects from mirror 1 at angle θM1 then strikes the second mirror and reflects at θM2 such that the angle between the ray reaching mirror 1 and the ray leaving mirror 2 is 180°. What is the angle between the two mirrors? a. 0° b. 45° c. 90° d. 150° e. 235° ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 34.3 Analysis Model: Wave Under Reflection 12. The angle between two plane mirrors that meet at one edge is 45°. A ray strikes the first mirror at a 60° angle of incidence. What is the total change in the ray’s direction after it reflects from the second mirror, relative to its direction before striking the first mirror? a. 0° b. 45° c. 90° d. 150° Copyright Cengage Learning. Powered by Cognero.

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e. 270° ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 34.3 Analysis Model: Wave Under Reflection 13. Two flat, rectangular mirrors are set edge to edge and placed perpendicular to a flat, nonreflecting surface. The edges of the two mirrors meet at a 30° angle. A light ray that approaches mirror 1 is parallel to mirror 2. What is the angle of reflection of that ray from mirror 1? a. 0° b. 30° c. 60° d. 90° e. 120° ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 34.3 Analysis Model: Wave Under Reflection 14. Two flat, rectangular mirrors are set edge to edge and placed perpendicular to a flat, nonreflecting surface. The edges of the two mirrors meet at a 30° angle. A light ray that enters parallel to mirror 2 reflects from mirror 1 and then from mirror 2. What is the angle of reflection of that ray from mirror 2? a. 0° b. 30° c. 60° d. 90° e. 120° ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 34.3 Analysis Model: Wave Under Reflection 14

15. A light ray whose frequency is 6.00 × 10 Hz in vacuum is incident on water (n = 1.33). The wavelength of the light after it enters the water is (in nm) a. 798. b. 500. c. 665. d. 376. e. 266.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 16. The speed of light changes when it goes from ethyl alcohol (n = 1.36) to carbon tetrachloride (n = 1.46). What is the ratio of the speed in carbon tetrachloride to the speed in ethyl alcohol, v2/v1? a. 1.99 Copyright Cengage Learning. Powered by Cognero.

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b. 1.07 c. 0.932 d. 0.511 e. 0.760 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 17. Light is refracted through a diamond. If the angle of incidence is 30°, and the angle of refraction is 12°, what is the index of refraction? a. 1.3 b. 2.4 c. 2.6 d. 1.8 e. 0.4 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 18. A person in a boat sees a fish in the water (n = 1.33), the light rays making an angle of 40° relative to the water's surface. What is the true angle (in degrees) relative to the water's surface of the same rays when beneath the surface? a. 40 b. 35 c. 50 d. 55 e. 61 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 19. A diver shines light up to the surface of a flat, glass-bottomed boat at an angle of 30° relative to the normal. If the index of refraction of water and glass are 1.33 and 1.5, respectively, at what angle (in degrees) does the light leave the glass (relative to its normal)? a. 26 b. 35 c. 42 d. 22 e. 48 ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 34.4 Analysis Model: Wave Under Refraction 20. A person looks horizontally at the edge of a swimming pool. If its length is 5 m, and the pool is filled to the surface, to Copyright Cengage Learning. Powered by Cognero.

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what depth (in m) could the observer see? (n for water is 1.33.) a. 3.2 b. 4.4 c. 2.1 d. 1.0 e. 0.3 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 34.4 Analysis Model: Wave Under Refraction 21. An aquarium contains a 5-cm layer of water (n = 1.33) floating on top of carbon tetrachloride (n = 1.461). If the angle of incidence into the water from the air is 30°, what is the angle of refraction into the carbon tetrachloride? a. 58° b. 69° c. 37° d. 20° e. 75° ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 22. An aquarium contains a 5-cm layer of water (n = 1.333) floating on top of carbon tetrachloride (n = 1.461). If the angle of incidence into the water from the carbon tetrachloride is 20°, what is the angle of refraction into the air? a. 20° b. 30° c. 38° d. 69° e. 26° ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 23. Light strikes a diamond (n = 2.42) at an angle of 60° relative to the normal to the surface. What is the angle of refraction? a. 21° b. 30° c. 38° d. 69° e. 71° ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction Copyright Cengage Learning. Powered by Cognero.

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24. Light strikes a diamond (n = 2.42) immersed in glycerin (n = 1.473) at an angle of 60° relative to the normal to the surface. What is the angle of refraction? a. 20° b. 60° c. 32° d. 64° e. 15° ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 25. A monochromatic (single frequency, single wavelength) light ray in air (n = 1) enters a glass prism (n = 1.5). In the glass prism, a. both the frequency and the wavelength are the same as in air. b. the frequency is the same, but the wavelength is greater than in air. c. the frequency is the same, but the wavelength is smaller than in air. d. the wavelength is the same, but the frequency is greater than in air. e. the wavelength is the same, but the frequency is smaller than in air.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.4 Analysis Model: Wave Under Refraction 26. A light ray is partially reflected and partially refracted at a boundary between two media, the upper one having index of refraction n, the lower one having index of refraction n', as shown in the figure. If the reflected ray is perpendicular to the refracted ray, which of the following is true?

a. b. c.

d.

e.

ANSWER:

a

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POINTS: 3 DIFFICULTY: Challenging REFERENCES: 34.4 Analysis Model: Wave Under Refraction 27. A light ray strikes a hexagonal ice crystal floating in the air perpendicular to one face, as shown below. The hexagonal faces of the crystal are perpendicular to the plane of the page. All the rays shown are in the plane of the page, and nice = 1.30. Which outgoing ray is correct when the incoming ray strikes the crystal face on the left head on?

a. A b. B c. C d. D e. E ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.4 Analysis Model: Wave Under Refraction 28. A light ray strikes a hexagonal ice crystal floating in the air at a 30° angle to one face, as shown below. The hexagonal faces of the crystal are perpendicular to the plane of the page. All the rays shown are in the plane of the page, and nice = 1.30. Which outgoing ray is the correct one?

a. A b. B c. C d. D e. E ANSWER:

b

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POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 29. When a light ray travels between any two points, the path it takes is the one that (Hint: Eliminate answers you know are wrong.) a. covers the greatest distance. b. follows the greatest index of refraction. c. avoids travel in more than one medium. d. is the mean between the longest and the shortest paths. e. takes the least time.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 30. The wavefront shown at the left for light in air reaches the plane boundary between air and two transparent media with n1 = 1.5 and n2 = 3.00, respectively.

Which diagram below correctly illustrates the wavefront after it has entered the two media at the right?

a. A b. B c. C d. D e. E ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 31. The wavefront shown at the left for light in air reaches the plane surface (shown by a slanted line) that bounds a medium with n = 1.50.

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Which diagram below correctly shows the wavefront while entering the medium at the right?

a. A b. B c. C d. D e. E ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.4 Analysis Model: Wave Under Refraction 32. When light is either reflected or refracted, the quantity that does not change in either process is its a. direction of travel. b. dispersion. c. frequency. d. speed. e. wavelength.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 34.4 Analysis Model: Wave Under Refraction 33. A laser beam is incident from the air at an angle of 30.00° to the vertical onto a solution of Karo syrup in water. If the beam is refracted to 19.24° to the vertical, what is the index of refraction of the syrup solution?

ANSWER: 1.517 POINTS: 2 DIFFICULTY: Average REFERENCES: 34.4 Analysis Model: Wave Under Refraction 34. The laws of refraction and reflection are the same for sound as for light. The speed of sound in air is 340 m/s and in water it is 1 510 m/s. If a sound wave approaches a plane water surface at an angle of incidence of 12.0°, what is the angle of refraction?

ANSWER: 67.4° POINTS: 3 DIFFICULTY: Challenging REFERENCES: 34.4 Analysis Model: Wave Under Refraction 35. The index of refraction for red light in water is 1.331 and for blue light is 1.340. If a ray of white light enters the water at an angle of incidence of 83.00°, what are the underwater angles of refraction for the blue and red components of the light?

ANSWER: 47.79° (blue), 48.22° (red) Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 34.6 Dispersion 36. A diver shines an underwater searchlight at the surface of a pond (n = 1.33). At what angle (relative to the surface) will the light be totally reflected? a. 47.3° b. 41.2° c. 51.1° d. 58.7° e. 49.8° ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 34.7 Total Internal Reflection 37. A layer of ethyl alcohol (n = 1.361) is on top of water (n = 1.333). To the nearest degree, at what angle relative to the normal to the interface of the two liquids is light totally reflected? a. 78° b. 88° c. 68° d. 49° e. the critical angle is undefined ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 34.7 Total Internal Reflection 38. A layer of water (n = 1.333) floats on carbon tetrachloride (n = 1.461) contained in an aquarium. To the nearest degree, what is the critical angle at the interface between the two liquids? a. 88° b. 78° c. 66° d. 58° e. 43° ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 34.7 Total Internal Reflection 39. A layer of kerosene (n = 1.45) is floating on water (n = 1.33). For what angles of incidence at the kerosene-water interface will light be totally internally reflected within the kerosene?

ANSWER: θ > 66.5° POINTS: 3 DIFFICULTY: Challenging REFERENCES: 34.7 Total Internal Reflection Copyright Cengage Learning. Powered by Cognero.

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1. A clown 2 m tall looks at himself in a full-length mirror (floor-to-ceiling). Where in the mirror must he look to see his feet? a. 1 m from the floor b. 50 cm from the floor c. 25 cm from the floor d. at the bottom of the mirror e. 1.5 m from the floor ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 35.1 Images Formed by Flat Mirrors 2. The inhabitants of a planet in another galaxy have their eyes at the exact center of their 4.0-m-long bodies. How long must a plane mirror be for such a creature to be able to see all of its body in the mirror? a. 1.0 m b. 2.0 m c. 2.5 m d. 4.0 m e. 8.0 m ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 35.1 Images Formed by Flat Mirrors 3. A concave mirror has a focal length of 20 cm. What is the position (in cm) of the resulting image if the image is inverted and four times smaller than the object? a. 15 b. 25 c. 50 d. 100 e. −15 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 4. A convex mirror has a focal length of −20 cm. What is the position of the resulting image (in cm) if the image is upright and four times smaller than the object? a. −100 b. −25 c. −50 d. −15 e. −10 ANSWER: d POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 35.2 Images Formed by Spherical Mirrors 5. A concave mirror has a focal length of 20 cm. What is the position (in cm) of the object if the image is upright and is two times larger than the object? a. 30 b. 20 c. 10 d. 40 e. 60 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 6. A concave mirror has a focal length of 20 cm. What is the magnification if the object's distance is 100 cm? a. 1/2 b. 1/4 c. −2 d. 4 e. −1/4 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 7. A convex mirror has a focal length of −20 cm. What is the object distance if the image distance is −10 cm? a. 10 cm b. 40 cm c. 60 cm d. 20 cm e. 30 cm ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 8. A concave mirror has a focal length of 20 cm. What is the magnification if the object and image distances are 10 cm and −20 cm, respectively? a. 1 b. 2 c. 1/2 d. 1/4 e. −1/2 ANSWER: b POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 35.2 Images Formed by Spherical Mirrors 9. A concave mirror has a radius of curvature of 1.0 m. An object is placed 2.0 m in front of the mirror. Determine the location of the image (in cm). a. 130 b. 83 c. 67 d. 150 e. 200 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 10. An object 4 cm high is placed 15 cm in front of a convex mirror with a focal length of −10 cm. What is the image position (in cm)? a. −8 b. −4 c. −2 d. −6 e. 30 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 11. An object 15 cm high is placed 15 cm in front of a convex mirror with a focal length of −10 cm. What is the image height (in cm)? a. 2 b. 4 c. 6 d. 8 e. 30 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 12. An object is placed 10 cm in front of a concave mirror with a 20-cm focal length. Determine the image location (in cm). a. −20 b. −15 c. −10 d. −5 e. 6.7 ANSWER: a POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 13. An object is placed 15 cm in front of a concave mirror with a focal length of 30 cm. What is the magnification? a. 1 b. 2 c. 1/2 d. 1/4 e. −2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 14. A dentist uses a concave mirror (focal length 2 cm) to examine some teeth. If the distance from the object to the mirror is 1 cm, what is the magnification of the tooth? a. 6 b. 1 c. 4 d. 2 e. 1.5 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 15. If you stand closer to a concave mirror than a distance of one focal length, the image you see is a. real and inverted. b. real and upright. c. virtual and inverted. d. virtual and upright. e. none of the above because you do not get an image.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 35.2 Images Formed by Spherical Mirrors 16. When you stand in front of a convex mirror, the image you see is a. real and inverted. b. real and upright. c. virtual and inverted. d. virtual and upright. e. real and inverted if your distance from the mirror is greater than two focal lengths.

ANSWER: d POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 35.2 Images Formed by Spherical Mirrors 17. A magician can make a candle look as if it is burning under water by focusing light from a candle flame burning in air directly on top of an underwater candle. To do this you want to use a (Hint: eliminate those that cannot work.) a. concave mirror farther than one focal length from the burning candle. b. a convex mirror farther than one focal length from the burning candle. c. a biconcave lens farther than one focal length from the burning candle. d. a concave mirror closer than one focal length to the burning candle. e. a convex lens closer than one focal length to the burning candle.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 35.2 Images Formed by Spherical Mirrors 18. The object in a ray diagram is perpendicular to the principal axis but does not have one end lying on the principal axis.

The minimum number of rays that must be drawn in this ray diagram in order to determine the position of the image is a. 1. b. 2. c. 3. d. 4. e. 5.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 19. A concave mirror with a radius of curvature of 1.0 m is illuminated by a candle located on the symmetry axis 3.0 m from the mirror. Where is the image of the candle?

ANSWER: 60 cm in front of the mirror POINTS: 2 DIFFICULTY: Average REFERENCES: 35.2 Images Formed by Spherical Mirrors 20. The actual depth of a shallow pool 1.00 m deep is not the same as the apparent depth seen when you look straight down at the pool from above. How deep (in cm) will it appear to be? (nwater = 1.33.) a. 133 b. 75.2 c. 90.6 d. 117 e. 100 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 35.3 Images Formed by Refraction 21. Bottles of perfume sometimes have thick glass (n = 1.5) walls which give the impression the volume is larger than it is. Assume a cylindrical bottle has an inner radius of 1.0 cm and an outer radius of 2.0 cm. How thick (in cm) would the Copyright Cengage Learning. Powered by Cognero.

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wall appear if you could see a mark on the inside surface? a. 0.80 b. 0.51 c. 0.72 d. 80 e. 12 ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 35.3 Images Formed by Refraction 22. Bottles of perfume sometimes have thick glass (n = 1.5) walls which give the impression the volume is larger than it really is. Assume a cylindrical bottle with an inner radius of 1.0 cm and an outer radius of 2.0 cm. What percentage of the apparent volume is the real volume? a. 95% b. 60% c. 80% d. 64% e. 75% ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 35.3 Images Formed by Refraction 23. The image of an object beneath the surface of a medium of refractive index n > 1 is seen in air by a person looking down on the surface. This image, formed by light rays leaving the flat refractive surface, is a. real and closer to the viewer than the object. b. virtual and closer to the viewer than the object. c. real and farther from the viewer than the object. d. virtual and farther from the viewer than the object. e. virtual and the same distance from the viewer as the object.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 35.3 Images Formed by Refraction 24. A girl is sitting on the edge of a pier with her legs dangling over the water. Her soles are 80.0 cm above the surface of the water. A boy in the water looks up at her feet and wants to touch them with a reed. (nwater = 1.333.) He will see her soles as being a. right at the water surface. b. 53.3 cm above the water surface. c. exactly 80.0 cm above the water surface. d. 107 cm above the water surface. e. an infinite distance above the water surface.

ANSWER: d POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 35.3 Images Formed by Refraction 25. A fish is 80 cm below the surface of a pond. What is the apparent depth (in cm) when viewed from a position almost directly above the fish? (For water, n = 1.33.) a. 50 b. 60 c. 40 d. 70 e. 110 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 35.3 Images Formed by Refraction 26. A soda straw is stuck into water at an angle of 36° to the vertical. Looking straight down, what does the angle of the submerged portion of the straw to the vertical appear to be?

ANSWER: 44° POINTS: 3 DIFFICULTY: Challenging REFERENCES: 35.3 Images Formed by Refraction 27. A plane convex lens is made of glass (n = 1.5) with one flat surface and the other having a radius of 20 cm. What is the focal length (in cm) of the lens? a. 20 b. 30 c. 40 d. 10 e. 50 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 35.4 Images Formed by Thin Lenses 28. An object 20-cm high is placed 50.0 cm in front of a lens whose focal length is 5.00 cm. Where will the image be located (in cm)? a. 5.13 b. 5.56 c. 5.72 d. 5.93 e. 4.55 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 35.4 Images Formed by Thin Lenses 29. An object 50-cm high is placed 1.0 m in front of a converging lens whose focal length is 1.5 m. Determine the image Copyright Cengage Learning. Powered by Cognero.

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height (in cm). a. 77 b. 150 c. 52 d. 17 e. 83 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 35.4 Images Formed by Thin Lenses 30. An object is placed 15 cm in front of a diverging lens whose focal length is 12 cm. Where will the image be located (in cm)? a. −6.7 b. −7.2 c. −0.15 d. −60 e. −5.0 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 35.4 Images Formed by Thin Lenses 31. If a convex lens were made out of very thin clear plastic filled with air, and were then placed underwater where n = 1.33 and where the lens would have an effective index of refraction n = 1, the lens would act in the same way a. as a concave mirror in air. b. as a concave lens in air. c. as a convex lens in air. d. as a flat, refracting surface between water and air as seen from the water side. e. as the glasses worn by a farsighted person.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 35.4 Images Formed by Thin Lenses 32. Of the possible statements that parallel rays are brought to a focus by a 1) 2) 3) 4)

concave mirror, convex mirror, converging lens, diverging lens,

the correct answer is a. 1 and 2. b. 3 and 4. c. 1 and 3. d. 2 and 3. e. 2 and 4.

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ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 35.4 Images Formed by Thin Lenses 33. Which ray diagrams are correct? The three rays in each diagram are distinguished by different types of lines. Hint: Check the behavior of each ray as it interacts with the lens.

a. B and C b. C and D c. D and E d. C and E e. C, D and E ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 35.4 Images Formed by Thin Lenses 34. Which ray diagram is correct? The three rays in each diagram are distinguished by different types of lines. Hint: Check the behavior of each ray as it interacts with the lens.

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a. A b. B c. C d. D e. E ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 35.4 Images Formed by Thin Lenses

35. Ilona and Olivia observe a virtual image formed by an object placed a distance

in front of a convex lens of focal

length f. They argue about where to place a concave lens of focal length −f to have a virtual image at the same location relative to the lens that they had with the convex lens. Ilona says that the object should also be placed a distance

in

front of the concave lens. Olivia says that this won't work. Which one, if either, is correct, and why? a. Ilona, because concave and convex lenses produce virtual images at equal image distances when the object distances are equal. b. Ilona, because both p and q are negative for a concave lens. c. Olivia, because both p and q are positive for a concave lens. d.

Olivia, because if , then p was p = ∞. e. Olivia, because if q = −f, then p was p = ∞.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 35.4 Images Formed by Thin Lenses Copyright Cengage Learning. Powered by Cognero.

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36. An object is placed a distance y0 = −2f in front of a convex lens of focal length f that is located at y = 0. An identical object is placed a distance

in front of a concave lens of focal length −f that is located at

difference between the two image positions,

. What is the

?

a.

b. f c. d. 2f e.

ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 35.4 Images Formed by Thin Lenses 37. An object is placed a distance y0 = −2f in front of a concave mirror of focal length f that is located at y = 0. An identical object is placed a distance

in front of a convex mirror of focal length −f that is located at

What is the difference between the two image positions,

.

?

a.

b. f c. d. 2f e.

ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 35.4 Images Formed by Thin Lenses 38. An object is placed 25 cm in front of a lens of focal length 20 cm. 60 cm past the first lens is a second lens of focal length 25 cm. How far past the 25-cm lens does the final image form? a. 20 cm b. 40 cm c. 16 cm d. 25 cm e. 47 cm ANSWER: c POINTS: 3 DIFFICULTY: Challenging Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 35.4 Images Formed by Thin Lenses 39. An object is placed 25 cm in front of a lens of focal length 20 cm. 60 cm past the first lens is a second lens of focal length 25 cm. What is the resulting magnification of the object in this setup? a. b. c. d. e.

ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 35.4 Images Formed by Thin Lenses 40. Suppose an object is placed 6.0 cm in front of a lens that has a focal length of 4.0 cm. Where is the image located?

What are the magnification and the character of the image?

ANSWER: 12 cm beyond the 4.0 cm lens, M = −2.0, the image is real and inverted POINTS: 2 DIFFICULTY: Average REFERENCES: 35.4 Images Formed by Thin Lenses 41. The purpose of prescription glasses for a near-sighted person is to bring the apparent positions of distant objects a. to the far point of the eye. b. to the near point of the eye. c. to the retina of the eye. d. none of the above.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 35.6 Optical Instruments 42. A far-sighted student has a near point of 1.0 m. Calculate the focal length (in cm) of the glasses needed so the near point will be normal (25 cm). a. 72 b. 25 c. 33 d. 100 e. −33 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 35.6 Optical Instruments 43. A 10-cm-focal-length converging lens is used to magnify small newspaper print 2.0 mm high. Calculate the height of the image (in mm) for the maximum magnification for a normal eye. a. 3.5 Copyright Cengage Learning. Powered by Cognero.

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b. 7.0 c. 9.2 d. 12 e. 2.5 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 35.6 Optical Instruments 44. A compound microscope is made with an objective lens ( = 0.90 cm) and an eyepiece ( = 1.1 cm). The lenses are separated by a distance of 10 cm. If an object is 1.0 cm in front of the objective lens, where will the final image of the eyepiece be located? a. −30 b. −15 c. −23 d. −11 e. −9 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 35.6 Optical Instruments 45. A compound microscope is made with an objective lens (f0 = 0.900 cm) and an eyepiece (fe = 1.10 cm). The lenses are separated by a distance of 10.0 cm. What is the angular magnification? (Assume the near point is 25.0 cm.) a. −253 b. −450 c. −770 d. −980 e. −635 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 35.6 Optical Instruments 46. A telescope is constructed with two lenses separated by a distance of 25 cm. The focal length of the objective is 20 cm. The focal length of the eyepiece is 5 cm. Calculate the magnitude of the angular magnification of the telescope. a. 6 b. 4 c. 8 d. 10 e. 5 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 35.6 Optical Instruments Copyright Cengage Learning. Powered by Cognero.

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47. A magnifying glass has a convex lens of focal length 15 cm. At what distance from a postage stamp should you hold this lens to get a magnification of +2.0?

ANSWER: 7.5 cm POINTS: 2 DIFFICULTY: Average REFERENCES: 35.6 Optical Instruments 48. A contact lens is made of plastic with an index of refraction of 1.50. The lens has an outer radius of curvature of +2.0 cm and an inner radius of curvature of +2.5 cm. What are the focal length and the power of the lens?

ANSWER: +20 cm, +5.0 diopters POINTS: 2 DIFFICULTY: Average REFERENCES: 35.6 Optical Instruments

1. A laser beam (λ = 694 nm) is incident on two slits 0.100 mm apart. Approximately how far apart (in m) will the bright interference fringes be on the screen 5.00 m from the double slits? a. 3.47 × 10-3 b. 3.47 × 10-2 c. 3.47 × 10-4 d. 3.47 × 10-6 e. 3.47 × 10-5 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 2. Estimate the distance (in cm) between the central bright region and the third dark fringe on a screen 5.00 m from two double slits 0.500 mm apart illuminated by 500-nm light. a. 3.47 b. 2.15 c. 1.75 d. 1.50 e. 1.25 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 3. Light is incident on a double slit. The fourth bright band has an angular distance of 7.0° from the central maximum.

14 What is the distance between the slits (in μm)? (Assume the frequency of the light is 5.4 × 10 Hz.) a. 27 b. 21 c. 24 d. 18 e. 14 Copyright Cengage Learning. Powered by Cognero.

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ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 4. For small angle approximations, a. the angle must be 10° or less. b. the angle must be 10 radians or less. c. the angle must be 1° or less. d. the angle must be 1 radian or less. e. the angle must be 45° or less.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 5. Two slits separated by 0.10 mm are illuminated with green light (λ = 540 nm). Calculate the distance (in cm) from the central bright region to the fifth bright band if the screen is 1.0 m away. a. 2.3 b. 2.5 c. 2.7 d. 2.1 e. 2.0 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 6. Two slits separated by 0.050 mm are illuminated with green light (λ = 540 nm). How many bands of bright lines are there between the central maximum and the 12-cm position? (The distance between the double slits and the screen is 1.0 m.) a. 1111 b. 111 c. 11 d. 1 e. 11111 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 7. Two slits are illuminated with green light (λ = 540 nm). The slits are 0.05 mm apart and the distance to the screen is 1.5 m. At what distance (in mm) from the central maximum on the screen is the average intensity 50% of the intensity of the central maximum? a. 1 b. 3 c. 2 Copyright Cengage Learning. Powered by Cognero.

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d. 4 e. 0.4 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 36.2 Analysis Model: Waves in Interference 8. Two slits are illuminated with red light (λ = 650 nm). The slits are 0.25 mm apart and the distance to the screen is 1.25 m. What fraction of the maximum intensity on the screen is the intensity measured at a distance 3.0 mm from the central maximum? a. 0.94 b. 0.92 c. 0.96 d. 0.98 e. 0.99 ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 36.2 Analysis Model: Waves in Interference 9. In a double-slit experiment, the distance between the slits is 0.2 mm, and the distance to the screen is 150 cm. What wavelength (in nm) is needed to have the intensity at a point 1 mm from the central maximum on the screen be 80% of the maximum intensity? a. 900 b. 700 c. 500 d. 300 e. 600 ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 36.2 Analysis Model: Waves in Interference 10. In a double-slit experiment, the distance between the slits is 0.2 mm and the distance to the screen is 150 cm. What is the phase difference (in degrees) between the waves from the two slits arriving at a point P when the angular distance of P is 10° relative to the central peak, and the wavelength is 500 nm? (Convert your result so the angle is between 0 and 360°.) a. 145° b. 155° c. 165° d. 135° e. 95° ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 36.2 Analysis Model: Waves in Interference Copyright Cengage Learning. Powered by Cognero.

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11. In a double-slit experiment, the distance between the slits is 0.2 mm and the distance to the screen is 100 cm. What is the phase difference (in degrees) between the waves from the two slits arriving at a point 5 mm from the central maximum when the wavelength is 400 nm? (Convert your result so the angle is between 0 and 360°.) a. 90° b. 180° c. 270° d. 360° e. 160° ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 36.2 Analysis Model: Waves in Interference 12. The electric fields arriving at a point P from three coherent sources are described by E1 = E0 sin ωt, E2 = E0 sin (ωt + π/4) and E3 = E0 sin (ωt + π/2). Assume the resultant field is represented by Ep = ER sin (ωt + α). What is the amplitude of the resultant wave at P? a. E0 b. 1.5E0 c. 1.7E0 d. 2.4E0 e. 2.9E0 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 13. The figure shows two point sources of light, A and B, that emit light waves in phase with each other. A is 3λ from point P. B is 5λ from P. (λ is the wavelength.) What is the phase difference between the waves arriving at P from A and B?

a. 0 rad b. π rad c. 2π rad d. 3π rad e. 4π rad ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference Copyright Cengage Learning. Powered by Cognero.

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14. The bright and dark bands you see in a photograph of a double slit interference pattern represent a. the respective positions of the crests and the troughs of the light wave. b. an interference pattern that is not present unless it is produced by the camera lens. c. the respective positions of constructive and destructive interference of light from the two sources. d. the respective positions of destructive and constructive interference of light from the two sources. e. the respective positions of bright and dark particles of light.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 15. In an interference pattern, the wavelength and frequency are a. the same in both the regions of constructive interference and the regions of destructive interference. b. greater in regions of constructive interference than in regions of destructive interference. c. smaller in regions of constructive interference than in regions of destructive interference. d. unchanged in regions of destructive interference but greater in regions of constructive interference. e. unchanged in regions of destructive interference but smaller in regions of constructive interference.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 16. A planar cross section through two spherical waves emanating from the sources S1 and S2 in the plane is shown in the figure. S1 and S2 are in phase. The black circles are one and two wavelengths from their respective sources. The lighter circles are one half and one and a half wavelengths distant from their respective sources. If the waves shown arriving at P1 both arrive with amplitude A, what is the resultant amplitude at point P1?

a. 0 b. c. A d.

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e. 2A ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 17. A planar cross section through two spherical waves emanating from the sources S1 and S2 in the plane is shown in the figure. S1 and S2 are in phase. The black circles are one and two wavelengths from their respective sources. The lighter circles are one half and one and a half wavelengths distant from their respective sources. If the waves shown arriving at P2 both arrive with amplitude A, what is the resultant amplitude at point P2?

a. 0 b. c. A d. e. 2A ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 18. A planar cross section through two spherical waves emanating from the sources S1 and S2 in the plane is

shown in the figure. The black circles are one and two wavelengths from their respective sources. The lighter circles are one half and one and a half wavelengths distant from their respective sources. The phase at S1 and S2 is zero at this instant, and the waves shown arriving at P1 both arrive with amplitude A. What is the magnitude of the phase angle of each wave at point P1 (in radians)?

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a. 0 b. π c. 2π d. 3π e. π/2 ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 19. A planar cross section through two spherical waves emanating from the sources S1 and S2 in the plane is

shown in the figure. The black circles are one and two wavelengths from their respective sources. The lighter circles are one half and one and a half wavelengths distant from their respective sources. The phase at S1 and S2 is zero at this instant, and the waves shown arriving at P2 both arrive with amplitude A. What is the difference in phase angle at point P2 (in radians)?

a. 0 b. π/2 c. π d. 3π/2 e. 2π ANSWER:

c

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 20. Which of the following is the correct expression for E, the superposition of two waves E1 = E0 sin(ωt) and E2 = E0 sin(ωt + φ) arriving at the same point in space at the same time? a.

b. 2E0 sin(ωt)cos(υ) c.

d.

e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 21. Ray says that interference effects cannot be observed with visible light because random phase changes occur in time intervals less than a nanosecond. Stacy says that doesn't matter if collimated light from a single source reaches multiple openings. (They are arguing about a light source 50.0 cm away from two 0.010 0-mm-wide slits, 2.00 mm apart, with a screen 1.00 m away from the slits.) Which one, if either, is correct, and why? a. Ray, because the phases at the two slits will be random and different. b. Ray, because it takes light over 3 ns to travel 1.00 m to the screen. c. Stacy, because the difference in time of travel from the source to the slits is no more than about 7 × 10-12 s. d. Stacy, but only if a lens is placed in front of the slits. e. Both, because interference of light never occurs outside a physics lab.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 22. Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart. The locations of bright and dark fringes can be interchanged if a thin film is placed in front of one of the slits. Which of the following gives the minimum thickness d of this film? (Here λair is the wavelength in air, and nfilm is the film’s index of refraction.) a.

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b.

c.

d.

e.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 23. Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart. Each bright fringe will shift to the location of the adjacent bright fringe if a thin film is placed in front of one of the slits. Which of the following gives the minimum thickness d of this film? (Here λair is the wavelength in air, and nfilm is the film’s index of refraction.) a.

b.

c.

d.

e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 24. Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart. The number of fringes per unit length on the screen can be doubled a. if the distance between the slits is doubled. b. if the wavelength is changed to .

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c. if the distance between the slits is quadruple the original distance and the wavelength is changed to d. if any of the above occurs. e. only if the width of the slits is changed to

.

.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 25. Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart. The number of fringes per unit length on the screen can be halved a. if the distance between the slits is changed to . b. if the wavelength is changed to c. if the distance between the slits is

. the wavelength is changed to

.

d. if any of the above occurs. e. only if the width of the slits is changed to

.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 26. The figures below represent interference fringes. The distances from the screen to the slits is the same for each figure, and the planes of the screen and the slits are parallel. Which figure(s) represent(s) slits with the smallest spacing d between the slits? The white spaces represent the interference maxima.

a. I. b. II. c. III. d. IV. e. V. ANSWER: POINTS:

e 1

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DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 27. The figures below represent interference fringes. The distances from the screen to the slits is the same for each figure, and the planes of the screen and the slits are parallel. Which figure(s) represent(s) slits with the greatest spacing d between the slits? The white spaces represent the interference maxima.

a. I. b. II. c. III. d. IV. e. V. ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 28. The figures below represent interference fringes. The distances from the screen to the slits is the same for each figure, and the planes of the screen and the slits are parallel. In each figure the spacing d between the slits is the same. Which figure(s) represent(s) slits illuminated with light of the greatest wavelength λ? The white spaces represent the interference maxima.

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b. II. c. III. d. IV. e. V. ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 29. The figures below represent interference fringes. The distances from the screen to the slits is the same for each figure, and the planes of the screen and the slits are parallel. In each figure the spacing d between the slits is the same. Which figure(s) represent(s) slits illuminated with light of the shortest wavelength λ? The white spaces represent the interference maxima.

a. I. b. II. c. III. d. IV. e. V. ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.2 Analysis Model: Waves in Interference 30. In a double-slit experiment using light of wavelength 486 nm, the slit spacing is 0.600 mm and the screen is 2.00 m from the slits. Find the distance along the screen between adjacent bright fringes.

ANSWER: 1.62 mm POINTS: 2 DIFFICULTY: Average REFERENCES: 36.2 Analysis Model: Waves in Interference 31. Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.4) that is 50 mm thick. What is the change of phase of the light reflected from the front surface? a. 0 b. 180° Copyright Cengage Learning. Powered by Cognero.

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c. λ/2 d. π/2 e. 55° ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.4 Change of Phase Due to Reflection 32. When a central dark fringe is observed in reflection in a circular interference pattern, waves reflected from the upper and lower surfaces of the medium must have a phase difference, in radians, of a. 0. b. π/2. c. π. d. 3π/2. e. 2π.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.4 Change of Phase Due to Reflection 33. Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.40). What is the wavelength of the light (in nm) in the bubble film? a. 255 b. 500 c. 700 d. 357 e. 422 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 36.5 Interference in Thin Films 34. Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.4) that is 500 nm thick. Calculate the change of phase of the light that penetrates the front surface, reflects from the second surface, and emerges through the first surface as an angle between 0° and 360°? a. 280° b. 160° c. 220° d. 100° e. 290° ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 36.5 Interference in Thin Films 35. Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.40). How thick is the bubble (in nm) if destructive interference occurs in the reflected light?

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a. 102 b. 179 c. 54 d. 1 e. 89 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 36.5 Interference in Thin Films 36. The light reflected from a soap bubble (n = 1.40) appears red (λ = 640 nm) at its center. What is the minimum thickness (in nm)? a. 124 b. 104 c. 114 d. 134 e. 234 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 36.5 Interference in Thin Films 37. A thin sheet of plastic (n = 1.60) is inserted between two panes of glass to reduce infrared (λ = 700 nm) losses. What thickness (in nm) is necessary to produce constructive interference in the reflected infrared radiation? a. 218 b. 109 c. 55 d. 318 e. 443 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 36.5 Interference in Thin Films 38. In a Newton's rings apparatus, find the phase difference (in radians) when an air wedge of 500-nm thickness is illuminated with red light (λ = 640 nm). a. 13 b. 11 c. 9 d. 7 e. 3 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 36.5 Interference in Thin Films Copyright Cengage Learning. Powered by Cognero.

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39. A film of index of refraction n1 coats a surface with index of refraction n2. When n1 > n2, what is the condition for constructive interference for reflected monochromatic light of wavelength λ in air? a.

b.

c.

d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.5 Interference in Thin Films 40. A film of index of refraction n1 coats a surface with index of refraction n2. When n1 > n2, what is the condition for destructive interference for reflected monochromatic light of wavelength λ in air? a.

b.

c.

d.

e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.5 Interference in Thin Films 41. A film of index of refraction n1 coats a surface with index of refraction n2. When n1 < n2, what is the condition for constructive interference for reflected monochromatic light of wavelength λ in air? a.

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b.

c.

d.

e.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.5 Interference in Thin Films 42. A film of index of refraction n1 coats a surface with index of refraction n2. When n1 < n2, what is the condition for destructive interference for reflected monochromatic light of wavelength λ in air? a.

b.

c.

d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 36.5 Interference in Thin Films 43. Nonreflective coatings for camera lenses reduce the loss of light at various surfaces of multi-lens systems, as well as preventing internal reflections that might mar the image. Find the minimum thickness of a layer of magnesium fluoride (n = 1.38) on flint glass (n = 1.66) that will cause destructive interference of reflected light of wavelength λ = 550 nm, a wavelength which is near the middle of the visual spectrum.

ANSWER: 99.6 nm POINTS: 2 DIFFICULTY: Average REFERENCES: 36.5 Interference in Thin Films 44. Suppose two flat, glass plates 30-cm long are in contact along one end and separated by a human hair at the other end.

If the diameter of the hair is 50 μm, find the separation of the interference fringes when the plates are illuminated by green Copyright Cengage Learning. Powered by Cognero.

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light, λ = 546 nm.

ANSWER: 1.64 mm POINTS: 2 DIFFICULTY: Average REFERENCES: 36.5 Interference in Thin Films 45. A soap bubble (n = 1.35) is floating in air. If the thickness of the bubble wall is 115 nm, what visible light wavelength is most strongly reflected?

ANSWER: 621 nm (red) POINTS: 2 DIFFICULTY: Average REFERENCES: 36.5 Interference in Thin Films 46. A uniform film of oil (n = 1.31) is floating on water. When sunlight in air is incident normally on the film, an observer finds that the reflected light has a brightness maximum at λ = 450 nm and a brightness minimum at λ = 600 nm. What is the thickness of the oil film?

ANSWER: 343.5 nm POINTS: 3 DIFFICULTY: Challenging REFERENCES: 36.5 Interference in Thin Films 47. When the adjustable mirror on the Michelson interferometer is moved 20 wavelengths, how many fringe pattern shifts would be counted? a. 5 b. 10 c. 20 d. 40 e. 80 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 36.6 The Michelson Interferometer

-7

1. Helium-neon laser light (λ = 6.33 × 10 m) is sent through a 0.30-mm-wide single slit. What is the width of the central maximum on a screen 1.0 m from the slit? a. 2.0 cm b. 4.2 mm c. 1.1 cm d. 2.0 mm e. 0.70 mm ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 2. The pupil of a cat's eye narrows to a slit width of 0.5 mm in daylight. What is the angular resolution of the cat's eye in Copyright Cengage Learning. Powered by Cognero.

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daylight (λ = 500 nm)? a. 0.01 rads b. 10-5 rads c. 10-3 rads d. 10-4 rads e. 0.1 rads ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 3. A narrow slit is illuminated with sodium yellow light of wavelength 589 nm. If the central maximum extends to ±30.0°, how wide is the slit? a. 0.500 mm b. 2.20 × 10-6 m c. 3.33 × 10-5 m d. 1.18 μm e. 5.89 μm ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 4. How wide must a narrow slit be if the first diffraction minimum occurs at ±12° with laser light of 633 nm? a. 3.0 × 10-6 m b. 3.0 × 10-5 m c. 6.1 × 10-6 m d. 6 .1× 10-5 m e. 1.5 × 10-6 m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 5. Plane waves of ultrasound, f = 51.0 kHz, impinge on a flat plane with a 1.00-cm-wide slit. What is the total angular width (2θ) of diffracted sound waves when the speed of sound in air is 340 m/s? a. 167° b. 83.6° c. 19.5° d. 41.8° e. 0.11° ANSWER: b POINTS: 3 DIFFICULTY: Challenging Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 6. A ruby laser beam (λ = 694.3 nm) is sent outwards from a 2.7-m diameter telescope to the Moon, 384 000 km away.

What is the radius of the big red spot on the Moon? a. 500 m b. 250 m c. 120 m d. 1.0 km e. 2.7 km ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 7. When you look at a single-slit diffraction pattern produced on a screen by light of a single wavelength, you see a bright central maximum and a number of maxima on either side, their intensity decreasing with distance from the central maximum. If the wavelength of the light is increased, a. the pattern shrinks in size. (central maximum less wide; other maxima in closer to it) b. the pattern increases in size. (central maximum wider; other maxima farther from it) c. it does not affect the size of the pattern. d. the width of the central maximum increases, but the other maxima do not change in position or width. e. the width of the central maximum decreases, but the other maxima do not change in position or width.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 8. When you look at a single-slit diffraction pattern produced on a screen by light of a single wavelength, you see a bright central maximum and a number of maxima on either side, their intensity decreasing with distance from the central maximum. If the width of the slit is decreased, a. the pattern shrinks in size. (central maximum less wide; other maxima in closer to it) b. the pattern increases in size. (central maximum wider; other maxima farther from it) c. it does not affect the size of the pattern. d. the width of the central maximum increases, but the other maxima do not change in position or width. e. the width of the central maximum decreases, but the other maxima do not change in position or width.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 9. When you look at a single slit diffraction pattern produced on a screen by light of a single wavelength, you see a bright central maximum and a number of maxima on either side, their intensity decreasing with distance from the central maximum. If the width of the slit is increased, a. the pattern shrinks in size. (central maximum less wide; other maxima in closer to it) b. the pattern increases in size. (central maximum wider; other maxima farther from it) c. it does not affect the size of the pattern. d. the width of the central maximum increases, but the other maxima do not change in position or width.

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e. the width of the central maximum decreases, but the other maxima do not change in position or width.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 10. A slit of variable width illuminated by light of wavelength λ is widened until the first-order diffraction minimum moves out to a distance infinitely far away from the brightest location in the central maximum. In terms of the wavelength, the width of the slit is then a. 0. b. . c. λ. d. . e. 2λ.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 11. The centers of two slits of width a are a distance d apart. If the fourth minimum of the interference pattern occurs at the location of the first minimum of the diffraction pattern for light of wavelength λ, what is the ratio a/d equal to? a. 0. b. . c. . d. . e. .

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 12. Which of the patterns shown below would appear on a screen when monochromatic light first passes through a narrow slit for which a = λ and then strikes the screen? Note that the darkest area in each illustration represents the brightest area on the screen. a. b.

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c. d. e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 13. When you look through a sheer curtain at a distant street lamp, you see a pattern of colored spots of light. This occurs by a. polarization of light in scattering and partial absorption by the threads. b. interference of light waves that pass through the threads with light waves that pass through the openings between the threads. c. refraction of light waves differentially in the cylindrical threads. d. diffraction of light waves passing through the two dimensional pattern of openings between the threads. e. reflection of light waves by the sides of the threads.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 14. Each pattern shown below would appear on a screen when monochromatic light first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen. In which case is the slit illuminated with light of the shortest wavelength? a. b. c. d. e.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 15. Each pattern shown below would appear on a screen when monochromatic light first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen. In which case is the slit illuminated with light of the longest wavelength? a. b.

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c. d. e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 16. Each pattern shown below would appear on a screen when monochromatic light of wavelength λ first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen.

In which case does the slit have the narrowest width? a. b. c. d. e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 17. Each pattern shown below would appear on a screen when monochromatic light of wavelength λ first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen.

In which case does the slit have the greatest width? a. b. c. d. e.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 18. A single slit of width a is illuminated by light of wavelength λ. If a = 4.3λ, the maximum number of dark fringes on a semi-circular screen surrounding the slit is a. 2. b. 4. c. 6.

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d. 8. e. 9.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 19. Light from a helium-neon laser (λ = 632.8 nm) is incident upon a 0.200-mm-wide slit. Find the total width of the central maximum 2.00 m from the slit.

ANSWER: 1.27 cm POINTS: 2 DIFFICULTY: Average REFERENCES: 37.2 Diffraction Patterns from Narrow Slits 20. The large space telescope that has been placed into an Earth orbit has an aperture diameter of 2.40 meters. What -7 angular resolution will this telescope achieve for visible light of wavelength λ = 4.80 × 10 m? a. 2.44 × 10-7 rads b. 2.44 × 10-4 rads c. 2.44 × 10-3 rads d. 1.22 × 10-6 rads e. 2.00 × 10-6 rads ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 37.3 Resolution of Single-Slit and Circular Apertures 21. At what distance could one theoretically distinguish two automobile headlights separated by 1.5 meters? Assume a -7 pupil diameter of 0.50 cm and yellow headlights seen at the wavelength 5.0 × 10 m. Assume eye fluid has an average n = 1.33. a. 6.0 km b. 12 km c. 9.0 km d. 3.0 km e. 16 km ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 37.3 Resolution of Single-Slit and Circular Apertures -5

22. A binary star system in the constellation Orion has an angular separation between the two stars of 1.2 × 10 radians.

-7 If λ = 5 × 10 m, what is the smallest aperture (diameter) telescope that may be used to resolve the two stars? a. 10 cm b. 5 cm c. 50 cm d. 1 m Copyright Cengage Learning. Powered by Cognero.

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e. 4 cm ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 37.3 Resolution of Single-Slit and Circular Apertures 23. A radar installation operates at 9 000 MHz with an antenna (dish) that is 15 meters across. Determine the maximum distance (in kilometers) for which this system can distinguish two aircraft 100 meters apart. a. 7.4 km b. 370 km c. 3700 m d. 37 km e. 740 km ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 37.3 Resolution of Single-Slit and Circular Apertures 24. What, approximately, are the dimensions of the smallest object on Earth that the astronauts can resolve by eye at a height of 200 km from the space shuttle? Assume λ = 500 nm light and a pupil diameter D = 0.50 cm. Assume eye fluid has an average n = 1.33. a. 150 m b. 100 m c. 250 m d. 25 m e. 18 m ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 37.3 Resolution of Single-Slit and Circular Apertures 25. Suppose a 5.0-meter diameter telescope were constructed on the dark side of the Moon. The viewing there (except for brief periods of sunlight) would be excellent. As an example, what would be the separation between two objects that could just be resolved on the planet Mars in 500 nm light? [The distance to Mars at closest approach is 50 million miles.]

ANSWER: 9.8 km which equals 6.1 miles POINTS: 2 DIFFICULTY: Average REFERENCES: 37.3 Resolution of Single-Slit and Circular Apertures 26. Monochromatic light from a He-Ne laser (λ = 632.8 nm) is incident on a diffraction grating containing 5 000 lines/cm.

Determine the angle of the first-order maximum. a. 18.4° b. 39.2° c. 14.6° d. 27.7° e. 13.9° ANSWER: a Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 37.4 The Diffraction Grating 27. A helium-neon laser (λ = 632.8 nm) is used to calibrate a diffraction grating. If the first-order maximum occurs at 20.5°, what is the line spacing, d? a. 1.81 × 10-6 m b. 1.00 × 10-5 m c. 1.00 × 10-4 m d. 1.31 × 10-6 m e. 6.76 × 10-7 m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 37.4 The Diffraction Grating 28. White light is spread out into spectral hues by a diffraction grating. If the grating has 1 000 lines per cm, at what angle will red light (λ = 640 nm) appear in first order? a. 14.7° b. 7.35° c. 17.7° d. 3.67° e. 1.84° ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 37.4 The Diffraction Grating 29. The hydrogen spectrum has a red line at 656 nm, and a blue line at 434 nm. What is the first-order angular separation between the two spectral lines obtained with a diffraction grating with 5 000 rulings/cm? a. 7.7° b. 16.6° c. 6.6° d. 3.2° e. 19.2° ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 37.4 The Diffraction Grating 30. A diffraction grating with 4 000 lines/cm is illuminated by light from the Sun. The solar spectrum is spread out on a white wall across the room. At what angle from the center line does blue light (400 nm) appear? At what angle from the center line does red light (650 nm) appear?

ANSWER: 9.21°, 15.1° POINTS: 3 DIFFICULTY: Challenging Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 37.4 The Diffraction Grating 31. In an x-ray diffraction experiment using x-rays of λ = 0.500 × 10 the crystal plane spacing. a. 2.87 × 10-10 m

-10

m, a first-order maximum occurred at 5.00°. Find

b. 1.36 × 10-10 m c. 6.24 × 10-9 m d. 1.93 × 10-9 m e. 5.74 × 10-9 m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 37.5 Diffraction of X-Rays by Crystals 32. A beam of x-rays of different frequencies is reflected at 10 degrees off a crystal of interatomic spacing 0.2 nm. Which x-ray wavelength is preferentially reflected? a. 0.0943 nm b. 0.139 nm c. 0.0695 nm d. 1.02 × 10-10 m e. 3.47 × 10-11 m ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 37.5 Diffraction of X-Rays by Crystals -10

33. If the interplanar spacing of NaCl is 2.814 × 10 m, what is the predicted angle at which x-rays of wavelength 0.140 nm will be diffracted in a first-order maximum? a. 31.3° b. 7.20° c. 20.5° d. 14.4° e. 29.8° ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 37.5 Diffraction of X-Rays by Crystals 34. Potassium Iodide (chemical formula: KI) has a face-centered cubic structure (just like sodium chloride). If the distance between crystal planes is d = 0.353 nm and x-rays of wavelength λ = 0.093 4 nm are used, what is the smallest angle θ at which a diffraction maximum may be obtained? a. 9.92° b. 7.60° c. 13.3° d. 15.5° Copyright Cengage Learning. Powered by Cognero.

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e. 6.52° ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 37.5 Diffraction of X-Rays by Crystals -10

35. The spacing between reflecting planes in a crystal is 2.82 × 10 m. A beam of x-rays is strongly reflected at an angle of 160° with the crystal face. What is the wavelength of the x-rays?

-10 ANSWER: 1.55 × 10 m POINTS: 2 DIFFICULTY: Average REFERENCES: 37.5 Diffraction of X-Rays by Crystals 36. Unpolarized light is passed through three successive Polaroid filters, each with its transmission axis at 45.0° to the preceding filter. What percentage of light gets through? a. 0% b. 12.5% c. 25.0% d. 50.0% e. 33.3% ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 37.6 Polarization of Light Waves 37. Sunlight reflected from a smooth ice surface is completely polarized. Determine the angle of incidence. (nice = 1.31) a. 52.6° b. 25.6° c. 65.2° d. 56.2° e. 49.8° ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 37.6 Polarization of Light Waves 38. How far above the horizon is theMoon when its image, reflected in a calm lake, is completely polarized? (nwater = 1.33.) a. 22.2° b. 7.7° c. 16.6° d. 36.9° e. 53.1° ANSWER: d POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 37.6 Polarization of Light Waves 39. Light reflected off a plate-glass window (n = 1.5) is found to be completely polarized at an angle of incidence of θ.

Find θ. a. 56.3° b. 5.7° c. 21.2° d. 18.6° e. 33.7° ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 37.6 Polarization of Light Waves 40. If the polarizing angle (the angle at which reflected light is completely plane polarized) of a flat piece of sapphire is 60.5°, what is its index of refraction? a. 1.97 b. 1.77 c. 1.59 d. 2.36 e. 1.82 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 37.6 Polarization of Light Waves 41. The polarizing angle in air for diamond is 67.4°. Calculate the critical angle inside the diamond for total internal reflection. a. 32.6° b. 22.6° c. 24.6° d. 28.6° e. 48.8° ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 37.6 Polarization of Light Waves 42. Polarized light is to have its polarization plane rotated by 90°. In which of the following cases does the final beam have the greatest intensity? a. 3 polarizing filters, each rotate beam by 30°. b. 2 polarizing filters, both rotate beam by 45°. c. 1 polarizing filter, rotating beam by 90°. d. None of the above, polarized light can't be rotated.

ANSWER: a POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 37.6 Polarization of Light Waves 43. If the polarizing angle for cubic zirconia (zirconium oxide) is 65.6°, what is the index of refraction of the material? a. 1.84 b. 2.00 c. 2.20 d. 2.43 e. 1.17 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 37.6 Polarization of Light Waves 44. You could determine the index of refraction for visible light of a dark but reflective medium such as black glass by measuring the a. angles of incidence and refraction. b. angle of reflection for an arbitrary angle of incidence. c. angle at which reflected light is completely polarized. d. smallest angle at which X-ray diffraction occurs in the glass. e. smallest angle at which diffraction occurs for visible light when a diffraction pattern is scratched onto the surface.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.6 Polarization of Light Waves 45. Scattered light in the atmosphere is often partially polarized. The best way to determine whether or not light from a particular direction in the sky shows polarization is to a. diffract the light through a single slit. b. squint while looking in that direction. c. rotate a piece of polaroid film about an axis parallel to the ray while looking through it in that sky direction. d. rotate a piece of polaroid film about an axis perpendicular to the ray while looking through it in that sky direction. e. reflect the rays from that direction on a shiny metal surface.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 37.6 Polarization of Light Waves 46. Jane's flashy boyfriend has just given her a ring with a huge "diamond". Jane, who has studied physics, measures the polarizing angle for the stone and finds that the polarizing angle is 62.97°. The stone is a. fluoride, n = 1.560. b. crown glass, n = 1.517. c. spinel, n = 1.712. d. zircon, n = 1.960. e. diamond, n = 2.417.

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ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 37.6 Polarization of Light Waves 47. Light strikes a flat water surface (n = 1.333) at the Brewster angle. Calculate the angle between the reflected and the refracted ray.

ANSWER: 90.00° POINTS: 2 DIFFICULTY: Average REFERENCES: 37.6 Polarization of Light Waves

1. A 1 000-kg automobile moving with a speed of 24 m/s relative to the road collides with a 500-kg automobile initially at rest. If the two stick together, what is the velocity in m/s of the two cars after the collision according to an observer in a truck moving 10 m/s in the same direction as the moving cars? a. 6 b. 11 c. 24 d. 26 e. 31 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 38.1 The Principle of Galilean Relativity 2. A 1 000-kg automobile moving with a speed of 24 m/s collides with a 500-kg car initially at rest. If the two stick together, what is the velocity (in m/s) of the two cars after the collision relative to an automobile moving in the same direction at 15 m/s? a. 14 b. 16 c. 24 d. 48 e. 1.0 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 38.1 The Principle of Galilean Relativity 3. A boat has an initial velocity of 2 m/s in the y direction on a stream which is moving in the x direction at 1 m/s. The 2 2 boat is accelerating in its direction of motion at 1 m/s . What is the acceleration of the boat (in m/s ) relative to the water? a.

1 b.

2 c.

3 + d.

3 −

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e.

1

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 38.1 The Principle of Galilean Relativity 4. Boat 1 goes directly across a stream a distance L and back taking a time t1. Boat 2 goes down stream a distance L and back taking a time t2. If both boats had the same speed relative to the water, which of the following statements is true? a. t2 > t1 b. t2 < t1 c. t2 = t1 d. t2 = 2t1 e. t2 = 0.5t1 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 38.1 The Principle of Galilean Relativity 5. As a spaceship heads directly to Earth at a velocity of 0.8c, it sends a radio signal to Earth. When those radio waves arrive on Earth, what is their velocity relative to Earth? a. 0.8c b. c c. 1.8c d. , where vE is the velocity of the Earth e. , where vE is the velocity of the Earth ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 38.3 Einstein’s Principle of Relativity 8

6. The speed of FM waves will be observed to be c = 2.9979 × 10 m/s when the antenna emitting the waves is a. at rest relative to the receiving antenna. b. moving to the right of the detecting antenna at 0.5c. c. moving to the left of the detecting antenna at 0.5c. d. moving as described in (a), (b) or (c) above. e. moving at 2.9979 × 108 m/s.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 38.3 Einstein’s Principle of Relativity

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7. A fancy sports car passes Big Ben at a speed of 0.600c. What time interval will the driver measure for a one-second interval on the large clock? a. 1.67 s b. 0.800 s c. 1.25 s d. 0.600 s e. 1.00 s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 8. A fancy sports car moves past an observer on a corner at a speed of 0.600c. When the observer indicates a one-second interval has passed, what time interval will be shown on the driver's watch? a. 1.67 s b. 0.800 s c. 1.25 s d. 0.600 s e. 1.00 s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 9. Two fireworks explode at the same position on the 4th of July. A stationary observer notices that the time interval between the two events was 5.00 seconds. A second observer flies past the fireworks at a speed of 0.600c. What value does she obtain when she measures the time interval between the two explosions? a. 8.33 s b. 6.25 s c. 4.00 s d. 3.00 s e. 5.00 s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 10. The half-life of a muon is 2.20 μs as measured in a stationary reference frame. What is the half-life of the muon (in μs) when it is moving with a speed of v = 0.800c? a. 8.13 b. 2.75 c. 3.67 d. 15.8 e. 1.32 ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 38.4 Consequences of the Special Theory of Relativity 11. The half-life of a muon is 2.2 μs. How fast is it moving relative to an observer who says its half-life is 4.4 μs? a. 0.87c b. 0.75c c. 0.97c d. 0.72c e. 0.50c ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 12. A 30-year-old woman takes a trip on a rocket, leaving her 20-year-old brother behind. She travels at a speed of 0.8c, and is gone 20 years, according to the younger brother. When she returns, how many years older/younger is she than her brother? a. 2 years younger b. 2 years older c. 3 years older d. 10 years older e. 8 years older ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 13. A jet plane travels around the world at 2 000 mi/hr (894 m/s). Two accurate atomic clocks measure the times of flight, one on board the plane and the second on Earth. If it takes 12 hours to complete the journey, what will the time difference (in μs) be? a. 0.75 b. 0.50 c. 0.25 d. 1.0 e. 0.19 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 14. A meterstick is shot from a meterstick projector at a speed of 0.90c. How long will it be relative to an observer's frame of reference? a. 2.3 m b. 0.91 m c. 1.0 m d. 0.44 m e. 0.81 m ANSWER: d Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 15. A starship navigator measures the distance between the Earth and the Sun. If the ship is moving at a speed of 0.90c, instead of obtaining 93 million miles, what distance does the navigator measure (in millions of miles)? a. 41 b. 30 c. 80 d. 215 e. 90 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 16. An astronaut traveling with a speed v = 0.90c holds a meterstick in his hand. If he measures its length, what value will he obtain? a. 1.0 m b. 2.3 m c. 0.19 m d. 0.43 m e. 0.81 m ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 38.4 Consequences of the Special Theory of Relativity 17. A spaceship from another galaxy passes over the solar system directly above a radial line from the Sun to the Earth.

11 (We measure that distance to be 1.5 × 10 m.) On Earth, the spaceship is observed to be traveling at a speed of 0.80c, for which γ = 5/3. As measured on Earth it takes the spaceship 625 seconds to travel from the Sun to Earth. A scientist in the spaceship measures the Earth-sun distance and the time it takes her to travel that distance. What results does she find? a. 9.0 × 1010 m; 375 s. b. 9.0 × 1010 m; 625 s. c. 1.5 × 1011 m; 625 s. d. 2.5 × 1011 m; 625 s. e. 2.5 × 1011 m; 1042 s.

ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 38.4 Consequences of the Special Theory of Relativity 18. Fireworks go off at the same time according to Earth clocks in two cities, Alum and Boron, that are 300 km apart. The people in a spaceship that is flying in a straight line from Alum to Boron at 0.80c also observe the fireworks. Do they see the fireworks in the two cities simultaneously? If the people in the spaceship say the fireworks were not simultaneous in Alum and Boron, how long before or after the fireworks flashed at Alum did the fireworks flash at Boron according to Copyright Cengage Learning. Powered by Cognero.

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their calculations? (The spaceship is directly over Alum when the fireworks flash.) a. Yes; 0 b. Before; 1.0 × 10-3 s c. After; 1.0 × 10-3 s d. Before; 1.3 × 10-3 s e. After; 1.3 × 10-3 s ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 38.4 Consequences of the Special Theory of Relativity 19. The first intergalactic spaceship is headed toward the Magellanic Clouds at a speed of 0.8c. The spaceship is 1 000 m long. Clocks at the front and the rear of the spaceship both read 3:00 P.M. Can it be 3:00 P.M. simultaneously at the front and the back of the spaceship? a.

No, because , where Δx is the length of the spaceship. b. No, because one clock has to move after being synchronized with the other. c. Yes, because Δx in (a) is zero for different points of the same spaceship. d. Yes, because two clocks at rest relative to each other can be synchronized by means of light signals when the distance between them is known. e. The question cannot be answered unless we know the object relative to which the spaceship's velocity is 0.8c.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 38.4 Consequences of the Special Theory of Relativity 4

20. Captain Jirk reports to headquarters that he left the planet Senesca 1.88 × 10 seconds earlier. Headquarters sends back the message: "Was that spaceship proper time?" It will be spaceship proper time if it was a. measured by one clock fixed at one spot on Senesca. b. measured by one clock fixed at one spot on the spaceship. c. measured by a clock on Senesca at departure and by a clock on the spaceship when reporting. d. measured by a clock on the spaceship when departing and by a clock on Senesca when reporting. e. calculated by dividing the distance from Senesca according to Senesca by the speed of the spaceship.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 38.4 Consequences of the Special Theory of Relativity 21. In a classroom on the first spaceship to an extrasolar planet--there are children because the trip will take 200 years--a teacher is showing charge Q uniformly distributed along a conducting rod of length L0 to produce linear charge density λ0. What is the linear charge density as observed on Pluto when the spaceship passes it at 0.800c? a. 0.360 λ0 b. 0.600 λ0 c. 0.800 λ0 Copyright Cengage Learning. Powered by Cognero.

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d. 1.00 λ0 e. 1.67 λ0 ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 38.4 Consequences of the Special Theory of Relativity 22. A spaceship leaves Earth and maintains a constant force by means of a nuclear engine. As the speed of the spaceship increases, an observer on Earth finds that relative to her the magnitude of the spaceship's acceleration is a. 0. b. decreasing. c. constant. d. increasing. e. proportional to the kinetic energy of the spaceship.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 38.4 Consequences of the Special Theory of Relativity 23. The 500-m-long spaceship Springbrake is at rest on the planet Hitest for refueling. Another spaceship, Summerbrake, passes parallel to Springbrake at 0.600c. The crew on Springbrake measure the length of Summerbrake as it passes and find that the length they measure is exactly the same as the known 500-m rest length of Springbrake. If Summerbrake were at rest next to Springbrake, what would its length then be measured to be? a. 180 m b. 320 m c. 500 m d. 625 m e. 781 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 24. Clovis wants to lose weight. Clotilde tells him that he will be thin enough for her if he travels past her at 0.600 c. If the distance she sees from the front of his stomach to his back is then 24.0 cm, what distance in cm does she see when he is standing still? a. 15.4 b. 19.2 c. 24.0 d. 30.0 e. 37.5 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 25. Captain Ray, on the Galactic Explorer, sets off bright signal lights at the two ends of his spaceship so that they are Copyright Cengage Learning. Powered by Cognero.

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seen as flashing simultaneously by General Kay, who is watch the ship go by. General Kay concludes that she was next to the midpoint of the ship at the instant when the lights flashed in her reference frame. This can only happen if Captain Ray, at the center of the Galactic Explorer, a. sees the lights flash simultaneously in his coordinate system. b. sees the bow (front) light flash before the aft (rear) light. c. sees the aft (rear) light flash before the bow (front) light. d. can calculate that the light flashes reach General Kay so that the flash from the bow light reaches her before the flash from the aft light. e. can calculate that the light flashes reach General Kay so that the flash from the aft light reaches her before the flash from the bow light.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 26. When at rest, a spacecraft has the same height as length. When moving at relativistic speeds in the direction of its length, which one of the following describes its length and height to an observer at rest? a. Its length is decreased and its height is increased. b. Its length is decreased and its height is decreased. c. Its length is decreased and its height is unchanged. d. Its length is unchanged and its height is increased. e. Its length is increased and its height is decreased.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 38.4 Consequences of the Special Theory of Relativity 27. The period of a pendulum is 2.0 s in a stationary inertial frame of reference. What is its period when measured by an observer moving at a speed of 0.60c with respect to the inertial frame of reference?

ANSWER: 2.5 s POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 28. A supertrain (rest-length = 100 m) travels at a speed of 0.950c as it passes through a tunnel (rest-length 50.0 m). As seen by a trackside observer, is the train ever completely within the tunnel? If so, by how much?

ANSWER: yes, by 18.8 meters POINTS: 2 DIFFICULTY: Average REFERENCES: 38.4 Consequences of the Special Theory of Relativity 29. A spaceship moves at a speed of 0.95c away from the Earth. It shoots a star wars torpedo toward the Earth at a speed of 0.90c relative to the ship. What is the velocity of the torpedo relative to the Earth? (The direction in which the spaceship moves is the positive direction.) a. −0.34c b. 0.34c c. 0.060c d. −0.060c Copyright Cengage Learning. Powered by Cognero.

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e. 0 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 38.6 The Lorentz Velocity Transformation Equations 30. A satellite moves east, taken as the positive x axis direction, at a speed of 0.5c and a spaceship moves toward it (to the west) at a speed of 0.8c as measured by an observer on the Earth. What is the speed of the satellite as measured by an observer in the spaceship? a. 8.7c b. 0.21c c. −0.21c d. 0.93c e. −0.93c ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 38.6 The Lorentz Velocity Transformation Equations 31. A spaceship moving past the Earth with a speed of 0.800c signals to the Earth with pulsed laser photons emitted at 10.0-second intervals according to the spaceship's clock. What is the time interval between pulses as measured by observers on Earth who see the flashes? a. 13.4 s b. 16.7 s c. 12.5 s d. 9.70 s e. 6.03 s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 38.6 The Lorentz Velocity Transformation Equations 32. Which of the following quantities does not change in magnitude from that observed in system S when observed in system S' moving away from system S at speed v? a. m b. m c. (γ − 1)mc2 d. E2 − p2c2 e. x2 + y2 + z2 ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 38.6 The Lorentz Velocity Transformation Equations 33. Two spaceships traveling in opposite directions along parallel lines measure their own and the other spaceship's length while passing one another. The crew on spaceship A says that their ship is 1000 m long and that ship B is 800 m long. The Copyright Cengage Learning. Powered by Cognero.

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crew on ship B says that their ship is 1000 m long and that ship A is 800 m long. At what speed does each crew say that the other ship is traveling relative to their own ship? a. 0.36 c b. 0.60 c c. 0.64 c d. 0.80 c e. 1.25 c ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 38.6 The Lorentz Velocity Transformation Equations 34. Lydia proposes to send an interstellar probe off in stages. The first stage, traveling radially outward at 0.500c relative to Earth, will send off a second stage traveling in the same direction as the first stage at a speed of 0.500c relative to the first stage. Finally, the second stage will send off a third stage traveling in the same direction at 0.500c relative to the second stage. Relative to Earth, what will be the speed of the third stage? a. 0.500c b. 0.800c c. 0.929c d. 0.972c e. 1.500c ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 38.6 The Lorentz Velocity Transformation Equations -31

35. An electron (m = 9.1 × 10 kg) has a speed of 0.90c. What is the difference between its relativistic momentum and its non-relativistic momentum (in kg m/s)? a. 4.3 × 10-22 b. 3.2 × 10-22 c. 5.4 × 10-22 d. 6.5 × 10-22 e. 2.5 × 10-22 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 38.7 Relativistic Linear Momentum 36. A proton's rest mass is 1.67 × 10 a. 1.5 × 10-10 J

-27

kg. Calculate its total energy when it is accelerated to a speed of 0.80c.

b. 1.0 × 10-10 J c. 2.5 × 10-10 J d. 2.0 × 10-10 J e. 7.5 × 10-10 J Copyright Cengage Learning. Powered by Cognero.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 38.7 Relativistic Linear Momentum 37. Hanna, at rest in her spaceship which is moving past Earth at 0.800c, observes a neutron (mass mn) at rest relative to her spaceship decay into a proton, an electron, and a neutrino. She notes that the total momentum, , of the decay products is zero after the decay. According to an observer on Earth, what is the magnitude of the total momentum of the decay products, ? a. 0 b. 0.600mn(0.800c) c. 0.800mn(0.800c) d. 1.00mn(0.800c) e. 1.67mn(0.800c) ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 38.7 Relativistic Linear Momentum 38. Find the momentum and speed of a proton whose kinetic energy equals its rest energy. (The mass of a proton is 938.3 2 MeV/c .)

ANSWER: 1625 MeV/c, 0.866 0c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 38.7 Relativistic Linear Momentum -31

39. An electron (m = 9.11 × 10 kg) has a speed of 0.50c. Determine the difference between its relativistic kinetic energy and the kinetic energy calculated without considering relativity. a. 3.0 × 10-15 J b. 2.0 × 10-15 J c. 1.5 × 10-15 J d. 2.4 × 10-15 J e. 1.8 × 10-15 J ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 38.8 Relativistic Energy 40. An electron has a kinetic energy that is twice its rest energy. Determine its speed. a. 0.76c b. 0.81c c. 0.94c d. 0.54c Copyright Cengage Learning. Powered by Cognero.

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e. 0.87c ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 38.8 Relativistic Energy 41. A proton's rest mass is 1.67 × 10 a. 1.0 × 10-10 J

-27

kg. Calculate its kinetic energy when it is accelerated to a speed of 0.80c.

b. 1.5 × 10-10 J c. −2.0 × 10-10 J d. 2.5 × 10-10 J e. 7.5 × 10-10 J ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 38.8 Relativistic Energy 42. Energy is released during a nuclear reaction due to a conversion between mass and energy. Mass is not conserved. The initial and final amounts are different. If a total of 1.0 gram of mass is "missing", how much energy has been released? a. 9.0 × 1011 J b. 9.0 × 1017 J c. 9.0 × 1015 J d. 9.0 × 1013 J e. 9.0 × 1016 J ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 38.8 Relativistic Energy 43. Assume a gram of a substance marketed as "Pure Energy" is annihilated by a gram of a second substance "Anti-Pure 9 Energy." How long would the energy released power a city which uses 10 watts of power? a. 40 hrs b. 25 hrs c. 50 hrs d. 65 hrs e. 50 000 hrs ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 38.8 Relativistic Energy -10

44. A proton has a total energy of 2.5 × 10 a. 0.90c Copyright Cengage Learning. Powered by Cognero.

-27

J. How fast is it moving? (M = 1.67 × 10

kg)

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b. 0.80c c. 0.70c d. 0.60c e. 0.40c ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 38.8 Relativistic Energy 45. In a color television tube, electrons are accelerated through a potential difference of 20 000 volts. With what velocity do the electrons strike the screen?

ANSWER: v = 0.27c POINTS: 2 DIFFICULTY: Average REFERENCES: 38.8 Relativistic Energy 46. When 1.0 gram of hydrogen combines with 8.0 grams of oxygen, 9.0 grams of water is formed. But is this true?

5 During the reaction 2.86 × 10 J of energy is released. How much mass is actually lost in this reaction?

-12 ANSWER: 3.18 × 10 kg POINTS: 2 DIFFICULTY: Average REFERENCES: 38.8 Relativistic Energy

1. Your temperature is 98.6°F. Assuming your skin is a perfect radiator (ε = 1), determine the wavelength corresponding to the largest intensity (in μm). a. 8.0 b. 9.3 c. 3.0 d. 5.7 e. 29.4 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 39.1 Blackbody Radiation and Planck’s Hypothesis 2. How much energy is in a 63-kHz photon of AM radiation? a. 1.0 × 10-38 J b. 6.6 × 10-30 J c. 4.2 × 10-29 J d. 3.1 × 10-30 J e. 13 × 10-29 J ANSWER: c POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 39.1 Blackbody Radiation and Planck’s Hypothesis 3. How much energy is in an 89.7-MHz photon of FM radiation? a. 2.2 × 10-33 J b. 9.5 × 10-27 J c. 7.4 × 10-42 J d. 5.9 × 10-26 J e. 3.7 × 10-25 J ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 39.1 Blackbody Radiation and Planck’s Hypothesis 4. The threshold wavelength for photoelectric emission of a particular substance is 500 nm. What is the work function (in eV)? a. 4.2 b. 4.0 × 10-19 c. 4.0 × 10-10 d. 2.5 × 10-19 e. 2.5 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 5. What is the maximum velocity (in km/s) of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm? a. 460 b. 650 c. 420 d. 550 e. 1 480 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 6. A stopping potential of 3.2 V is needed for radiation whose wavelength is 200 nm. What is the work function (in eV) of the material? a. 4.0 b. 3.0 c. 5.0 d. 6.0 e. 2.0 ANSWER: b Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 7. What is the maximum kinetic energy (in eV) of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm? a. 1.9 b. 1.2 c. 3.1 d. zero e. 6.2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 8. What is the maximum kinetic energy (in eV) of a photoelectron when a surface, whose work function is 5.0 eV, is illuminated by photons whose wavelength is 400 nm? a. 3.1 b. −1.9 c. 1.9 d. 0 e. 1.2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 9. The light intensity incident on a metallic surface produces photoelectrons with a maximum kinetic energy of 2 eV. The light intensity is doubled. Determine the maximum kinetic energy of the photoelectrons (in eV). a. 4 b. 2 c. d. 3 e. 16 ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 39.2 The Photoelectric Effect 10. The light intensity incident on a metallic surface with a work function of 3 eV produces photoelectrons with a maximum kinetic energy of 2 eV. The frequency of the light is doubled. Determine the maximum kinetic energy (in eV). a. 3 b. 2 c. d. 4 Copyright Cengage Learning. Powered by Cognero.

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e. 7 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 11. Assume electrons are accelerated through a potential difference of 25 000 V inside a TV picture tube. What is the −10 minimum wavelength that could be produced when the electrons strike the phosphor? (1 Å = 10 m) a. 0.50 Å b. 1.0 Å c. 10 Å d. 100 Å e. 0.25 Å ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 12. A solid-state pulsed laser has an energy of 400 mJ per pulse. If its wavelength is 1.06 × 10 are in each pulse? a. 2 × 1025

−6

m, how many photons

b. 2 × 1021 c. 3 × 1018 d. 6 × 1038 e. 2 × 1018 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect -7

13. A helium-neon laser emits red light having a wavelength of 6.4 × 10 m and a power of 0.5 mW. How many photons are emitted each second? a. 6.4 × 1038 b. 1.6 × 1021 c. 3.2 × 1025 d. 2.6 × 1018 e. 1.6 × 1015 ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 14. In an experiment different wavelengths of light, all able to eject photoelectrons, shine on a freshly prepared (oxidefree) zinc surface. Which statement is true?

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a. The number of photoelectrons emitted per second is independent of the intensity of the light for all the different wavelengths. b. The number of photoelectrons emitted per second is directly proportional to the frequency for all the different wavelengths. c. The maximum kinetic energy of the photoelectrons emitted is directly proportional to the frequency for each wavelength present. d. The maximum kinetic energy of the photoelectrons has a linear relationship with the frequency for each wavelength present. e. The maximum kinetic energy of the photoelectrons is proportional to the intensity of the light and independent of the frequency.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 39.2 The Photoelectric Effect 15. The number of photons per second passing a plane perpendicular to a collimated monochromatic (one frequency) beam of light transporting power P is directly proportional to a. the wavelength of the light. b. the frequency of the light. c. the power of the beam. d. all of the above. e. only (a) and (c) above.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 16. Photoelectrons are ejected when monochromatic light shines on a freshly-prepared (oxide-free) sodium surface. In order to obtain the maximum increase in the number of electrons ejected per second, the experimenter needs to a. increase the frequency of the light. b. increase the intensity of the light. c. increase the area illuminated by the light. d. do all of the above. e. do only (b) and (c) above.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 17. The experimental observation(s) below that require(s) a quantum explanation for the photoelectric effect a. is that more photoelectrons are emitted when the light frequency increases. b. is that the maximum kinetic energy of the photoelectrons is related linearly to the frequency of the light. c. is that every metal surface has a work function, a minimum amount of energy needed to free electrons. d. is that the stopping potential measures the kinetic energy of the photoelectrons. e. are all of the above.

ANSWER: b POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 18. If a rubidium surface is irradiated with blue light of wavelength 450.0 nm, what is the kinetic energy of the electrons emitted? (The work function for rubidium is υ = 2.09 eV.) ANSWER: 0.67 eV POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 19. What is the shortest x-ray wavelength that can be produced in a 12-keV x-ray machine?

ANSWER: POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 20. What is the energy in eV of a photon of yellow light? λ = 500 nm.

ANSWER: 2.48 eV POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect 2

21. On a bright and sunny day, the intensity of solar radiation on the Earth's surface is 1 000 W/m . If the average wavelength of the sunlight is 500 nm, how many photons are incident on a square meter of the Earth's surface per second?

21 ANSWER: 2.51 × 10 photons/s POINTS: 2 DIFFICULTY: Average REFERENCES: 39.2 The Photoelectric Effect -15

22. A photon whose energy is 8.00 × 10 scattered wave? a. 2.73 × 10-11 m

J is scattered off an electron at a 90° angle. What is the wavelength of the

b. 2.25 × 10-11 m c. 2.50 × 10-11 m d. 2.40 × 10-12 m e. 2.48 × 10-11 m ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 39.3 The Compton Effect -11

23. A photon whose wavelength is 5.0 × 10 wave? a. 5.0 × 10-11 m Copyright Cengage Learning. Powered by Cognero.

m is scattered straight backward. What is the wavelength of the scattered

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b. 4.5 × 10-11 m c. 5.5 × 10-11 m d. 6.0 × 10-11 m e. 6.5 × 10-11 m ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 39.3 The Compton Effect 24. A photon collides with an electron. After the collision, the wavelength of the scattered wave at a scattering angle greater than is a. greater than or equal to the initial wavelength. b. equal to the initial wavelength. c. less than or equal to the initial wavelength. d. greater than the initial wavelength. e. less or greater depending on the scattering angle.

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 39.3 The Compton Effect 25. When a photon collides with a free electron at rest and the direction of motion of the photon changes, a. the magnitude of the momentum of the photon does not change. b. the momentum of the electron does not change. c. the kinetic energy of the electron does not change. d. the total energy of the photon does not change. e. both the magnitude of the momentum and the total energy of the photon decrease.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 39.3 The Compton Effect 26. A neutron has a mass of 1.67 × 10 (in m/s)? a. 3.4 × 103

-27

kg. The de Broglie wavelength is 1.4 × 10

-10

m. How fast is the neutron going

b. 2.8 × 103 c. 3.9 × 103 d. 2.6 × 103 e. 1.7 × 103 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 39.5 The Wave Properties of Particles Copyright Cengage Learning. Powered by Cognero.

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-27

-10

-27

-10

27. A neutron has a mass of 1.67 × 10 kg. Its de Broglie wavelength is 1.4 × 10 eV)? a. 4 b. 0.4 c. 0.04 d. 40 e. 0.08 ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 39.5 The Wave Properties of Particles

m. What is its kinetic energy (in

28. A neutron has a mass of 1.67 × 10 kg. Its de Broglie wavelength is 1.4 × 10 m. What temperature would it correspond to if we had a monatomic gas having the same average kinetic energy (in °C)? a. 273 b. 25 c. 36 d. 309 e. 51 ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 39.5 The Wave Properties of Particles 29. An electron is accelerated through a potential difference of 25 000 V. What is the de Broglie wavelength of the electron (in m)? a. 5.9 × 10-12 b. 6.8 × 10-12 c. 6.5 × 10-12 d. 7.8 × 10-12 e. 5.5 × 10-12 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 39.5 The Wave Properties of Particles 30. Microscopes are inherently limited by the wavelength of the light used. How much smaller (in order of magnitude) can we "see" using an electron microscope whose electrons have been accelerated through a potential difference of 50 000 V than using red light (500 nm)? a. 3 b. 4 c. 5 d. 6 e. 14 ANSWER: c Copyright Cengage Learning. Powered by Cognero.

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POINTS: 3 DIFFICULTY: Challenging REFERENCES: 39.5 The Wave Properties of Particles 31. What is the approximate wavelength of a 45-kg teenager moving at 5 m/s on a skateboard? a. 5 × 10-37 m b. 3 × 10-36 m c. 7 × 10-34 m d. 0.1 m e. 5 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 39.5 The Wave Properties of Particles

32. A pendulum located where

has a 0.500-kg bob and a 4.00-Hz oscillation frequency. If it is released

from a point 0.150 m above the lowest point it reaches, how many quanta make up the energy of this oscillation? a. 2.77 × 1032 b. 1.11 × 1033 c. 4.87 × 10-34 d. 0.184 e. 4.00 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 39.5 The Wave Properties of Particles 33. A quantum particle a. can be localized in space. b. can be represented by an infinitely long wave having a single frequency. c. can be represented by a wave packet. d. travels at the phase speed of the infinitely long wave having the highest frequency. e. has the highest probability of being present in those regions of space where its component waves interfere destructively.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 39.6 A New Model: The Quantum Particle 34. A wave packet can represent a quantum particle because a. it has the localized nature of a particle. b. the group velocity is identical to the speed of the particle. c. the waves that compose the packet can show interference and diffraction.

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d. of all of the above. e. of only (a) and (b) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 39.6 A New Model: The Quantum Particle 35. Film behind a double slit is exposed to light in the following way: First one slit is opened and light is allowed to go through that slit for time Δt. Then it is closed and the other slit is opened and light is allowed to go through that slit for the same time Δt. When the film is developed the pattern will be a. one single slit pattern. b. two superimposed single slit patterns, their centers displaced from each other by the distance between the two slits. c. one double slit pattern. d. two double slit patterns, their centers displaced from each other by the distance between the two slits. e. random darkening of the film. (no pattern at all) ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 39.7 The Double-Slit Experiment Revisited 36. In electron diffraction, an electron moving at speed v << c acts like a. a particle with momentum mv. b. a particle with position coordinate v/t. c. a wave with wavelength v/t. d. a wave with wavelength h/mv. e. both a particle with position coordinate v/t and a wave with wavelength v/t.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 39.7 The Double-Slit Experiment Revisited 37. Find the uncertainty in the momentum (in kg ⋅ m/s) of an electron if the uncertainty in its position is equal to 3.4 × −10 10 m, the circumference of the first Bohr orbit. a. 6.2 × 10-25 b. 1.6 × 10-25 c. 15.5 × 10-25 d. 19.4 × 10-25 e. 2.0 × 10-24 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 39.8 The Uncertainty Principle 38. Because the factor h on the right side of Heisenberg's uncertainty principle has units of joule-seconds, it suggests that Copyright Cengage Learning. Powered by Cognero.

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the energy of a system also has uncertainty. The uncertainty in energy depends on the length of the time interval during which a system exists. ΔEΔt ≥ h/4π. Suppose an unstable mass is produced during a high-energy collision such that the -31 uncertainty in its mass is me/100 (me = 9.11 × 10 kg). How long will this particle exist? a. 6.4 × 10-20 s b. 2.3 × 10-23 s c. 1.0 × 1015 s d. 1.2 × 1013 s e. 8.1 × 10-19 s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 39.8 The Uncertainty Principle 39. Assume we can determine the position of a particle within an uncertainty of 0.5 nm. What will be the resulting uncertainty in the particle's momentum (in kg ⋅ m/s)? a. 1.9 × 10-25 b. 4.2 × 10-25 c. 1.1 × 10-25 d. 1.3 × 10-24 e. 6.6 × 10-25 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 39.8 The Uncertainty Principle 6

40. How accurate can the position of an electron be made if its speed is 5 × 10 m/s and if the uncertainty in its energy is 10 eV? a. 7.7 × 10-18 m b. 1.3 × 10-23 m c. 6.2 × 10-15 m d. 1.6 × 10-10 m e. 1.2 × 10-9 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 39.8 The Uncertainty Principle 41. An electron has been accelerated by a potential difference of 100 V. If its position is known to have an uncertainty of 1 nm, what is the percent uncertainty

of the electron?

a. 1% b. 2% c. 10% Copyright Cengage Learning. Powered by Cognero.

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d. >>10% e. 5% ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 39.8 The Uncertainty Principle 42. A baseball (1 kg) has an energy of 100 joules. If its uncertainty in position is 1 m, what is the percentage uncertainty in the momentum of the baseball? a. <<1% b. 1% c. 2% d. 5% e. 10% ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 39.8 The Uncertainty Principle -31

43. If the position of an electron (m = 9.11 × 10 approximate minimum uncertainty in its speed? a. 6 × 10-34 m/s

-30

kg) could be measured to within 10

m, what would be the

b. 6 × 1025 m/s c. 6 × 1030 m/s d. 1031 m/s e. 1061 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 39.8 The Uncertainty Principle 44. Because of Heisenberg's uncertainty principle, the velocity of a particle is known least precisely when the length of the wave packet representing the particle is a. < 10-15 m. b. < 10-10 m. c. of the order of 1.00 m. d. >10 m. e. the length of a plane wave (infinite) ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 39.8 The Uncertainty Principle Copyright Cengage Learning. Powered by Cognero.

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45. An atomic level has a lifetime, τ, of a.

. What is the line width,

, of this level?

b. c. d. e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 39.8 The Uncertainty Principle 46. The "seeing ability" or resolution of radiation is determined by its wavelength. If an atom is approximately 10 diameter, how fast must an electron travel to have a wavelength smaller than the size of an atom?

6 ANSWER: 7.3 × 10 m/s

-10

m in

POINTS: 2 DIFFICULTY: Average REFERENCES: 39.8 The Uncertainty Principle 47. An electron is sitting on a pinpoint having a diameter of 2.5 μm. What is the minimum uncertainty in the speed of the electron?

ANSWER: 23 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 39.8 The Uncertainty Principle 48. Suppose we use optical radiation (λ = 500 nm) to determine the position of the electron to within the wavelength of the light. What will be the resulting uncertainty in the electron's velocity?

ANSWER: 116 m/s POINTS: 2 DIFFICULTY: Average REFERENCES: 39.8 The Uncertainty Principle

1. The fact that we can only calculate probabilities for values of physical quantities in quantum measurements means that a. radiation and matter are not described by mathematical relations between measurements. b. the probabilities cannot be calculated from mathematical relationships. c. the results of physical measurements bear no relationship to theory. d. the average values of a large number of measurements correspond to the calculated probabilities. e. the average of the values calculated in a large number of different theories corresponds to the results of a measurement.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.1 The Wave Function Copyright Cengage Learning. Powered by Cognero.

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2. When the potential energy of a system is independent of time, the wave function of the system a. is a constant. b. is directly proportional to the time. c. cannot be normalized. d. depends only on the center of mass, , of the system. e. depends on the vector positions, i, of each particle in the system.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.1 The Wave Function 3. Which of the following gives < x >, the average position, or expectation value, of a particle whose wave function Ψ(x) depends only on the value of x? a. . b. . c. . d. . e. .

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.1 The Wave Function 4. Which of the following gives the expectation value < f(x) > of a function f(x) of x when the wave function ψ(x)depends only on x? a. . b. . c. . d. .

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e. .

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.1 The Wave Function 5. The graph below represents a wave function ψ(x) for a particle confined to −2.00 m ≤ x ≤ +2.00 m. The value of the normalization constant A may be

a. . b. . c. . d. . e. either

or

.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 40.1 The Wave Function 6. The graph below represents a wave function ψ(x) for a particle confined to −2.00 m ≤ x ≤ +2.00 m. The value of the normalization constant A may be

a. . b. . c. .

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d. . e. either

or

.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 40.1 The Wave Function 7. The graph below represents a wave function ψ(x) for a particle confined to −4.00 m ≤ x ≤ +4.00 m. What is the magnitude of the normalization constant A?

a. b.

c. d. e. 4 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 40.1 The Wave Function 2

8. The graph below shows the value of the probability density |ψ(x)| in the region −3.00 m ≤ x ≤ +3.00 m. What is the value of the constant A?

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a. b.

c.

d. e. either

or

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 40.1 The Wave Function 9. The wave function ψ(x) of a particle confined to 0 ≤ x ≤ L is given by ψ(x) = Ax. ψ(x) = 0 for x < 0 and x > L. When the wave function is normalized, which of the following gives the probability density at coordinate x? a. . b. . c. . d. . e. .

ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 40.1 The Wave Function 10. A 15-kg mass, attached to a massless spring whose force constant is 2 500 N/m, has an amplitude of 4 cm. Assuming the energy is quantized, find the quantum number of the system, n, if En = nhf. a. 1.5 × 1033 b. 3.0 × 1033 c. 4.5 × 1033 d. 5.4 × 1033 e. 1.0 × 1033 Copyright Cengage Learning. Powered by Cognero.

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ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 11. Find the kinetic energy (in terms of Planck's constant) of a baseball (m = 1 kg) confined to a one-dimensional box that is 25 cm wide if the baseball can be treated as a wave in the ground state. a. 3 h2 b. 2 h2 c. h2 d. 4h2 e. 0.5 h2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 12. Calculate the ground state energy (in eV) for an electron in a box (an infinite well) having a width of 0.050 nm. a. 10 b. 75 c. 24 d. 150 e. 54 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 13. A particle is in the ground state of a one-dimensional box of length 1.0 m. What is the minimum value of its momentum (in kg ⋅ m/s)? a. 9.9 × 10-34 b. 6.6 × 10-34 c. 3.3 × 10-34 d. 13 × 10-34 e. cannot be solved unless mass of particle is known.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 14. A particle is in the first excited state of a one-dimensional box of length 1.0 m. What is the minimum value of its momentum (in kg ⋅ m/s)? a. 3.3 × 10-34 b. 6.6 × 10-34 Copyright Cengage Learning. Powered by Cognero.

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c. 9.9 × 10-34 d. 13 × 10-34 e. 22 × 10-34 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 15. A particle is in the second excited state of a one-dimensional box of length 1.0 m. What is its momentum (in kg ⋅ m/s)? a. 6.6 × 10-34 b. 3.3 × 10-34 c. 9.9 × 10-34 d. 13 × 10-34 e. cannot be solved unless mass of particle is known ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 16. What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L? a. 1 b. 4 c. 2 d. 8 e. 16 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 17. What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its energy 2 2 is 2 h /mL ? a. 2 b. 8 c. 4 d. 1 e. 16 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 18. The wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by Ψ(x) = Copyright Cengage Learning. Powered by Cognero.

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A sin (nπx/L) + B cos (nπx/L) . The constants A and B are determined to be a. , 0. b. , . c.

0, . d. , . e. 2/L, 0.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions

19. The wave function for a particle in a one-dimensional box is

. Which statement is correct?

a. This wavefunction gives the probability of finding the particle at x. b. |Ψ(x)|2 gives the probability of finding the particle at x. c. |Ψ(x)|2 Δx gives the probability of finding the particle between x and x + Δx. d. gives the probability of finding the particle at a particular value of x. e. gives the probability of finding the particle between x and x + Δx.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 20. If the interaction of a particle with its environment restricts the particle to a finite region of space, the result is the quantization of ____ of the particle. a. the momentum b. the energy c. the velocity d. all of the above properties e. only properties (a) and (b) ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 21. A particle is restricted to the region 0 < x < L where U(x) = 0, and U(x) is infinitely large elsewhere. Which of the following gives the form of the particle’s wave function ψ(x) in the region 0 < x < L? a. .

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b. . c. Aenπx / L. d. . e. .

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 22. Frank says that quantum mechanics does not apply to baseballs because they do not jump from quantum state to quantum state when being thrown. Francine agrees with him. She says that there is no uncertainty in a baseball's position or momentum. Are they correct, or not, and why? a. They are correct because the first excited state of a baseball is at a higher energy that any baseball ever receives. Therefore we cannot determine whether or not there is uncertainty in its position or momentum. b. They are correct because the first excited state of a baseball is at a higher energy that any baseball ever receives. Therefore its position and momentum are completely uncertain until it is caught. c. They are wrong because the baseball goes through so many quantum states in being thrown that we cannot observe the transitions. The uncertainties in its position and momentum are too small to observe. d. They are wrong because the baseball goes through so many quantum states in being thrown that we cannot observe the transitions. Because of the number of transitions its position and momentum are completely uncertain until it is caught. e. Quantum mechanics states that they are correct as long as they do not make any observations, but wrong as soon as they begin to make observations.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 23. The wave function for a particle in a box of length L is given by

. If the box extends from x = 0

to x = L, at which of the following positions is the highest probability for finding the particle? a. x = 0.33 L b. x = 0.04 L c. x = 0.60 L d. Both (a) and (b). e. Both (b) and (c).

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions

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24. The wave function for a particle in a box of length L is given by

. If the box extends from x = 0

to x = L, What is the probability of finding the particle between x = 0.60 L and x = 0.70 L? a. 0.10 b. 0.20 c. 0.25 d. 0.05 e. The probability is not given.

ANSWER: a POINTS: 3 DIFFICULTY: Challenging REFERENCES: 40.2 Analysis Model: Quantum Particle Under Boundary Conditions 25. A physically reasonable wave function, ψ(x), for a one-dimensional system must a. be defined at all points in space. b. be continuous at all points in space. c. be single-valued. d. obey all the constraints listed above. e. obey only (b) and (c) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.3 The Schrödinger Equation 26. A particle in a finite potential well has energy E, as shown below.

Which of the following gives the form of the wave function ψI in region I where x < 0? a. αe−κx b. βeκx c. A sin kx d. B cos kx e. A sin kx + B cos kx ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.4 A Particle in a Well of Finite Height 27. A particle in a finite potential well has energy E, as shown below.

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Which of the following gives the form of the wave function ψII in region II where 0 < x < L? a. αe−κx b. βeκx c. A sin kx d. B cos kx e. A sin kx + B cos kx ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.4 A Particle in a Well of Finite Height 28. A particle in a finite potential well has energy E, as shown below.

Which of the following gives the form of the wave function ψIII in region III where x > L? a. αe−κx b. βeκx c. A sin kx d. B cos kx e. A sin kx + B cos kx ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.4 A Particle in a Well of Finite Height 29. Classically, the concept of "tunneling" is impossible. Why? a. The kinetic energy of the particle would be negative. b. The velocity of the particle would be negative. c. The total energy of a particle is equal to the kinetic and potential energies. d. The kinetic energy must be equal to the potential energy. e. The total energy for the particle would be negative.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.5 Tunneling Through a Potential Energy Barrier Copyright Cengage Learning. Powered by Cognero.

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30. When a particle approaching a potential energy barrier has a total energy that is greater than the potential energy barrier, what is the probability that the particle will be reflected? a. P < 0 b. P = 0 c. P = 1 d. P > 0 e. P = ∞ ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.5 Tunneling Through a Potential Energy Barrier 31. A particle has a total energy that is less than that of a potential energy barrier. When the particle penetrates the barrier, its wave function is a. a positive constant. b. exponentially increasing. c. oscillatory. d. exponentially decreasing. e. none of the above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.5 Tunneling Through a Potential Energy Barrier 32. Quantum tunneling occurs in a. nuclear fusion. b. radioactive decay by emission of alpha particles. c. the scanning tunneling microscope. d. all of the above. e. only (b) and (c) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 40.5 Tunneling Through a Potential Energy Barrier 33. Which of the following gives the ground state energy E of a harmonic oscillator with angular frequency ω? a. b. c. d. E = 0 e.

ANSWER: b POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 40.7 The Simple Harmonic Oscillator

1. An energy of 13.6 eV is needed to ionize an electron from the ground state of a hydrogen atom. Selecting the longest wavelength that will work from the those given below, what wavelength is needed if a photon accomplishes this task? a. 60 nm b. 80 nm c. 70 nm d. 90 nm e. 40 nm ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 41.1 Atomic Spectra of Gases 7

-1

2. What value of wavelength is associated with the Lyman series for n = 2? (R = 1.097 × 10 m ) a. 8.2 × 106 m b. 1.2 × 10-7 m c. 2.7 × 106 m d. 3.6 × 10-7 m e. 8.8 × 10-7 m ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 41.1 Atomic Spectra of Gases 7 -1 3. What wavelength (in μm) is associated with the Paschen series for n = 4? (R = 1.097 × 10 m ) a. 320 b. 530 c. 2.7 d. 1.9 e. 0.5 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 41.1 Atomic Spectra of Gases

4. Rutherford's experiment, in which he fired alpha particles of 7.7-MeV kinetic energy at a thin gold foil, showed that nuclei were very much smaller than the size of an atom because a. some alpha particles passed through the foil undeflected. b. some alpha particles were deflected backwards. c. some alpha particles were captured by the gold nuclei. d. the alpha particles could not get closer than 10−10 m to the gold nuclei. e. the alpha particles split into deuterium nuclei when they encountered the gold nuclei.

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ANSWER: b POINTS: 2 DIFFICULTY: Easy REFERENCES: 41.2 Early Models of the Atom 5. Light is emitted by hydrogen atoms in the visible range for a hydrogen atom. Its wavelength is 656 nm. What value of n 7 -1 is associated with the light? (R = 1.097 × 10 m ) a. 5 b. 2 c. 4 d. 3 e. 6 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 6. An electron in a hydrogen atom makes a transition from the n = 4 to the n = 3 energy state. Determine the energy (in eV) of the emitted photon. a. 0.54 b. 0.66 c. 0.85 d. 1.51 e. 10.2 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 7. An electron in a hydrogen atom makes a transition from the n = 3 to the n = 1 energy state. Determine the wavelength of the emitted photon (in nm). a. 1006 b. 209 c. 306 d. 103 e. 821 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 8. A hydrogen atom is in its first excited state (n = 2). What is the linear momentum of the electron (in kg ⋅ m/s)? a. 3 × 10-24 b. 2 × 10-24 c. 1 × 10-24 Copyright Cengage Learning. Powered by Cognero.

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d. 4 × 10-24 e. 3 × 10−15 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 9. How fast is the electron moving in the first Bohr orbit? a. 3.3 × 106 m/s b. 2.2 × 106 m/s c. 4.4 × 106 m/s d. 5.5 × 106 m/s e. 5.5 × 1015 m/s ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 6

10. An electron is moving at a speed of 2.1 × 10 m/s in the first Bohr orbit. Determine its de Broglie wavelength. a. 0.30 × 10-10 m b. 1.7 × 10-10 m c. 0.50 × 10-10 m d. 3.5 × 10-10 m e. 1.5 × 10-10 m ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 11. Suppose Bohr had chosen the potential energy of the electron in the hydrogen atom to be V = 0 when the electron is in the orbit with n = 1. He could do this by a. choosing n = 1 for the orbit where the kinetic energy of the electron is zero. b. adding a constant 13.6 eV to the potential energy for all values of n. c. adding a constant 27.2 eV to the potential energy for all values of n. d. subtracting a constant 13.6 eV from the potential energy for all values of n. e. subtracting a constant 27.2 eV from the potential energy for all values of n.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 12. One of the main problems with the Bohr model of the hydrogen atom when compared with the results of the methods of quantum mechanics used to describe atoms, was that the Bohr model predicted Copyright Cengage Learning. Powered by Cognero.

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a. the ground state angular momentum was L = 1 . b. the frequency of the radiation emitted when an electron "jumps" from one allowed orbit to another was hf = Ei − Ef. c. the potential energy function for the hydrogen atom was given by V(r) = −ke2/r. d. the energy of the ground state of the hydrogen atom was En = −13.6 eV. ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 13. What is the energy needed to remove an electron from the first excited state of a Li a. 53 eV b. 31 eV c. 92 eV d. 122 eV e. 61 eV ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom +

14. What is the energy needed to change a He ion in the ground state into a He a. 13.6 eV b. 54.4 eV c. 112.4 eV d. 92.9 eV e. 27.2 eV ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom

2+

2+

ion?

ion?

2+

15. A Li ion undergoes a transition from the n = 4 to the n = 3 state. What is the energy of the emitted photon? a. 4.5 eV b. 10.2 eV c. 5.95 eV d. 2.6 eV e. 0.66 eV ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 16. Which of the following, in which n and m have integer values, is a correct formula for a wavelength emitted by a hydrogen atom?

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a. b. c. d. e.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 17. Which of the following gives the total energy of the electron-proton system in the Bohr model of the hydrogen atom? a.

b.

c. 0 d.

e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 18. In terms of rB, where rB = 0.0529 nm, the radii of the allowed orbits in the Bohr model of the hydrogen atom are given by rn = a. b. c. d. e.

ANSWER:

e

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POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.3 Bohr’s Model of the Hydrogen Atom 2+

19. The allowed values of n for the Li ion are a. 1 to ∞. b. 2 to ∞. c. 3 to ∞. d. any real numbers. e. 1 to 10.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 2+

20. The allowed values of for the n = 3 shell in a Li ion are a. 1, 2. b. 0, 1. c. 0, 1, 2. d. 0, 1, 2, 3. e. 1, 2, 3.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 2+

21. In the subshell of the Li are

ion with orbital quantum number , the allowed values of the magnetic quantum number

a. − to . b. −( + 1) to ( + l). c. −( + 2) to ( + 2). d. −( + 3) to ( + 3). e. 0 to n − 1.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 22. In a shell of the hydrogen atom with n = 3, the permitted values of the orbital magnetic quantum number

are

a. −1, 0, 1. b. 2, 1, 0. c. 2, 1, 0, −1, −2. d. 0. e. 3, 2, 1, 0, −1, −2, −3.

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ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 23. The K, L, M symbols represent values of which quantum number? a. n b. c. d. ms e. mj ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 24. The s, p, d, f, symbols represent values of which quantum number? a. ms b. n c. d. e. mj ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom +

25. What is the number of states in the He ion corresponding to the principal quantum number n = 5? a. 18 b. 25 c. 50 d. 9 e. 11 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 26. Of the following states, 5s, 3p, 4f, 5p, 4g, 3d, and 2p, which one is NOT allowed? a. 3p b. 4f c. 3d d. 4g e. 2p Copyright Cengage Learning. Powered by Cognero.

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ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 27. For the following allowed transitions, which photon would have the largest wavelength when an electron "jumps" from one energy level, characterized by the quantum number n, to another? a. n = 2 to n = 1 b. n = 3 to n = 2 c. n = 3 to n = 1 d. n = 1 to n = 3 e. n = 4 to n = 1 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 28. Quantum physics agrees with the classical physics limit when a. the total angular momentum is a small multiple of . b. the total energy is a small multiple of the energy in the lowest quantized state. c. the difference in energy between adjacent quantized levels becomes vanishingly small. d. all electron spins are paired so that L = 0. e. there is a vacancy in an inner level in the atom.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 29. The number of electrons in the n = 4, = 2 subshell in strontium (Z = 38) is ____ the number of electrons in the n =4, =2 subshell in barium (Z = 56). a. times b. times c. equal to d. times e. times ANSWER: c POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 30. What is the difference in frequency for spectral lines emitted by hydrogen for transitions from the n = 16 level to the 7 -1 n = 2 level and transitions from the n = 15 level to the n = 2 level? (R = 1.097 × 10 m ) a. 5.65 × 10-13 Hz b. 31 Hz c. 1.77 × 1012 Hz d. 2.55 × 1016 Hz e. 1.02 × 1017 Hz ANSWER: c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 31. What is the difference in wavelength for spectral lines emitted by hydrogen for transitions from the n = 16 level to the 7 -1 n = 2 level and transitions from the n = 15 level to the n = 2 level? (R = 1.097 × 10 m ) a. 1.0 × 10-10 m b. 2.0 × 10-10 m c. 4.1 × 10-10 m d. 8.1 × 10-10 m e. 1.6 × 10-9 m ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 32. All quantum states forming a shell have the same a. principal quantum number n. b. orbital quantum number . c. orbital magnetic quantum number d. n, and

.

.

e. n and only.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 33. All quantum states forming a subshell have the same a. principal quantum number n. b. orbital quantum number . c. orbital magnetic quantum number d. n, and

.

.

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e. n and only.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 34. Adam and Eve are contemplating the beauty of the hydrogen atom. Adam claims that the quantum states with a given value of the principal quantum number n can have any value of the orbital quantum number . Eve says that the Snake told her that a state with a given value of could have any value of n. Which one, if either, is correct, and why? a. Adam, because the man is always right. b. Adam because n ≤ − 1. c. Eve, because n ≤ − 1. d. Eve, because ≤ n − 1. e. Neither, because Adam is wrong and the Snake told a subtle lie.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 35. Suppose a beam of electrons is incident on a collection of hydrogen atoms, all of which are in the lowest energy state (n = 1). What is the minimum energy the electrons can have if they are to excite the hydrogen atoms into the n = 2 state?

ANSWER: 10.2 eV POINTS: 2 DIFFICULTY: Average REFERENCES: 41.4 The Quantum Model of the Hydrogen Atom 2

36. The probability density for the 1s state is given by |Ψ1s| . Which of the following gives the probability of finding the particle somewhere in space? a. b. c. d. e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.5 The Wave Functions for Hydrogen 37. If P(r) is the radial probability density function for an electron in the ground state of a hydrogen atom, the most probable value for r can be found from a. dP/dt.

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b. dP/dr. c. d.

. .

e. d2P/dr2.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.5 The Wave Functions for Hydrogen 38. The radial portion of the de Broglie wavefunction for an electron in the ground state of the hydrogen atom is , where rB is the Bohr radius. Which of the following gives the probability of finding the electron? a. b.

c.

d. e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.5 The Wave Functions for Hydrogen 39. The probability density of a particle at a distance r from the nucleus is essentially the a. probability of finding the particle within a small volume about r. b. probability per unit area of finding the particle within a unit area centered on r. c. probability per unit length of finding the particle within a unit length of r. d. probability per unit volume of finding the particle within a small volume about r. e. .

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.5 The Wave Functions for Hydrogen Copyright Cengage Learning. Powered by Cognero.

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40. What is the magnitude of the total angular momentum (in terms of ) of a hydrogen atom in the 4f state? a. b. 3 c. 6 d. 9 e. 12 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers 41. Which of the following statements is true? a. can never be perpendicular to . b. can be aligned parallel to . c. must be perpendicular to . d. can never be aligned parallel to .

ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers 42. In 1920, Stern and Gerlach performed an experiment that first demonstrated a. orbital angular momentum quantization. b. energy quantization. c. space quantization. d. magnetic orbital quantization. e. that particles behave like waves.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers 43. What is the magnitude of the spin angular momentum for an electron? a. . b. . c. /2. d. ± /2. e. .

ANSWER: POINTS:

b 2

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DIFFICULTY: Average REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers 44. What angle does the orbital angular momentum make with the z axis of a hydrogen atom in the state n = 3, = 2, −1? a. −66° b. 66° c. 24° d. 114° e. 73° ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers

=

45. Forbidden transitions and selection rules suggest that a. a photon has linear momentum. b. a photon has energy. c. a photon has angular momentum. d. a photon has parity. e. a photon has mass.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers 46. In an atom that has an electron in a subshell for which = 4, with respect to the magnetic field vector moment vector of the electron is allowed to be oriented in a. any direction. b. discrete directions. c.

− 1 discrete directions.

d.

+ 1 discrete directions.

the magnetic

e. 2 + 1 discrete directions.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers 47. In an allowed electron transition in a hydrogen atom, a. Δ = 0; = 0, ±1. b. Δ = 0, ±1;

= ±1.

c. Δ = 0, ±1;

= 0, ±1.

d. Δ = ±1;

= 0, ±1.

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e. Δ = ±1;

= ±1.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers 48. Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = . Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector a. b. c. d.

is

. Which one, if either, is correct, and why?

Ruth, because the maximum value of L is

.

Ruth, because the orbital angular momentum always lines up with a magnetic field so that value along the field.

Zeke, because the maximum magnitude of

is L =

.

Zeke, because the orbital angular momentum always lines up with a magnetic field so that value along the field.

e.

has its maximum

Neither, because they have interchanged the maximum magnitude of projection along a magnetic field direction.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers

,

, and

has its maximum , its maximum

49. Aline says that the magnetic moment of an atom originates in the orbital angular momentum of the electron. Bevis says that it comes from the electron spin. Which one, if either, is correct, and why? a. Aline, because only atoms, not electrons, can have angular momentum. b. Bevis, because only atoms, not electrons, can have angular momentum. c. Neither, because electron spin and orbital angular momentum always cancel exactly. d. Neither, because the magnetic moment of an atom comes only from the spin of the nucleus. e. Both, because both the orbital angular momentum and the spins of the electrons contribute to the magnetic moment of an atom.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.6 Physical Interpretation of the Quantum Numbers 50. When using the Pauli exclusion principle, we assume the particle's spin angular momentum is of magnitude a. b.

c. d. ± Copyright Cengage Learning. Powered by Cognero.

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e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 41.7 The Exclusion Principle and the Periodic Table 51. The Pauli exclusion principle states a. no two electrons in the same atom can have the same set of quantum numbers. b. there is an inherent uncertainty in the position and momentum of a particle. c. when an atom has orbitals of equal energy, the maximum number of electrons will have unpaired spins. d. when an atom has orbitals of equal energy, the maximum number of electrons will be paired spins. e. no two atoms can have the same set of quantum numbers.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.7 The Exclusion Principle and the Periodic Table 52. What is the ground state configuration of chlorine (Z = 17)? a. 1s2 2s2 2p5 3s2 3p6 b. 1s2 2s2 2p6 3s2 3p5 c. 1s2 2s2 2p6 3s2 3p4 3d1 d. 1s2 2s2 2p6 3s2 3p5 4s1 e. 1s2 2s2 2p6 3s1 3p7 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 41.7 The Exclusion Principle and the Periodic Table 53. Rubidium (Z = 37) and potassium (Z = 19) are similar to sodium in that they have ____ electron(s) in the outermost shell. a. five p b. three p c. two s d. one d e. one s ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 41.7 The Exclusion Principle and the Periodic Table 54. When electrons fill a subshell in which the orbitals have equal energy, the order in which the orbitals are filled is such that a. a minimum number of electrons has unpaired spins. b. a minimum number of electrons has intrinsic angular momentum.

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c. a maximum number of electrons has unpaired spins. d. a maximum number of electrons first fills the next energy level. e. the maximum number of electrons has the same set of quantum numbers.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.7 The Exclusion Principle and the Periodic Table 55. In a completely filled atomic shell, a. the intrinsic spin of the electrons does not produce a resultant magnetic moment. b. the orbital motion of the electrons does not produce a resultant magnetic moment. c. the atom will be an alkali metal. d. only (a) and (b) are correct. e. none of the above are correct.

ANSWER: d POINTS: 1 DIFFICULTY: Average REFERENCES: 41.7 The Exclusion Principle and the Periodic Table 56. A head waiter at a restaurant decides to apply the exclusion principle to the seating of patrons. He will treat tables as subshells and will only seat patrons if the number of the people to be seated adds up to a complete subshell. Of the numbers below, which number would he NOT be willing to seat at one table? a. 2 b. 4 c. 6 d. 10 e. 14 ANSWER: b POINTS: 2 DIFFICULTY: Easy REFERENCES: 41.7 The Exclusion Principle and the Periodic Table 57. Characteristic X-rays can be produced by bombarding targets with electrons. These X-rays occur when a. electrons from higher shells fill the vacant lower shell. b. electrons fill the vacant valence shell. c. photons are emitted with energies on the order of 103 eV. d. photons are emitted with wavelengths on the order of 103 nm.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 41.8 More on Atomic Spectra: Visible and X-Ray 58. In the operation of a laser a. stimulated emission occurs. b. there is a population inversion. c. the excited state will tend to be metastable.

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d. the photons emitted will have transitioned to the ground state. e. For the answers (a), (b), (c), and (d), three are correct and one is incorrect.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 41.10 Lasers 59. The energy difference between the upper and lower levels in a certain laser is 1.9593 eV. What is the wavelength of the light emitted by the laser?

ANSWER: 632.9 nm POINTS: 2 DIFFICULTY: Average REFERENCES: 41.10 Lasers 60. A hydrogen atom emits a photon of wavelength 657.7 nm. From what energy state to what lower energy state did the electron jump?

ANSWER: n = 3 to n = 2 POINTS: 3 DIFFICULTY: Challenging REFERENCES: 41.10 Lasers

1. The energy released when an atom takes an electron is called what? a. internal energy b. dissociation energy c. binding energy d. electron affinity e. ionization energy ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.1 Molecular Bonds 2. The dissociation energy of the hydrogen molecule is approximately 5 eV. What is the temperature of a monatomic molecule whose kinetic energy is equal to 5.000 eV? a. 28 990 K b. 57 970 K c. 38 650 K d. 23 190 K e. 12 880 K ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 42.1 Molecular Bonds

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3. In the Lennard-Jones model of the hydrogen molecule, the potential is given by

. In this model, what

is the minimum internuclear separation, r0? a.

b.

c.

d.

e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 42.1 Molecular Bonds 4. Which of the following refer to the basic categories associated with the energy of a single molecule in a gaseous phase? a. nuclear, electronic, interval b. electronic, translation, rotation, vibration c. ionic, covalent, hydrogen, Van der Waals d. translation, rotation, vibration e. dipole-dipole, covalent, ionic, translation ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.2 Energy States and Spectra of Molecules 5. How many degrees of freedom does a diatomic molecule have? a. 3 b. 6 c. 5 d. 7 e. 9 ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.2 Energy States and Spectra of Molecules

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6. Assume a diatomic molecule can be considered to be two point masses separated by a distance r. The center of mass of the system is located a distance x from m1, equal to what? a. m1r/(m1 + m2) b. m2r/(m1 + m2) c. (m1 + m2) r/m1 d. (m1 + m2) r/m2 e. r(m2/m1) ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 42.2 Energy States and Spectra of Molecules 7. A diatomic molecule consists of two point masses, m1 and m2, separated by a distance r. If x is the distance from m1 to the center of mass, find the moment of inertia in terms of x about an axis perpendicular to the molecular axis through the center of mass. a. 0 b. m1m2 r2/m1 + m2 c. m1(r − x)2 + m2x2 d. m1x2 + m2(r − x)2 e. m2x2 + m1r2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 42.2 Energy States and Spectra of Molecules 8. A diatomic molecule consists of two point masses, m1 and m2, separated by a distance r. If x is the distance from m1 to the center of mass, find the moment of inertia in terms of x about an axis parallel to the molecular axis through the center of mass. a. 0 b. m1x2 + m2(r − x)2 c. m1m2 r2(m1m2) d. m1(r − x)2 + m2x2 e. m1x2 + m2r2 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 42.2 Energy States and Spectra of Molecules 9. A diatomic molecule consists of two point masses, m1 and m2, separated by a distance r. Find the moment of inertia through the center of mass about an axis perpendicular to the molecular axis. a. m1m2r2/(m1 + m2) b. [(m1m2/m1) + m2]r2 Copyright Cengage Learning. Powered by Cognero.

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c. (m1 + m2)/m1m2r2 d. (m1 + m1)r2 /m1m2 e. m1m2r2/m1 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 42.2 Energy States and Spectra of Molecules 10. The rotational kinetic energy of a diatomic molecule can take which of the following forms? a. (1/2)mω2 b. (1/2)Iω2 c. [m1m2/(m1 + m2)]r2ω2 d. (1/2)mv2 e. 1/2 μω2 ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.2 Energy States and Spectra of Molecules 11. Assume the angular momentum of a diatomic molecule is quantized according to the relation What are the allowed rotational kinetic energies? a.

.

b. c. d. e.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.2 Energy States and Spectra of Molecules 12. An experiment determines that there are 49 allowed rotational energies for a diatomic molecule whose moment of 46 2 inertia is 2 × 10− kg ⋅ m . What is the maximum rotational kinetic energy (in eV)? a. 0.6 b. 0.2 c. 0.4 d. 0.8 e. 1.0 ANSWER: c POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 42.2 Energy States and Spectra of Molecules 13. A molecule makes a transition from the J = 1 to the J = 0 rotational energy state. The wavelength of the emitted -3 2 photon is 2.6 × 10 m. What is the moment of inertia of the molecule (in kg ⋅ m )? a. 2.9 × 10-46 b. 5.7 × 10-45 c. 1.1 × 10-44 d. 1.5 × 10-46 e. 9.1 × 10-46 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 42.2 Energy States and Spectra of Molecules 14. The frequency of a microwave absorbed by a molecule when changing from the J = 3 to J = 4 rotation energy state is 11 2 4.61 × 10 Hz. The moment of inertia of the molecule (in kg ⋅ m ) is what? a. 5.70 × 10-45 b. 1.45 × 10-46 c. 1.12 × 10-44 d. 2.91 × 10-46 e. 9.11 × 10-46 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 42.2 Energy States and Spectra of Molecules -46

2

15. The moment of inertia of a CO molecule is 1.46 × 10 kg ⋅ m . What is the wavelength of the photon emitted if a rotational transition occurs from the J = 3 to the J = 2 state? a. 4.36 × 10-4 m b. 8.71 × 10-4 m c. 17.4 × 10-3 m d. 5.53 × 10-4 m e. 2.90 × 10-4 m ANSWER: b POINTS: 2 DIFFICULTY: Challenging REFERENCES: 42.2 Energy States and Spectra of Molecules 16. An oxygen molecule has a moment of inertia of 5 × 10 -27 atomic mass of oxygen is 16 u (1 u = 1.66 × 10 kg). a. 0.3 Copyright Cengage Learning. Powered by Cognero.

-46

2

kg ⋅ m . Calculate the bond length (in nm). Recall that the

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b. 0.1 c. 0.2 d. 0.4 e. 0.5 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 42.2 Energy States and Spectra of Molecules -6

17. The rotation spectrum of the HCl molecule has been observed in the far infrared, around 50 × 10 m. The spacing -6 between successive lines in the spectrum corresponds to radiation of wavelength equal to 5 microns (1 μm = 10 m).

Determine the frequency of the photon associated with this transition. a. 6 × 1014 Hz b. 6 × 1012 Hz c. 6 × 1011 Hz d. 6 × 1013 Hz e. 6 × 1010 Hz ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 42.2 Energy States and Spectra of Molecules -6

18. The rotation spectrum of the HCl molecule suggests a photon in the far infrared (around 5.0 × 10 m) can excite the 2 first rotational level. From this data, the moment of inertia of the HCl molecule (in kg ⋅ m ) is what? a. 2.8 × 10-48 b. 2.8 × 10-49 c. 2.8 × 10-47 d. 2.8 × 10-46 e. 2.8 × 10-45 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 42.2 Energy States and Spectra of Molecules 13

-27

19. The fundamental frequency of CO is 6.42 × 10 Hz. If the atomic masses are 12 u and 16 u (1 u = 1.66 × 10 find the force constant (in N/m) for the diatomic molecule. a. 970 b. 1 530 c. 1 850 d. 480 e. 47 ANSWER: c POINTS: 3

kg),

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DIFFICULTY: Challenging REFERENCES: 42.2 Energy States and Spectra of Molecules 20. The force constant of HCl is 480 N/m. If the atomic masses are 1 u and 35 u (1 u = 1.66 × 10 fundamental frequency (in Hz). a. 6.4 × 1013

-27

kg), find the

b. 9.2 × 1013 c. 7.7 × 1013 d. 8.7 × 1013 e. 1.4 × 1013 ANSWER: d POINTS: 3 DIFFICULTY: Challenging REFERENCES: 42.2 Energy States and Spectra of Molecules 13

21. The fundamental frequency of HF is 8.72 × 10 Hz. The energy associated with a transition from the 10th to the 9th vibrational quantum number (in eV) is what? a. 3.61 b. 0.361 c. 0.060 5 d. 0.605 e. 0.182 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 42.2 Energy States and Spectra of Molecules 22. The energy of a molecule can normally be divided into the following categories: a. rotational and vibrational b. translational, rotational, and vibrational c. electronic, translational, rotational, and vibrational d. rotational e. electronic ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.2 Energy States and Spectra of Molecules 23. In comparing vibrational and rotational levels in molecules, we find that the energy separation between adjacent energy levels is a. the same in rotational and vibrational levels. b. greater in rotational than in vibrational levels. c. greater in vibrational than in rotational levels. d. directly proportional with one rotational level for each vibrational level. e. inversely proportional with one rotational level for each vibrational level.

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ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.2 Energy States and Spectra of Molecules 24. When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J − 1, what is the change in energy EJ – EJ - 1? (Assume I is the molecule’s moment of inertia.) a.

b.

c.

d.

e.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.2 Energy States and Spectra of Molecules 25. When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J + 1, what is the change in energy EJ + 1 − EJ? (Assume I is the molecule’s moment of inertia.) a.

b.

c.

d.

e.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 42.2 Energy States and Spectra of Molecules 26. A diatomic molecule consists of two atoms, with masses m1 and m2. The separation between the two atoms is r.

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Which of the following gives the molecule’s moment of inertia, used when calculating its rotational kinetic energy? a.

b.

c.

d.

e.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.2 Energy States and Spectra of Molecules 27. Ellis and Randy are looking at a molecular absorption spectrum. The spectral lines appear to fall into two groups with a gap in the middle. Ellis says that this must be an absorption spectrum for transitions between the v = 0 and v = 1 vibrational states of a diatomic molecule. Randy says the gap in the middle must occur because a ΔJ = 0 transition is forbidden. Which one, if either, is correct, and why? a. Ellis, because rotational levels are separated by greater energy differences than vibrational levels. b. Randy, because rotational levels are separated by greater energy differences than vibrational levels. c. Ellis, because the ΔJ = 0 transition is the most prominent spectral line in transitions between vibrational levels. d. Neither, because rotational levels are separated by greater energies that vibrational levels and ΔJ = 0 transitions are not forbidden. e. Both, because vibrational levels are separated by greater energy differences than rotational levels and ΔJ = 0 transitions are forbidden.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.2 Energy States and Spectra of Molecules 28. What is the energy of the first rotational state of the hydrogen (H2) molecule? The separation between the protons is −10 -27 -34 -19 10 m and the mass of each proton is 1.67 × 10 kg. (h = 6.626 × 10 J ⋅ s and 1 eV = 1.6 × 10 J.) ANSWER: 0.008 eV POINTS: 3 DIFFICULTY: Challenging REFERENCES: 42.2 Energy States and Spectra of Molecules -10

29. In the hydrogen molecule, H2, the separation between the protons is 10 m. If the molecule is in its first rotational energy state, what is the angular velocity of the molecule about its center of mass?

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ANSWER:

13

1.8 × 10 rad/s POINTS: 3 DIFFICULTY: Challenging REFERENCES: 42.2 Energy States and Spectra of Molecules 30. The wave functions of some molecules are a combination of wave functions with different values of the orbital 3 quantum number . The wave function of PF5 combines s, p and d states in an sp d hybrid orbital. We would expect such an overlap of wave functions in individual molecules to represent a. ionic bonding. b. metallic bonding. c. covalent bonding. d. Van der Waal's bonding. e. hydrogen bonding.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.3 Bonding in Solids 31. Because HF, hydrogen fluoride, is a covalent gaseous molecule at room temperature, we might reasonably expect that at room temperature HCl, hydrogen chloride, is a. a covalent gaseous molecule. b. a covalent solid. c. a metallic gas. d. a metallic solid. e. an ionic solid.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.3 Bonding in Solids 32. The diagram below shows the distance between the nuclei, pA and pB, and the electrons, e1 and e2, in a hydrogen molecule. Which of the following gives the electrostatic potential energy of this molecule?

a.

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b.

c.

d.

e.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 42.3 Bonding in Solids 3

33. Solid argon has a density of 1650 kg/m . The atomic weight of argon is 40.0. Assuming each atom occupies a cubical volume, what is the distance between the argon atoms?

-10 ANSWER: 3.43 × 10 m POINTS: 3 DIFFICULTY: Challenging REFERENCES: 42.3 Bonding in Solids -9

34. The smallest object one can distinguish using the electron microscope is on the order of one nanometer (1 nm = 10 m). How many atoms of gold are contained in a cube whose edge is 1 nm long? The atomic mass of gold is 197 and its 3 density is 19.3 g/cm .

ANSWER: 59 atoms POINTS: 3 DIFFICULTY: Challenging REFERENCES: 42.3 Bonding in Solids 35. The Fermi energy corresponds to a. the maximum energy electrons can have in a metal at T = 0 K. b. the maximum energy electrons can have in a metal at T = 0 C. c. the minimum energy electrons can have in a metal at T = 0 K. d. the number of electrons per unit volume between E and E + dE. e. the minimum energy electrons can have in a metal at T = 0 C. ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.4 Free-Electron Theory of Metals 36. the minimum energy electrons can have in a metal at T = 0 C. a. a characteristic temperature of an electron gas at a physical temperature of absolute zero.

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b. a characteristic temperature of an electron gas at a physical temperature of 0° Celsius. c. the temperature of the electron gas in absolute degrees. d. related to the Fermi energy by the relation EF = (3/2) kT. e. independent of the Fermi energy.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.4 Free-Electron Theory of Metals 37. The Fermi temperature of copper is 80 000 K. The corresponding Fermi energy (in eV) is what? a. 7 b. 5 c. 3 d. 1 e. 4 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 42.4 Free-Electron Theory of Metals 38. The Fermi energy of a metal at a temperature T is 7.0 eV. What is the average energy (in eV) of a conduction electron at that temperature? a. 2.8 b. 7.0 c. 3.5 d. 4.2 e. 4.7 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 42.4 Free-Electron Theory of Metals 39. To find the number of electrons per unit volume with energy between E and E + dE in a metal we must multiply the number of allowed states per unit volume with energy E by a. the probability that a state is unoccupied,

.

b. the probability that a state is occupied,

.

c. the probability that a state is unoccupied,

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.

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d. the probability that a state is occupied,

.

e. dE alone.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.4 Free-Electron Theory of Metals 40. The energy gap for germanium is 0.670 eV at room temperature. What wavelength must a photon have (in nm) to excite the electron to the conduction band? a. 640 b. 1 090 c. 1 850 d. 2 200 e. 925 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 42.5 Band Theory of Solids 41. An energy band in a solid consists of a. an infinite number of levels, with each level corresponding to a point in a box. b. a large number of energy levels so closely spaced that they may be regarded as a continuous band. c. an infinite number of wave functions, with each wave function corresponding to a point in a box. d. a large number of electrons so closely spaced that they may be regarded as a continuous band of electric charge. e. an infinite number of electrons, with each electron corresponding to a point in a box.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.5 Band Theory of Solids 42. If an electric field is applied to a metal, a. very few electrons are excited into the conduction band. b. electrons having energies near the Fermi energy require only a small amount of additional energy from the applied field to reach nearby empty energy states. c. electrons having energies near the bottom of the band require only a small amount of additional energy from the applied field to reach nearby empty energy states. d. the principal mode of conduction is through the motion of holes in the filled part of the band. e. the Fermi energy Ef becomes equal to the applied electric field E. ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.6 Electrical Conduction in Metals, Insulators, and Semiconductors 43. The difference between donor and acceptor atoms in a doped semiconductor is that Copyright Cengage Learning. Powered by Cognero.

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a. the donor energy level lies halfway between the valence band and the acceptor level. b. the donor energy level lies near the valence band and the acceptor energy level lies near the conduction band. c. donor energy levels cannot exist unless acceptor energy levels are present. d. the donor energy level lies near the conduction band and the acceptor energy level lies near the valence band. e. the acceptor energy level lies halfway between the conduction band and the donor energy level.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.6 Electrical Conduction in Metals, Insulators, and Semiconductors 44. The energy gap for a semiconductor is 1.25 eV. Of the frequencies given below, what is the minimum frequency photon than can move an electron from the valence band to the conduction band? a. b. c. d. e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 42.6 Electrical Conduction in Metals, Insulators, and Semiconductors 45. When a voltage ΔV is applied to a p-n junction diode at absolute temperature T, the current voltage relationship is a. . b. . c. . d. . e. .

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 42.7 Semiconductor Devices 46. An LED emits light of wavelength 600 nm. What is its band gap? a. 1.11 eV Copyright Cengage Learning. Powered by Cognero.

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b. 1.54 eV c. 1.99 eV d. 2.07 eV e. 2.33 eV ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 42.7 Semiconductor Devices

1. What is the radius of the nucleus of

(in fm)?

a. 15.4 b. 5.5 c. 12.8 d. 6.6 e. 4.9 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.1 Some Properties of Nuclei 2. Two isotopes of uranium have the same a. mass number. b. neutron number. c. atomic number. d. nucleon number. e. nucleon number and neutron number.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.1 Some Properties of Nuclei 2

2

3. What is the ratio of the radius of a classical electron (re = ke /mec = 2.8 × 10 1/3 r0A )? a. 2.0 b. 0.68 c. 1.5 d. 0.92 e. 2.4 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 43.1 Some Properties of Nuclei 1/3

4. What is the ratio of the density of a neutron (r = r0A Copyright Cengage Learning. Powered by Cognero.

-15

4

m) to the radius of a He nucleus (r =

2

2

-

) to the density of a classical electron (re = ke /mec = 2.8 × 10

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15

m)? a. 4.3 × 102 b. 2.3 × 104 c. 1.4 × 102 d. 6.9 × 10-3 e. 4.3 × 103

ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 43.1 Some Properties of Nuclei 5. For stable nuclei with large mass number, the ratio of protons to neutrons is a. equal to 1. b. greater than 1. c. less than 1. d. unrelated to the stability of nuclei. e. almost 2 to 1.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.1 Some Properties of Nuclei 6. Heavy nuclei are unstable because a. each nucleon is a separate particle that is not acted on by the nuclear force. b. there are not enough protons present relative to the number of neutrons for the electrical force to be strong enough. c. the nuclear force dominates the Coulomb repulsive force at distances of roughly 1 fm or less, but falls off rapidly at greater distances. d. nuclei are stable only when the number of neutrons equals the number of protons. e. nuclei are stable only when the number of protons exceeds the number of neutrons.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.1 Some Properties of Nuclei 7. Two nuclei which share the same mass number A always are (Hint: Eliminate any wrong answers.) a. stable. b. unstable. c. isotopes. d. isobars. e. radioactive.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.1 Some Properties of Nuclei Copyright Cengage Learning. Powered by Cognero.

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8. Two nuclei which share the same atomic number Z always are a. stable. b. unstable. c. isotopes. d. isobars. e. radioactive.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.1 Some Properties of Nuclei 9. Two nuclei may have equal Z, but different A, because they contain a. equal numbers of protons and neutrons. b. equal numbers of protons but different numbers of neutrons. c. different numbers of protons but equal numbers of neutrons. d. different numbers of protons and neutrons. e. electrons as well as neutrons.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.1 Some Properties of Nuclei 10. Which of the following gives the radius r of an approximately spherical nucleus? a. r0Z3 b. r0Z1/3 c. r0A3 d. r0A1/3 e. r0(A − Z)1/3 ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.1 Some Properties of Nuclei 11. Find the number of nuclei per unit volume (n = nuclei/cm3) for lead.

atomic weight = 202.7 density = 11.5 g/cm3 Avogadro's number = 6.02 × 1023 a. 2.51 × 1022 b. 3.42 × 1022 c. 2.93 × 1022 d. 2.94 × 1023 e. 2.05 × 1021 Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 43.1 Some Properties of Nuclei 12. Calculate the binding energy per nucleon (MeV/nucleon) for tritium, (

) a radioactive isotope of hydrogen.

Assume: mp = 1.007 825 u mn = 1.008 665 u mt = 3.016 05 u -27 1 u = 1.66 × 10 kg a. 2.8 b. 3.1 c. 1.0 d. 8.5 e. 2.1 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 43.2 Nuclear Binding Energy 13. Find the ratio of the binding energy per nucleon for helium (

) to uranium-238 (

).

Assume: mp = 1.007 825 u mn = 1.008 665 u mHe = 4.002 603 u mU = 238.050 786 u -27 1 u = 1.66 × 10 kg a. 1.07 b. 0.934 c. 63.7 d. 1.6 × 10-2 e. 3.24 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 43.2 Nuclear Binding Energy 14. Find the binding energy (in MeV) of carbon-12.

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mn = 1.008 665 u -27 1 u = 1.66 × 10 kg a. 14.8 b. 0.511 c. 9.11 d. 92.3 e. 46.2 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.2 Nuclear Binding Energy 15. Find the binding energy per nucleon (in MeV/nucleon) of carbon-12.

Assume: mC = 12.000 000 u mp = 1.007 825 u mn = 1.008 665 u -27 1 u = 1.66 × 10 kg a. 1.2 b. 4.2 × 10-2 c. 7.4 d. 7.7 e. 5.6 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.2 Nuclear Binding Energy 16. An alpha particle is emitted from a radioactive source with an energy of 5 MeV. How fast is it moving (in m/s)? (m = -27 4.002 603 u, 1 u = 1.66 × 10 kg.) a. 2.4 × 107 b. 1.6 × 107 c. 3.7 × 107 d. 4.6 × 107 e. 2.1 × 107 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 43.2 Nuclear Binding Energy 17. It is often possible to use the atomic masses when calculating the binding energy of a nucleus. The reason for this is a. the electron masses do not cancel. b. the electron masses cancel. c. tables of nuclear masses are usually not available.

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d. the mass of the electron can usually be neglected when compared to the mass of the neutron. e. the atomic masses are the same as the nuclear masses.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.2 Nuclear Binding Energy 18. It is often possible to use atomic masses when calculating the binding energy of a nucleus. This is not true for + calculating the Q value for the e decay process since a. the electron masses do not cancel. b. a positron is an antiparticle. c. the electron masses cancel. d. the mass of a positron cannot be neglected when compared to the mass of a nucleus. e. none of the above.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.2 Nuclear Binding Energy 19. How can a nucleus be described by particular values of A, Z, and N when the mass of the nucleus is not equal to Zmp + Nmn, where mp and mn are the masses of free protons and neutrons? a. A, Z, and N have no intrinsic meaning. b. A, Z, and N describe the number of particles of given types, but mass has no meaning when part of the mass is elsewhere in the universe. c. A, Z, and N describe the number of particles an ideal rather than a real nucleus would have. d. A, Z, and N describe the number of particles of given types in the nucleus, but not their masses in a bound state. e. A, Z, and N describe the number of particles of given types in the nucleus since the missing mass consists of electrons that are also present in the nucleus.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.2 Nuclear Binding Energy 20. Linus claims that the added gravitational force of neutrons holds the particles in a nucleus together. Linnea says that they stick together because they lose their electric charge when they form a nucleus. Which one, if either, is correct, and why? a. Linus, because more particles exert gravitational forces on one another than exert electromagnetic forces. b. Linus, because the numerical magnitude of G/k is 7.42 × 10-21. c. Linnea, because the numerical magnitude of G/k is 7.42 × 10-21. d. Both, because electric charge is lost and then gravity holds the nucleus together. e. Neither, because gravity is not lost, and the numerical magnitude of k/G is 1.35 × 1020.

ANSWER: e POINTS: 1 DIFFICULTY: Easy Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 43.2 Nuclear Binding Energy 21. Which of the effects listed below is not a major effect influencing the binding energy of the nucleus in the liquid-drop model? a. The volume effect: the binding energy per nucleon is approximately constant when A > 50. b. The surface effect: nucleons in the surface have fewer neighbors. c. The quantum number effect: all nucleons in the nucleus have the same set of quantum numbers. d. The Coulomb repulsion effect: protons repel protons. e. The symmetry effect: stable nuclei tend to have N ≈ Z. ANSWER: c POINTS: 2 DIFFICULTY: Easy REFERENCES: 43.3 Nuclear Models 22. According to the shell model, binding energy per nucleon is greater when N or Z is equal to one of the numbers below except for a. 2. b. 8. c. 13. d. 20. e. 28.

ANSWER: c POINTS: 2 DIFFICULTY: Easy REFERENCES: 43.3 Nuclear Models 23. The isotope, tritium, has a half-life of 12.3 years. Assume we have 10 kg of the substance. What will be the initial decay rate, at t = 0 (in decays/s)? a. 1.09 × 1014 b. 1.8 × 10-9 c. 5.6 × 108 d. 3.6 × 1018 e. 3.6 × 1017 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.4 Radioactivity 24. The isotope, tritium, has a half-life of 12.3 years. Assume we have 10 kg of the substance. How much tritium will be left after 30 years? a. 0.20 kg b. 1.8 kg c. 0.18 kg d. 1.7 kg e. 4.1 kg Copyright Cengage Learning. Powered by Cognero.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 43.4 Radioactivity 131

25. The half-life of I is 8.04 days. Three days after it was prepared, its activity was 0.50 μCi. How many curies (in μCi) were initially prepared? a. 0.60 b. 0.70 c. 0.65 d. 0.55 e. 0.39 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 43.4 Radioactivity 26. How many radioactive atoms are present in a sample that has an activity of 0.5 μCi and a half-life of 10 years? (1 curie 10 = 3.7 × 10 decays/s) a. 9.5 × 1012 atoms b. 8.4 × 1012 atoms c. 7.3 × 1012 atoms d. 6.5 × 1012 atoms e. 2.7 × 105 atoms ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 43.4 Radioactivity 27. Because we know that the half-lives of many radioactive isotopes are millions of years, we can deduce that a. the longer it exists the more radioactive nuclei Earth produces. b. the Sun is the source of all the radioactive nuclei on Earth. c. there must have been many more radioactive nuclei on Earth when life began. d. there must have been far fewer radioactive nuclei on Earth before life began. e. the natural radioactivity of minerals on the Earth was created by the Earth's internal temperature.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.4 Radioactivity 28. A glass container holds equal numbers of atoms of phosphorus 30 with a half-life of 2.5 minutes and of nitrogen-13 with a half-life of 10 minutes. After 20 minutes, what is the ratio of the number of nitrogen atoms remaining to the number of phosphorus atoms remaining? a.

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b. c. d. 64 e. 256 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.4 Radioactivity 29. Homer says that we can safely use nuclear power because all radioactive nuclei are gone after two half-lives. Marge says that only the decay rate is zero after two half-lives. Which one, if either, is correct, and why? a. Homer, because half of the nuclei disintegrate in each half-life. b. Marge, because the number of decays per unit time is halved in each half-life. c. Homer, because it's safe to handle radioactive substances after two half-lives. d. Both, because when all nuclei disintegrate the decay rate is also zero. e. Neither, because one quarter of the nuclei are left after two half-lives.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.4 Radioactivity 226

14

30. A pure sample of Ra contains 2.0 × 10 atoms of the isotope. If the half-life of 10 decay rate of this sample? (1 Ci = 3.7 × 10 decays/s) -8 ANSWER: 7.4 × 10 Ci

226

3

Ra = 1.6 × 10 years, what is the

POINTS: 2 DIFFICULTY: Average REFERENCES: 43.4 Radioactivity 131

31. The half-life of I is 8 days. On a certain day, the activity of an later?

ANSWER: 200 μCi POINTS: 2 DIFFICULTY: Average REFERENCES: 43.4 Radioactivity

131

I sample is 6.4 mCi. What is its activity 40 days

32. A radioactive sample with decay rate R and decay energy Q has power output a. . b. RQ. c. Q2R. d. equal to any of the above. e. equal to (a) or (c) above.

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ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 43.4 Radioactivity 33. The theory of nuclear astrophysics is that all the heavy elements like uranium are formed in the interior of massive stars. These stars eventually explode, releasing these elements into space. If we assume that at the time of the explosion there were equal amount of U-235 and U-238, how long ago did the star(s) explode that released the elements that formed 9 9 our Earth? The present U-235/U-238 ratio is 0.0070. [The half-lives of U-235 and U-238 are 0.7 × 10 yr and 4.47 × 10 yr.]

ANSWER: 5.9 billion years POINTS: 3 DIFFICULTY: Challenging REFERENCES: 43.4 Radioactivity 34. The isotope, tritium, has a half-life of 12.3 years. Assume we have 10 kg of the substance. What is its disintegration -1 constant (in s )? a. 5.6 × 10-2 b. 5.6 × 108 c. 3.2 × 107 d. 1.8 × 10-9 e. 1.6 × 106 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.4 Radioactivity 14

35. 44 g of petrified wood was found in a petrified forest. A sample showed a C activity of 100 decays/minute. How 10 long has the tree been dead (in years)? (The half-life of carbon-14 is 5 730 years and freshly cut wood contains 6.5 × 10 14 atoms of C per gram.) a. 12 300 b. 15 600 c. 8 500 d. 4 700 e. 2 400 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 43.5 The Decay Processes 36. Naturally radioactive nuclei can decay spontaneously by emitting the following particles: a. helium nuclei, electrons, photons b. electrons, neutrons, protons c. helium nuclei, electrons, protons d. electrons, neutrons, photons Copyright Cengage Learning. Powered by Cognero.

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e. quarks and leptons ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.5 The Decay Processes 37. What value of Z (atomic number) and A (mass number) result in the following alpha decay?

a. Z = 92; A = 238 b. Z = 91; A = 238 c. Z = 90; A = 234 d. Z = 93; A = 238 e. Z = 88; A = 236 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 43.5 The Decay Processes 38. What value of Z (atomic number) and A (mass number) result in the following β-decay?

a. Z = 5; A = 14 b. Z = 4; A = 10 c. Z = 6; A = 14 d. Z = 7; A = 14 e. Z = 7; A = 13 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.5 The Decay Processes 39. What value of Z (atomic number) and A (mass number) result in the following β-decay?

a. Z = 6; A = 12 b. Z = 5; A = 8 c. Z = 6; A = 11 d. Z = 8; A = 12 e. Z = 8; A = 11 ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 43.5 The Decay Processes Copyright Cengage Learning. Powered by Cognero.

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40. What value of Z (atomic number) and A (mass number) result in the following gamma decay?

a. Z = 5; A = 12 b. Z = 4; A = 8 c. Z = 7; A = 12 d. Z = 6; A = 12 e. Z = 6; A = 11 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.5 The Decay Processes 41. What is the disintegration energy (in MeV) associated with this spontaneous decay?

mNd = 143.910 083 u mCe = 139.905 434 u mHe = 4.002 603 u −27 1 u = 1.66 × 10 kg a. 1.54 b. 2.37 c. 1.90 d. 4.13 e. 8.21 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 43.5 The Decay Processes 42. When a neutron decays, a proton and an electron are observed. When the electrons emitted from a sample of neutrons are observed, they are found to have different kinetic energies. This was accounted for by a. introducing a different particle, the neutrino. b. introducing the effect of gravity on the particles. c. including the kinetic energies of the neutron and proton. d. modifying the laws of conservation of momentum and energy. e. taking into account the uncertainties associated with Heisenberg's uncertainty principle.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.5 The Decay Processes 43. The Q value for the following reaction, Copyright Cengage Learning. Powered by Cognero.

, in MeV, is what?

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m(alpha) = 4.002 603 u m(Be) = 9.012 182 u m(n) = 1.008 665 u m(C) = 12.000 00 u -27 1 u = 1.66 × 10 kg a. 8.4 b. 6.2 c. 7.3 d. 5.7 e. 3.5 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.5 The Decay Processes 44. In beta decay, a. a proton changes to a neutron. b. a neutron changes to a proton. c. an electron is present in the nucleus before the decay. d. (a), (b) or (c) may occur. e. only (a) or (b) may occur.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.5 The Decay Processes 45. In which of the following decays does the atomic mass number of the daughter nucleus differ from that of the parent nucleus? a. b. c. d. e. Answers (a), (b), and (c) are correct.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 43.5 The Decay Processes 14

46. The radiocarbon content of C decreases after the death of a living system with a half-life of 5 730 y. If an archaeologist working a dig finds an ancient fire pit containing some partially consumed firewood and the wood contains 14 only 12.5 percent of the C content of an equal carbon sample from a present-day tree, what is the age of the ancient site?

ANSWER: 17 190 years POINTS: 2 DIFFICULTY: Average Copyright Cengage Learning. Powered by Cognero.

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REFERENCES: 43.5 The Decay Processes 47. The mass of

is 55.934 9 u and the mass of

possible processes?

ANSWER:

is 55.939 9 u. Which isobar decays into the other, and by what 2

+

by e decay or by electron capture.

POINTS: 3 DIFFICULTY: Challenging REFERENCES: 43.5 The Decay Processes 48. A beam of 1-MeV gamma rays incident on a piece of 0.50-cm-thick lead is reduced by 50% of its initial value. How thick must the lead be to reduce the beam to one percent of its initial value? a. 1.1 cm b. 2.2 cm c. 3.3 cm d. 4.4 cm e. 8.4 cm ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 43.5 The Decay Processes 49. The chart below shows part of the radioactive series beginning with the isotope

. Which of the following is the

isotope marked with an X?

a. b. c. d. e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 43.6 Natural Radioactivity Copyright Cengage Learning. Powered by Cognero.

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50. The chart below shows part of the radioactive series beginning with the isotope

. Which of the following is the

isotope marked with an X?

a. b. c. d. e.

ANSWER: b POINTS: 1 DIFFICULTY: Average REFERENCES: 43.6 Natural Radioactivity 51. One of the naturally occurring radioactive series begins with

. Which of the following isotopes is the stable

isotope at the end of this series? a. b. c. d. e. None of the above choices can be correct.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 43.6 Natural Radioactivity Copyright Cengage Learning. Powered by Cognero.

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52. The reaction energy associated with a nuclear reaction is a. the total change in rest energy as a result of the reaction. b. equivalent to the disintegration energy. c. the minimum energy necessary for such a reaction to occur. d. called the threshold energy. e. the binding energy of the nucleons.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.7 Nuclear Reactions −

53. A neutron is known to undergo beta decay (n → p + e + ). A reasonable mean lifetime for free neutrons is a. 10 years. b. 10 hours. c. 10 days. d. 10 minutes. e. 10−23 s.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.7 Nuclear Reactions 54. A neutron is characterized by the term "thermal neutron" when a. its energy is of the order kT, where T is on the order of 0°C. b. its energy is of the order kT, where T is on the order of 0 K. c. its energy is of the order kT, where T is on the order of 273°C. d. its energy is of the order kT, where T is on the order of 100°C. e. its energy is of the order kT, where T is on the order of 0°R. ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.7 Nuclear Reactions 55. A thermal neutron has an energy (in eV) on the order of what value? a. 40 b. 0.4 c. 4 d. 0.04 e. 400 ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.7 Nuclear Reactions 56. The nuclear probability of interacting with neutrons depends most strongly on the neutron's a. mass.

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b. area. c. volume. d. speed. e. charge.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.7 Nuclear Reactions 57. Find the unknown atomic number and mass number, respectively, for the following reaction:

a. 141, 53 b. 140, 54 c. 53, 41 d. 54, 140 e. 54, 141 ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 43.7 Nuclear Reactions 58. What is the average kinetic energy (in keV) of an ion that has a temperature of a. 8.2 b. 13 c. 4.3 d. 16 e. 21 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 43.7 Nuclear Reactions

8

10 K?

8

59. Approximately how fast is an ion of helium moving if it is in a plasma with a temperature of 10 K? m(He) = 4.002 -27 603 u and u = 1.66 × 10 kg. a. 106 m/s b. 104 m/s c. 102 m/s d. 10 m/s e. 1 m/s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 43.7 Nuclear Reactions Copyright Cengage Learning. Powered by Cognero.

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60. The reaction

is known as a ____ reaction.

a. beta capture b. beta emission c. neutron capture d. neutron emission e. photon emission ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.7 Nuclear Reactions 61. When a nucleus at rest spontaneously splits into fragments of mass m1 and m2, what is the ratio of the momentum of m1 to the mometum of m2 is a. . b. . c. −1. d. . e. .

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.7 Nuclear Reactions 62. When a nucleus at rest spontaneously splits into fragments of mass m1 and m2, what is the ratio of the velocity of m1 to the velocity of m2? a.

b.

c. −1 d.

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e.

ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 43.7 Nuclear Reactions 63. In neutron capture by an atomic nucleus, the atomic number changes by a. −2. b. −1. c. 0. d. +1. e. +2.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.7 Nuclear Reactions 64. In neutron capture by an atomic nucleus, the mass number of the nucleus changes by a. −2. b. −1. c. 0. d. +1. e. +2.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.7 Nuclear Reactions 65. How much energy (in MeV) is released when a

fissions to

and

in the following reaction?

m(n) = 1.008665 u m(U) = 235.043915 u m(Ba) = 140.9139 u m(Kr) = 91.8973 u −27 u = 1.66 × 10 kg a. 100 b. 50 c. 200 d. 150 e. 250 ANSWER: c POINTS: 2 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Average REFERENCES: 43.8 Nuclear Fission 66. Approximately how much uranium (in kg) must undergo fission per day to provide 1 000 MW of power? (Assume an efficiency of 30%). The nuclear reaction is . m(n) = 1.008 665 u m(U) = 235.043 915 u m(Ba) = 140.913 9 u m(Kr) = 91.897 3 u −27 u = 1.66 × 10 kg a. 1.0 b. 3.5 c. 2.3 d. 4.6 e. 0.1 ANSWER: b POINTS: 3 DIFFICULTY: Challenging REFERENCES: 43.9 Nuclear Reactors 67. When a fast neutron collides with a hydrogen or deuterium nucleus, the most likely result is that a. the neutron has an appreciable gain in kinetic energy, the gain being greatest for head-on collisions. b. the neutron has an appreciable gain in kinetic energy, the gain being greatest for oblique collisions. c. the neutron has an appreciable loss in kinetic energy, the loss being greatest for head-on collisions. d. the neutron has an appreciable loss in kinetic energy, the loss being greatest for oblique collisions. e. the neutron is absorbed by the hydrogen or deuterium nucleus.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.9 Nuclear Reactors 68. In order to control a nuclear reactor, control rods can be pulled out of or pushed into the reactor core by remote control. These rods control the reactor by a. slowing down the fast neutrons so the neutrons can be absorbed by 238U. b. speeding up slow neutrons so the neutrons can be absorbed by 238U. c. slowing down fast neutrons so they cannot initiate further fusion reactions in 235U. d. speeding up fast neutrons so they cannot initiate further fusion reactions in 235U. e. absorbing neutrons so they cannot initiate further fission reactions in 235U. ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.9 Nuclear Reactors

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69. A nuclear reactor is said to be critical when the average number of neutrons from each fission event that cause(s) another fission event is a. <1. b. 1. c. >1. d. any of the above. e. only (b) or (c) above.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.9 Nuclear Reactors 70. How many grams of U-235 must be fissioned every day to produce 1 000 MW of electricity in a nuclear power plant −13 that is 1/3 efficient? [Assume 208 MeV/fission and 1 MeV = 1.6 × 10 J] ANSWER: grams POINTS: 3 DIFFICULTY: Challenging REFERENCES: 43.9 Nuclear Reactors 71. The nuclear reaction(s) that is(are) most likely to be employed in fusion reactors on Earth is(are) a. . b. c.

. .

d. all of the above. e. only (a) and (b) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.10 Nuclear Fusion 72. What energy is needed (in MeV) so two deuterium atoms moving together will reach the necessary 10 fusion? a. 0.511 b. 0.14 c. 2.5 d. 4.3 e. 1.0 ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 43.10 Nuclear Fusion

-14

m for

73. How fast must two deuterium atoms be moving so they can overcome the Coulomb force of repulsion, and attain the Copyright Cengage Learning. Powered by Cognero.

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necessary 10

-14

m for fusion? (mass of

= 2.014 1 u)

a. 3.9 × 106 m/s b. 1.3 × 106 m/s c. 2.6 × 106 m/s d. 5.2 × 106 m/s e. 3.7 × 106 m/s ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 43.10 Nuclear Fusion 74. A principal mechanism for energy loss during nuclear fusion is bremsstrahlung. This loss is associated with a. x-rays emitted due to electron-ion collisions. b. radiation losses due to T4 losses. c. conduction losses associated with ΔT. d. convection losses associated with ΔT. e. neutron collisions with atoms of moderator.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.10 Nuclear Fusion -19

75. How much kinetic energy must a deuterium ion (charge 1.6 × 10 -13 deuterium ion? (1 MeV = 1.6 × 10 J) ANSWER: 140 keV POINTS: 2 DIFFICULTY: Average REFERENCES: 43.10 Nuclear Fusion

C) have to approach to within 10

-14

m of another

76. How many grams of deuterium (atomic mass = 2.014 1 u) must be fused to helium (atomic mass 4.002 6 u) in one -27 second to produce 3 000 MJ of energy? [1 u = 1.66 × 10 kg] ANSWER: 0.005 2 grams POINTS: 3 DIFFICULTY: Challenging REFERENCES: 43.10 Nuclear Fusion 77. One roentgen is defined as a. the amount of ionizing radiation that will produce 1/3 × 10-9 C of electric charge in 1 cm3 of air under standard conditions. b. the amount of radiation that deposits 10-2 J of energy into 1 kg of absorbing material. c. the amount of radiation needed for ionization of an atom. d. the amount of radiation needed for dissociation of a molecule. e. the amount of radiation that deposits 1 erg of energy in 1 g of air.

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ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.11 Biological Radiation Damage 78. One rad is a. the amount of radiation that deposits 10-2 J of energy into 1 kg of absorbing material. b. the amount of ionizing radiation that will produce 1/3 × 10-9 C of electric charge in 1 cm3 of air under standard conditions. c. the amount of radiation needed for ionization of an atom. d. the amount of radiation needed for dissociation of a molecule. e. the amount of radiation that deposits one erg of energy in 1g of material.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.11 Biological Radiation Damage 79. A rem (roentgen equivalent in man) is defined as (the product of) a. the dose in RBE. b. the dose in roentgen and the RBE factor. c. the dose in rad times the dose in roentgen. d. the dose in rad and the RBE factor. e. the dose in rad and energy of radiation.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.11 Biological Radiation Damage 80. Which of the following is not a radiation detector? a. cloud chamber b. Geiger counter c. scintillation counter d. neutron activation e. spark chamber ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.11 Biological Radiation Damage 81. Background radiation from cosmic rays and radioactive nuclei in our surroundings is about 0.13 rem/year. Suppose we assume this all comes from cosmic rays which have an RBE factor of 1.0. The RBE factor for the most dangerous types of radiation is 20. How many rads of the most dangerous radiation could a 100-year-old person have been exposed to in her lifetime without having gone over the recommended limit of 0.5 rem/year? a. 0.37 b. 0.50 c. 1.85 Copyright Cengage Learning. Powered by Cognero.

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d. 13 e. 37 ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 43.11 Biological Radiation Damage 82. A beam of high-energy α-particles is incident upon a person and deposits 0.35 J of energy in 0.80 kg of tissue. What dose in rads and what equivalent dose in rems does the individual receive? [RBE α = 20] ANSWER: 44 rad, 880 rem POINTS: 3 DIFFICULTY: Challenging REFERENCES: 43.11 Biological Radiation Damage 83. Radioactive technetium, a gamma emitter, is taken up by the heart muscle in a medical test. The detector for the radiation emitted from the heart could be a a. Tokamak. b. quarter-wavelength antenna. c. Geiger counter. d. photoelectric tube. e. diffraction grating.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.12 Uses of Radiation from the Nucleus 84. In nuclear magnetic resonance, nuclei absorb energy when flipping between nuclear a. mass states. b. spin states. c. charge states. d. decay states. e. isotope states.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 43.13 Nuclear Magnetic Resonance and Magnetic Resonance Imaging

-15

1. The strong nuclear interaction has a range of approximately 0.70 × 10 m. It is thought that an elementary particle is exchanged between the protons and neutrons, leading to an attractive force. Utilize the uncertainty principle, ΔxΔp = h/4π, to estimate the mass of the elementary particle if it moves at nearly the speed of light. a. 140 MeV/c2, a pion b. 511 keV/c2, an electron c. 96 GeV/c2, a Z boson d. 500 MeV/c2, a K meson Copyright Cengage Learning. Powered by Cognero.

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e. 106 MeV/c2, a muon ANSWER: a POINTS: 1 DIFFICULTY: Challenging REFERENCES: 44.1 Field Particles for the Fundamental Forces in Nature 0

0

2. The rest-energy of the Z boson is 96 GeV. Using this information, find the maximum length of time a virtual Z can -19 exist, in accordance with the uncertainty principle . (1 eV = 1.6 × 10 J.) a. 3.4 × 10-27 s b. 7.5 × 10-30 s c. 2.4 × 10-24 s d. 1.9 × 10-21 s e. 6.3 × 10-5 s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 44.1 Field Particles for the Fundamental Forces in Nature 3. The attractive force between protons and neutrons in the nucleus is brought about by the exchange of a virtual pi-meson 2 0 (mπ = 140 MeV/c ). Estimate the longest time a virtual π can exist, in accordance with the uncertainty principle -19 . (1 eV = 1.6 × 10 J.) a. 2.4 × 10-24 s b. 6.9 × 10-27 s c. 3.3 × 10-18 s d. 2.4 × 10-21 s e. 1.6 × 10-19 s ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 44.1 Field Particles for the Fundamental Forces in Nature 4. A model for how repulsive forces between two particles can be mediated by a third particle would be a. a person on a skateboard pushing against a wall. b. two people in two canoes throwing a ball back and forth. c. two people in two canoes each pulling on one end of a rope. d. two people in two skateboards giving each other a shove. e. two people in two skateboards each pulling on one end of a rope.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.1 Field Particles for the Fundamental Forces in Nature -27

5. Calculate the range of the force that might be produced by the virtual exchange of a proton. (mp = 1.67 × 10

kg, h =

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6.626 × 10 ANSWER:

-34

J ⋅ s) -16

1.05 × 10 m POINTS: 3 DIFFICULTY: Challenging REFERENCES: 44.1 Field Particles for the Fundamental Forces in Nature 6. An electron and a positron (antielectron), both nearly at rest, collide. What particle(s) is(are) produced? a. One photon of energy 1.02 MeV b. Two photons of energy 511 keV c. A pi-meson d. A K-meson and an anti-neutrino ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.2 Positrons and Other Antiparticles 7. A proton and an antiproton each with total energy of 400 GeV collide head-on. What is the total energy (particles + energy) released? a. zero b. 400 Gev c. 800 GeV d. 1 600 GeV e. 2 400 GeV ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.2 Positrons and Other Antiparticles 8. The minimum energy needed to produce a positron is a. 3 MeV b. 2 MeV c. 1 MeV d. 4 MeV e. 0.51 MeV ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.2 Positrons and Other Antiparticles 9. A photon with an energy of Eγ = 2.090 0 GeV creates a proton-antiproton pair in which the proton has a kinetic energy 2 of 95.0 MeV. What is the kinetic energy of the antiproton? (mpc = 938.3 MeV) ANSWER: 118.4 MeV POINTS: 2 DIFFICULTY: Average REFERENCES: 44.2 Positrons and Other Antiparticles Copyright Cengage Learning. Powered by Cognero.

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10. All particles can be classified into a. leptons and quarks. b. hadrons and leptons. c. baryons and leptons. d. mesons and baryons.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.4 Classification of Particles 0

-10

0

11. If a K meson at rest decays in 0.89 × 10 s, how far will a K meson moving at 0.96c travel through a bubble chamber? a. 17 cm b. 1.1 cm c. 53 cm d. 42 mm e. 9.2 cm ANSWER: e POINTS: 3 DIFFICULTY: Challenging REFERENCES: 44.4 Classification of Particles 12. Which one of the following is not true of neutrinos? a. They have no charge. b. They have no spin. c. One type of neutrino may change into another type of neutrino. d. They are leptons. e. They do not take part in strong nuclear interactions.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.4 Classification of Particles 13. Of the following leptons, which has the greatest rest energy? a. b. c. d. e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 44.4 Classification of Particles Copyright Cengage Learning. Powered by Cognero.

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0

+

−

0

14. A K particle at rest decays into a π and a π . What will be the speed of each of the pions? The mass of the K is 2 2 497.7 MeV/c and the mass of each π is 139.6 MeV/c .

ANSWER: 0.83c POINTS: 3 DIFFICULTY: Challenging REFERENCES: 44.4 Classification of Particles 15. Which of the following particle reactions cannot occur? a. p + p → p + p + p + b. p + → 2γ c. π+ + p → K+ + Σ+ d. γ + p → n + π0 e. e− + e+ → 2γ ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 44.5 Conservation Laws 16. Which of the following reactions cannot occur? a. n → p + e− + b. p + n → p + p + c. μ− → e− +

+

μ

d. π− → μ− + νμ e. π+ → μ+ + ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 44.5 Conservation Laws 17. The law of conservation of baryon number is that a. the total number of baryons and leptons is conserved. b. the total number of baryons is conserved. c. the (number of baryons) − (number of antibaryons) is conserved. d. the total number of quarks is conserved. e. the (number of baryons) + (number of antibaryons) is conserved.

ANSWER: c POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.5 Conservation Laws 18. Which of the following decays violates conservation of lepton number? a.

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b. c. d. e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 44.5 Conservation Laws 0

−

19. The omega-minus particle decays with the X and the π eventually decaying into stable baryon(s) and lepton(s). Utilizing conservation laws, which of the following is the correct accounting of the decay products? a. b. c. d.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 44.5 Conservation Laws 20. The decay

is not possible because

a. Le is not conserved. b. Lμ is not conserved. c. quark number is not conserved. d. all of the above are not conserved. e. only Le and Lμ are not conserved.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.5 Conservation Laws +

21. A Σ particle, composed of uus quarks, has the same ____ as a proton. a. baryon number and charm. b. baryon number and electric charge. c. baryon number and strangeness. d. baryon number, electric charge, and charm. e. electric charge and strangeness.

ANSWER: d Copyright Cengage Learning. Powered by Cognero.

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POINTS: 2 DIFFICULTY: Average REFERENCES: 44.5 Conservation Laws 22. Name at least one conservation law that prevents each of the following reactions: a) π− + p → Σ+ + π° b) p → π+ + π+ + π− ANSWER: a) charge, b) baryon number POINTS: 2 DIFFICULTY: Average REFERENCES: 44.5 Conservation Laws 23. Which of the following reactions violates conservation of strangeness? a. Ω− → 3γ b. c. d. e.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 44.6 Strange Particles and Strangeness 24. The particle reaction cannot occur because a. electric charge is not conserved. b. strangeness is not conserved. c. baryon number is not conserved. d. all of the above are not conserved. e. both (a) and (b) above are not conserved.

ANSWER: e POINTS: 2 DIFFICULTY: Average REFERENCES: 44.6 Strange Particles and Strangeness 25. Particles composed of quarks are a. photons. b. leptons. c. neutrinos. d. W and Z bosons. e. baryons and mesons.

ANSWER: e POINTS: 1 Copyright Cengage Learning. Powered by Cognero.

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DIFFICULTY: Easy REFERENCES: 44.8 Quarks 0

+

−

26. The following reaction can occur by the strong interaction: π + n → K + Σ . If the quark composition of the n is + − (udd), the π° is ( ), and the composition of the K is ( ), find the quark composition of the Σ . a. sss b. uds c. dds d. e.

ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 44.8 Quarks ++

27. The particle Δ has an electric charge twice that of the proton and baryon number +1. Strangeness, charm, bottomness, and topness are all 0. Its quark composition must be a. uuu. b. uud. c. udd. d. . e.

.

ANSWER: a POINTS: 2 DIFFICULTY: Average REFERENCES: 44.8 Quarks 28. If the quark content of the proton, p, is uud, the quark content of the antiproton, , is a. uud. b. udd. c. . d.

.

e.

.

ANSWER: e POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.8 Quarks 29. The three quarks in any baryon must all have different a. baryon number. b. color charge. c. electric charge. d. lepton number. e. spin.

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ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.9 Multicolored Quarks 30. In this course we have seen that baryons have inertial and gravitational mass, intrinsic angular momentum, and other internal properties that have been given names like baryon number, strangeness, charm, etc. The Standard Model's explanation for these properties of baryons is that a. the baryons are states of something more elementary that can exist in multiple quantum states. b. the leptons are states of something more elementary that can exist in multiple quantum states. c. photons are states of something more elementary that can exist in multiple quantum states. d. according to the Heisenberg Uncertainty Principle quantum numbers are indeterminate. e. quarks are states of something more elementary that can exist in multiple quantum states.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.10 The Standard Model 6

31. According to the Hubble law, where H0 = 22.6 km/s/10 light-years, what is the velocity of recession of a quasar at a distance of 2 billion light-years from Earth? a. 0.30c b. 0.44c c. 0.73c d. 0.15c e. 0.08c ANSWER: d POINTS: 2 DIFFICULTY: Average REFERENCES: 44.11 The Cosmic Connection 32. Spectrographic analysis of light from a distant galaxy shows that the galaxy is receding from Earth at v = 0.384c. Use 6 Hubble's law with H0 = 22.6 km/s/10 light years to estimate the distance to the galaxy. a. 2.5 × 108 light years b. 5.1 × 109 light years c. 7.5 × 108 light years d. 1.7 × 109 light years e. 4.9 × 106 light years ANSWER: b POINTS: 2 DIFFICULTY: Average REFERENCES: 44.11 The Cosmic Connection 33. The red shift of a quasar indicates that it is moving radially away from the Earth at a speed of 0.50c. What is the age of the Universe if we assume that this quasar has moved at the same speed relative to Earth since the big bang? (Assume H0 -3 15 = 22.6 × 10 m/s/ly, where 1 ly = 9.46 × 10 m.)

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a. 44 y b. 6.6 × 109 y c. 1.3 × 1010 y d. 4.2 × 1017 y e. 6.2 × 1025 y ANSWER: c POINTS: 2 DIFFICULTY: Average REFERENCES: 44.11 The Cosmic Connection 34. In the standard model of the expansion of the Universe, the total energy of a standard mass m is assumed to be zero.

When we solve the resulting energy equation for the critical mass density of the universe, we find that the critical mass density is given by which of the following? a.

b.

c.

d.

e.

ANSWER: b POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.11 The Cosmic Connection 35. The acceleration (or deceleration) of the expansion of the Universe is determined by a. the standard matter, baryons and leptons. b. the dark matter in the Universe. c. the dark energy in the Universe. d. all of the above. e. only (b) and (c) above.

ANSWER: d POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.11 The Cosmic Connection 36. According to string theory, six space-time dimensions cannot be measured except as quantum numbers of internal particle properties because they are curled up in size of the order of a. 10-35 m.

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b. 10-15 m. c. 10-10 m. d. 10-8 m. e. 10-3 m.

ANSWER: a POINTS: 1 DIFFICULTY: Easy REFERENCES: 44.12 Problems and Perspectives

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