Type:
Test Bank
Resource:
College Physics
Edition:
4th Edition
Author(s):
Randal Knight Brian Jones Stuart Field
College Physics, 1e (Pearson) Topic 1 Units, Conversions, and Estimation 1.1 Conceptual Questions 1.1.1 Significant Figures 1) Significant Figures: In the product A ∙ B ∙ C, A has 5 significant figures, B has 2 significant figures, and C has 3 significant figures. How many significant figures does the product have? A) 2 B) 3 C) 4 D) 5 E) 10 Answer: A Topic: Significant Figures 2) Significant Figures: In the quotient
, A has 5 significant figures, B has 2 significant
figures, and C has 3 significant figures. How many significant figures does the quotient have? A) 2 B) 3 C) 4 D) 0 E) 1 Answer: A Topic: Significant Figures 3) Significant Figures: In the sum A + B + C, A is accurate to 5 decimal places, B is accurate to 2 decimal places, and C is accurate to 3 decimal places. What is the correct number of decimal places in the sum? A) 2 B) 3 C) 4 D) 5 E) 10 Answer: A Topic: Significant Figures
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4) Significant Figures: In the difference A - B - C, A is accurate to 5 decimal places, B is accurate to 2 decimal places, and C is accurate to 3 decimal places. What is the correct number of decimal places in the difference? A) 2 B) 3 C) 4 D) 5 E) 0 Answer: A Topic: Significant Figures 5) Significant Figures: How many significant figures are in the number 0.0037010? A) four B) five C) six D) seven E) eight Answer: B Topic: Significant Figures 6) Significant Figures: How many significant figures are in the number 0.010? A) four B) three C) two D) one Answer: C Topic: Significant Figures 7) Significant Figures: How many significant figures are in the number 120.070? A) six B) five C) four D) three Answer: A Topic: Significant Figures 8) Significant Figures: The number of significant figures in 10,001 is A) two. B) three. C) five. D) six. Answer: C Topic: Significant Figures
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Topic: Estimation 3) Estimation: A reasonable estimate for the mass of a typical new-born baby is A) 1 kg. B) 3 kg. C) 10 kg. D) 20 kg. Answer: B Topic: Estimation 4) Estimation: A reasonable estimate for the height of the walls in an ordinary American home is A) 10 m. B) 8 m. C) 2.5 m. D) 1.5 m. Answer: C Topic: Estimation 5) Estimation: A reasonable estimate for the duration of a typical physics lecture is A) 600 s. B) 1000 s. C) 3500 s. D) 10,000 s. Answer: C Topic: Estimation 6) Estimation: A reasonable estimate for the mass of an ordinary passenger car is A) 100 kg B) 1000 kg C) 5000 kg D) 10,000 kg Answer: B Topic: Estimation 1.2 Problems 1.2.1 Significant Figures 1) Significant Figures: What is the product of 12.56 and 2.12 expressed to the correct number of significant figures? A) 27 B) 26.6 C) 26.23 D) 26.627 Answer: B Topic: Significant Figures 5 ..
2) Significant Figures: What is the quotient of 2.43 ÷ 4.561 expressed to the correct number of significant figures? A) 5.3278 × 10-1 B) 5.328 × 10-1 C) 5.33 × 10-1 D) 5.3 × 10-1 Answer: C Topic: Significant Figures 3) Significant Figures: What is
expressed to the correct number of significant figures?
A) 0.91 B) 0.911 C) 0.9108 D) 0.9 Answer: A Topic: Significant Figures 4) Significant Figures: What is 0.2052/3, to the correct number of significant figures? A) 0.348 B) 0.35 C) 0.3 D) 0.3477 Answer: A Topic: Significant Figures 5) Significant Figures: Add 1299 g and 45.1 kg and express your answer in milligrams (mg) to the correct number of significant figures. A) 4.64 × 107 mg B) 4.64 × 104 mg C) 4.64 × 105 mg D) 4.64 × 106 mg Answer: A Topic: Significant Figures 6) Significant Figures: What is
expressed to the correct number of significant
figures? Answer: 1.22 Topic: Significant Figures
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7) Significant Figures: The length and width of a rectangle are 1.125 m and 0.606 m, respectively. Multiplying, your calculator gives the product as 0.68175. Rounding properly to the correct number of significant figures, the area of the rectangle should be written as A) 0.68 m2 B) 0.682 m2 C) 0.6818 m2 D) 0.68175 m2 Answer: B Topic: Significant Figures 8) Significant Figures: What is the sum of 2.67 + 1.976 + 2.1 expressed to the correct number of significant figures? A) 6.7 B) 6.75 C) 6.746 D) 6.7460 Answer: A Topic: Significant Figures 9) Significant Figures: Express the sum of 420.77, 13.821, and 2317.8 to the correct number of significant figures. Answer: 2752.4 Topic: Significant Figures 10) Significant Figures: What is the difference between 103.5 and 102.24 expressed to the correct number of significant figures? A) 1.3 B) 1.26 C) 1.260 D) 1.2600 Answer: A Topic: Significant Figures 11) Significant Figures: What is the sum of 1.53 + 2.786 + 3.3 expressed to the correct number of significant figures? A) 7 B) 7.6 C) 7.62 D) 7.616 E) 7.6160 Answer: B Topic: Significant Figures
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12) Significant Figures: Express the result of the following calculation to the proper number of significant figures: 50.19 - 7966 × 10-3. Answer: 42.22 Topic: Significant Figures 13) Significant Figures: What is the result, expressed to the proper number of significant figures, of adding 23.4 to 91.237 and then subtracting 23.4? A) 91.237 B) 91.2 C) 91.3 D) 91.0 E) 91 Answer: B Topic: Significant Figures 14) Significant Figures: Express the result of the following calculation, in scientific notation, to the proper number of significant figures:
+ 19.
Answer: 5.9 × 104 Topic: Significant Figures 15) Significant Figures: Add the following lengths, each obtained from a different measuring instrument, and round the answer to the proper number of significant figures: 20.02 m, 5.91 m, 0.0097 m, and 2.467 m. Answer: 28.41 m Topic: Significant Figures 16) Significant Figures: The last page of a book is numbered 764. The book is 3.0 cm thick, not including its covers. What is the average thickness (in centimeters) of a page in the book, rounded to the proper number of significant figures? A) 0.0039 cm B) 0.072 cm C) 0.0079 cm D) 0.00393 cm E) 0.00785 cm Answer: C Topic: Significant Figures
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17) Significant Figures: The length and width of a rectangle are 1.125 m and 0.606 m, respectively. You calculate the rectangle's perimeter by adding these numbers and multiplying by two. Your calculator's display reads 3.462. To the correct number of significant figures, the perimeter should be written as A) 3.5 m. B) 3.46 m. C) 3.462 m. D) 3.4620 m. Answer: C Topic: Significant Figures 18) Significant Figures: A rectangular garden measures 15 m long and 13.70 m wide. What is the length of a diagonal from one corner of the garden to the other? A) 18 m B) 19 m C) 20 m D) 4.1 × 102 m Answer: C Topic: Significant Figures 19) Significant Figures: If a circle has a radius of 1.109 m, what is its area expressed to the correct number of significant figures? A) 3.86 m2 B) 3.863 m2 C) 3.864 m2 D) 3.8638 m2 E) 3.86379 m2 Answer: C Topic: Significant Figures 20) Significant Figures: A train travels at a constant speed of 60.4 mi/h for 101.5 min. What distance does the train cover expressed to the correct number of significant figures? A) 100 mi B) 102 mi C) 102.2 mi D) 102.18 mi E) 102.181 mi Answer: B Topic: Significant Figures
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21) Significant Figures: A dog has three puppies. Spot weighs 12 ounces. Rascal weighs 9.5 ounces. Socks weighs 10.2 ounces. What is the total weight of the litter expressed to the correct number of significant figures? A) 31.7 ounces B) 31 ounces C) 32 ounces D) 30 ounces E) 31.70 ounces Answer: C Topic: Significant Figures 22) Significant Figures: A traveler has about $536 in his checking account, about $2107 in his savings account and exactly $7.62 in his wallet. To the greatest precision warranted, how much money does this shopper have? A) $2651 B) $2650 C) $2650.6 D) $2650.62 E) $2650.620 Answer: A Topic: Significant Figures 23) Significant Figures: To get to her physics class, Alice walks 0.25 mi to the bus stop. She takes the bus 1.2 mi to the train station. She takes the train 13 mi and walks the remaining 0.17 mi to her class. How far is her commute expressed to the correct number of significant figures? A) 14.6 mi B) 10 mi C) 15 mi D) 14.62 mi E) 14.620 mi Answer: C Topic: Significant Figures 24) Significant Figures: What is 56 +
written with the correct number of
significant figures? A) 62.8 B) 62.812 C) 62.81 D) 63 E) 62.8123846 Answer: D Topic: Significant Figures
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25) Significant Figures: Using a digital balance the mass of a certain piece of wood is read as 12.946 g. Thinking in terms of accuracy and significant figures, what value would you record on your data sheet if the balance is accurate to one-tenth of a gram? A) 12.9 g B) 12.95 g C) 13 g D) 13.0 g Answer: A Topic: Significant Figures 1.2.2 Scientific Notation 1) Scientific Notation: Which of the following numbers is the smallest? A) 15 × 10-3 B) 0.15 × 100 C) 0.00015 × 103 D) 0.00000015 × 106 Answer: A Topic: Scientific Notation 2) Scientific Notation: Which one of the following numbers is equivalent to the number 0.0001776? A) 1.776 × 10-4 B) 17.76 × 10-3 C) 1776 × 10-5 D) 177.6 × 10-7 Answer: A Topic: Scientific Notation 3) Scientific Notation: Write out the number 8.42 × 10-5 in full with a decimal point and correct number of zeros. A) 0.00000842 B) 0.0000842 C) 0.000842 D) 0.00842 Answer: B Topic: Scientific Notation 4) Scientific Notation: What is the result of the calculation (0.410 + 0.021) × (2.20 × 103)? A) 880 B) 946 C) 948 D) 950 Answer: C Topic: Scientific Notation 11 ..
5) Scientific Notation: Express (2.2 × 106)-1/2 in scientific notation. A) 6.7 × 10-4 B) 1.5 × 103 C) 1.5 × 10-5 D) 1.5 × 104 Answer: A Topic: Scientific Notation 1.2.3 Metric System 1) Metric System: Express the number 13.5 gigameters in meters without using scientific notation. A) 135,000 m B) 135,000,000 m C) 135,000,000,000 m D) 13,500,000,000 m Answer: D Topic: Metric System 2) Metric System: A volume of 100 mL is equivalent to which one of the following volumes? A) 1 kL B) 10-6 μL C) 0.1 L D) 0.01 ML Answer: C Topic: Metric System 3) Metric System: The volume of a 10-mL test tube is equivalent to which one of the following quantities? A) 0.01 L B) 0.001 kL C) 0.1 L D) 1 × 10-6 L E) 0.001 ML Answer: A Topic: Metric System 4) Metric System: The number 0.00325 × 10-8 cm can be expressed in millimeters as A) 3.25 × 10-12 mm. B) 3.25 × 10-11 mm. C) 3.25 × 10-10 mm. D) 3.25 × 10-9 mm. Answer: C Topic: Metric System
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5) Metric System: An area of 1.00 × 102 cm2 is how many square meters? A) 1.00 m2 B) 1.00 × 102 m2 C) 1.00 × 10-2 m2 D) 1.00 × 104 m2 E) 1.00 × 10-3 m2 Answer: C Topic: Metric System 6) Metric System: The prefix yotta (Y) signifies a multiple of 1024. How many yottameters are there in a gigameter? Answer: 10-15 ym Topic: Metric System 7) Metric System: Express the sum 1.00 kg + 1531 g + 2.54 × 104 mg in kilograms with the correct number of significant figures. A) 2.56 kg B) 27.9 kg C) 2.53 kg D) 2.79 kg Answer: A Topic: Metric System 8) Metric System: The quantity 0.00325 × 10-8 cm is equivalent to A) 3.25 × 10-12 mm. B) 3.25 × 10-11 mm. C) 3.25 × 10-10 mm. D) 3.25 × 10-9 mm. E) 3.25 × 10-8 mm. Answer: C Topic: Metric System 9) Metric System: A weight lifter can bench press 171 kg. How many milligrams is this? A) 1.71 × 108 mg B) 1.71 × 109 mg C) 1.71 × 107 mg D) 1.71 × 106 mg Answer: A Topic: Metric System
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10) Metric system: How many nanoseconds does it take for a computer to perform one calculation if it performs 6.7 × 107 calculations per second? A) 15 ns B) 67 ns C) 11 ns D) 65 ns Answer: A Topic: Metric System 11) Metric system: A certain CD-ROM disk can store 600 megabytes of information. If an average word requires 9.0 bytes of storage, how many words can be stored on one disk? A) 6.7 × 107 words B) 5.4 × 109 words C) 2.1 × 107 words D) 2.0 × 109 words Answer: A Topic: Metric System 12) Metric system: The wavelength of the light from a certain laser is 0.66 microns, where 1 micron = 1.0 × 10-6 m. What is this wavelength in nanometers? (1 nm = 10-9m) A) 6.6 × 102 nm B) 6.6 × 103 nm C) 6.6 × 101 nm D) 6.6 × 104 nm Answer: A Topic: Metric System 1.2.4 Conversion of Units 1) Conversion of Units: If you are 5'10'' tall, what is your height in meters? (2.54 cm = 1.00 in.) A) 1.5 m B) 1.6 m C) 1.7 m D) 1.8 m Answer: D Topic: Conversion of Units 2) Conversion of Units: Given that 1.00 in. = 2.54 cm and 1.00 yd = 36.0 in., how many meters are in 7.00 yd? A) 6.40 m B) 36.3 m C) 640 m D) 1.78 × 103 m Answer: A Topic: Conversion of Units 14 ..
3) Conversion of Units: Hydraulicists often express rainfall in acre-feet. This is the amount of water required to cover an area of one acre to a depth of one foot. There are 640.0 acres in a square mile, and 5280 feet in one mile. How many cubic feet are there in one acre-foot? Answer: 43,560 ft3 Topic: Conversion of Units 4) Conversion of Units: Express 50 mi/h in units of meters per second. (1 mi = 1609 m) A) 49 m/s B) 2.2 m/s C) 22 m/s D) 45 m/s Answer: C Topic: Conversion of Units 5) Conversion of Units: Given that 1.00 in. = 2.54 cm, how many square centimeters are in 1.00 square inch? A) 1.59 B) 2.54 C) 5.08 D) 6.45 Answer: D Topic: Conversion of Units 6) Conversion of Units: A plot of land contains 5.8 acres. How many square meters does it contain? (1.0 acre = 43,560 ft2 and 2.54 cm = 1.00 in.) A) 2.3 × 104 m2 B) 7.1 × 103 m2 C) 7.0 × 104 m2 D) 5.0 × 104 m2 Answer: A Topic: Conversion of Units 7) Conversion of Units: The density of water is 1.00 g/cm3. What is its density in kg/m3? Answer: 1.00 × 103 kg/m3 Topic: Conversion of Units
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8) Conversion of Units: A light-year (ly) is the distance that light travels in one year. The speed of light is 3.00 × 108 m/s. How many miles are there in 1.00 ly? (1.00 mi = 1.609 km and one year is 365.25 days.) A) 2.87 × 1013 mi B) 9.46 × 1015 mi C) 5.88 × 1015 mi D) 9.46 × 1012 mi E) 5.88 × 1012 mi Answer: E Topic: Conversion of Units 9) Conversion of Units: A speed of 60 mi/h is closest to which of the following? (2.54 cm = 1.00 in.) A) 60 m/s B) 20 m/s C) 30 km/h D) 120 m/s E) 30 m/s Answer: E Topic: Conversion of Units 10) Conversion of Units: Which of the following speeds is greatest? (2.54 cm = 1.00 in.) A) 10 km/h B) 10 m/s C) 10 ft/s D) 10 mi/h E) 10 yd/s Answer: B Topic: Conversion of Units 11) Conversion of Units: A person on a diet loses 1.6 kg in a week. How many micrograms per second (μg/s) are lost? A) 2.6 × 103 μg/s B) 1.6 × 105 μg/s C) 44 μg/s D) 6.4 × 104 μg/s Answer: A Topic: Conversion of Units 12) Conversion of Units: There are 640 acres in a square mile, 5280 ft in one mile, and 3.28 ft in one meter. How many acres are there in a hectare, which is a square one hundred meters on each side? Answer: 2.47 acres Topic: Conversion of Units
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13) Conversion of Units: There are 2.00 dry pints to 1.00 dry quart, 8.00 dry quarts to 1.00 peck, 4.00 pecks to 1.00 bushel. An organic farmer wants to pick enough berries to fill 40,000 pint containers. How many bushels of berries does the farmer need? Answer: 625 bushels Topic: Conversion of Units 14) Conversion of Units: A typical ruby-throated hummingbird is 8 cm long. Express its length in millimeters and micrometers (µm). A) 80 mm; 800 µm B) 80 mm; 80,000 µm C) 800 mm; 0.008 µm D) 800 mm; 0.8 µm E) 0.8 mm; 8000 µm Answer: B Topic: Conversion of Units 15) Conversion of Units: A jogger has a mass of 50 kg. Express her mass in grams and micrograms (µg). A) 50,000 g; 5 × 106 µg B) 500,000 g; 500 × 106 µg C) 500,000 g; 5000 µg D) 50,000 g; 5 × 1010 µg E) 50,000 g; 50,000 µg Answer: D Topic: Conversion of Units 16) Conversion of Units: A jar of peanut butter costs $3.29. Express its price in dekadollars and decidollars. A) 0.329 dekadollars; 0.329 decidollars B) 32.9 dekadollars; 0.329 decidollars C) 329 dekadollars; 32.9 decidollars D) 0.329 dekadollars; 32.9 decidollars E) 32.9 dekadollars; 329 decidollars Answer: D Topic: Conversion of Units 17) Conversion of Units: The following conversion equivalents are given: 1.00 gal = 231 in3 1.0 ft = 12 in 1.0 min = 60 s If a pipe delivers water at the rate of 95 gal/min, its rate of flow in ft3/s is closest to A) 0.21 ft3/s. B) 0.19 ft3/s. C) 0.17 ft3/s. D) 0.15 ft3/s. E) 0.14 ft3/s. Answer: A Topic: Conversion of Units 17 ..
18) Conversion of Units: The following conversion equivalents are given: 1.0 m = 100 cm 1.0 in = 2.54 cm 1.0 ft = 12 in If a bin has a volume of 1.5 m3, the volume of the bin, in ft3, is closest to A) 35 ft3. B) 41 ft3. C) 47 ft3. D) 53 ft3. E) 59 ft3. Answer: D Topic: Conversion of Units 19) Conversion of Units: The following conversion equivalents are given: 1.0 mile = 5280 ft 1.0 ft = 12 in 1 m = 39.37 in 1.0 hour = 60 min 1.0 min = 60 s If a deer runs at 4.7 mi/h, its speed, in meters per second, is closest to A) 2.1 m/s. B) 1.7 m/s. C) 1.9 m/s. D) 2.3 m/s. E) 2.5 m/s. Answer: A Topic: Conversion of Units 20) Conversion of Units: speed of 65 miles per hour is the same as which of the following? (1.00 ft = 30.48 cm) A) 24 m/s B) 29 m/s C) 32 m/s D) 37 m/s E) 42 m/s Answer: B Topic: Conversion of Units 21) Conversion of Units: The following conversion equivalents are given: 1.0 kg = 1000 g 1.0 l = 1000 cm3 1.0 l = 0.0353 ft3 The density of a certain liquid is 0.83 g/cm3. The density of this liquid, expressed in kg/ft3, is closest to A) 24 kg/ft3. B) 19 kg/ft3. C) 21 kg/ft3. D) 26 kg/ft3. E) 28 kg/ft3. Answer: A Topic: Conversion of Units 18 ..
22) Conversion of Units: Your car gets 34.7 mi/gal on a vacation trip in the U.S. If you were figuring your mileage in Europe, how many km/L did it get? (3.79 L = 1.00 gal; 1.00 mi = 1.61 km) A) 14.7 km/L B) 9.16 km/L C) 55.9 km/L D) 32.4 km/L Answer: A Topic: Conversion of Units 23) Conversion of Units: An oak tree was planted 22 years ago. How many seconds does this correspond to? (Do not take leap days into account.) A) 6.9 × 108 B) 1.2 × 107 C) 2.9 × 107 D) 2.8 × 108 Answer: A Topic: Conversion of Units 24) Conversion of Units: At a certain time, the average size of a transistor in a microprocessor was 250 nanometers. A human hair has a diameter of 70 microns (micrometers). How many transistors fit across a human hair? A) 280 B) 28 C) 2800 D) 2.8 E) 0.28 Answer: A Topic: Conversion of Units 25) Conversion of Units: The king's chamber of the great pyramid in Egypt is 10.43 m long, 5.21 m wide, and 5.82 m high. What is the volume of the chamber in cubic feet, expressed to the correct number of significant figures? (1.00 in. = 2.54 cm) A) 316 ft3 B) 3720 ft3 C) 6530 ft3 D) 11,200 ft3 E) 13,200 ft3 Answer: D Topic: Conversion of Units
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26) Conversion of Units: Rover eats 0.50 pound of dry dog food per day. How many 5.0-kg sacks of dog food does his owner need to buy in a year? (1.0 kg weighs 2.2 lb) A) 17 B) 25 C) 52 D) 80 E) 81 Answer: A Topic: Conversion of Units 27) Conversion of Units: The peak of Mt. Everest, at 10,900 m, is the highest point above sea level in the world. What is its elevation in miles? (1.00 m = 3.281 ft) A) 17.6 mi B) 0.630 mi C) 6.77 mi D) 6.20 mi E) 67.1 mi Answer: C Topic: Conversion of Units 28) Conversion of Units: The Hope Diamond weighs 44.5 carats, and there are 200 mg per carat. What is the mass of the Hope Diamond in kilograms? A) 0.000890 kg B) 0.00890 kg C) 0.0890 kg D) 0.890 kg E) 8.90 kg Answer: B Topic: Conversion of Units 29) Conversion of Units: The column of Trajan, erected in Rome in 106-113 A.D., is 125 feet tall. What is its height in centimeters? (2.54 cm = 1.00 in.) A) 1510 cm B) 591 cm C) 2520 cm D) 3810 cm E) 38,100 cm Answer: D Topic: Conversion of Units
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30) Conversion of Units: There are 640 acres in a square mile, and 5280 feet in 1.00 mile. What is the length in feet (to the nearest foot) of the side of a square having an area of 1.00 acre? A) 660 feet B) 209 feet C) 165 feet D) 412 feet E) 435 feet Answer: B Topic: Conversion of Units 31) Conversion of Units: An American football field, including end zones, is 360 feet long and 160 feet wide. If you needed to describe it for someone in Europe using the metric system, which one of the following quantities would be closest to its area in square meters? (2.54 cm = 1.00 in.) A) 4920 m2 B) 5350 m2 C) 88.0 m2 D) 12,100 m2 E) 13,200 m2 Answer: B Topic: Conversion of Units 32) Conversion of Units: Leonardo da Vinci's Mona Lisa is 21 in. wide and 30.25 in. tall. What is the area of the painting in square centimeters? (1.00 m = 39.37 in.) A) 4100 cm2 B) 1600 cm2 C) 660 cm2 D) 3300 cm2 E) 2400 cm2 Answer: A Topic: Conversion of Units 33) Conversion of Units: A cylindrical drinking glass has a diameter of 2.5 in. and is 5.5 in. tall. What is the volume of the drinking glass in cubic centimeters? (2.54 cm = 1.00 in.) A) 170 cubic cm B) 440 cubic cm C) 350 cubic cm D) 710 cubic cm E) 530 cubic cm Answer: B Topic: Conversion of Units
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34) Conversion of Units: A football field is 120 yd long and 50 yd wide. What is the area of the football field, in square meters, given that 1.0 yd = 91.44 cm? A) 2.4 × 103 m2 B) 3.7 × 103 m2 C) 4.2 × 103 m2 D) 5.0 × 103 m2 Answer: D Topic: Conversion of Units 35) Conversion of Units: Wall posters are usually sold curled up in cylindrical cardboard tubes. If the length of the tube is 0.845 m, and the inside diameter of the tube is 2.40 mm, what is the area of the poster expressed in square centimeters to the correct number of significant figures? (Assume the poster is just as long as the tube and does not overlap itself.) A) 202.8 cm2 B) 637.1 cm2 C) 203 cm2 D) 319 cm2 E) 637 cm2 Answer: E Topic: Conversion of Units 36) Conversion of Units: A spherical fruit has a radius of 3.23 cm. What is the volume of the fruit in cubic meters? A) 1.41 × 10-4 m3 B) 1.41 m3 C) 4.23 × 10-4 m3 D) 4.23 m3 Answer: A Topic: Conversion of Units 37) Conversion of Units: A thick-walled metal pipe of length 0.200 m has an inside diameter of 20.0 mm and an outside diameter of 2.40 cm. What is the total surface area of the pipe, counting the ends, in square centimeters? A) 276 cm2 B) 277 cm2 C) 278 cm2 D) 279 cm2 Answer: D Topic: Conversion of Units
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38) Conversion of Units: The radius of the earth is 3963 mi. Which one of the following numbers is closest to the surface area of the earth? (1.0 mi = 1609 m) A) 4.9 × 107 m2 B) 1.3 × 1014 m2 C) 2.6 × 1014 m2 D) 5.1 × 1014 m2 Answer: D Topic: Conversion of Units 39) Conversion of Units: A large school district has 300 school buses. If each school bus is used 3.0 hours each day, the average speed of the school buses is 15 mi/h, and the fuel economy of the buses is 10 mi/gal. How much does it cost to run these buses for 22 school days if gasoline costs $4.10 a gallon? A) $60,000 B) $120,000 C) $180,000 D) $240,000 Answer: B Topic: Conversion of Units 40) Conversion of Units: A 2.00-qt bottle of soda is on sale for $1.29. What should be the price of a 2.00-L bottle of the same soda to yield the same value? (1.00 qt = 0.947 L) Answer: $1.36 Topic: Conversion of Units 41) Conversion of Units: In a country where the unit of currency is the Passi, kerosene costs 130 Passi per liter, and one dollar buys 227 Passi. What is the cost of kerosene in dollars per gallon? (1.00 gal = 3.79 L) Answer: $2.17 per gallon Topic: Conversion of Units 42) Conversion of Units: The tank of a certain car holds 16 gallons of gasoline. (1.00 gal = 3.785 L) (a) How many liters of gasoline does this tank hold? (b) How many kilometers can the car travel on one tank if it gets 25 miles per gallon? Answer: (a) 61 L (b) 640 km Topic: Conversion of Units
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1.2.5 Density 1) Density: The mass of Mars, 6.40 × 1023 kg, is about one-tenth that of Earth, and its radius, 3395 km, is about half that of Earth. What is the mean density (mass divided by volume) of Mars in kilograms per cubic meter? A) 9.76 × 102 kg/m3 B) 1.95 × 103 kg/m3 C) 3.90 × 103 kg/m3 D) 7.81 × 103 kg/m3 Answer: C Topic: Density 2) Density: The average density of blood is 1.06 × 103 kg/m3. If you donate a pint of blood to the Red Cross, how many grams of blood have you donated? (2.00 pt = 1.00 qt, 1.00 L = 1000 cm3, 1.00 qt = 0.947 L, and density is mass per unit volume.) A) 502 g B) 0.502 g C) 5020 g D) 5.02 × 105 g E) 5.02 g Answer: A Topic: Density 3) Density: Concrete is sold by the cubic yard. What is the mass, in kilograms, of 1.00 cubic yard of concrete that is 5.00 times as dense as water? (1.00 m = 1.094 yd, a cubic meter of water has a mass of 1000 kg, and density is mass per unit volume.) A) 764 kg B) 6550 kg C) 2420 kg D) 8730 kg E) 3820 kg Answer: E Topic: Density
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4) Density: A porch roof that slopes upward at 45° measures 3.0 m × 5.0 m. It is covered with a slab of insulating material that is 2.0 cm thick. If the density of the insulation is 15 kg/m3, what is the weight of the insulation, in pounds, on the roof? (1.00 kg weighs 2.2 lb and density is mass per unit volume.) A) 4.5 lb B) 9.0 lb C) 20 lb D) 990 lb E) 9.9 lb Answer: E Topic: Density 1.2.6 Dimensional Analysis 1) Dimensional Analysis: If we find v = A λ, where λ is a length and v is a speed, what are the SI units for A? A) s-1 B) m2/s C) m/s2 D) s E) kg ∙ m/s Answer: A Topic: Dimensional Analysis 2) Dimensional Analysis: The rate R at which paint can be sprayed from a spray gun can be expressed as R = a · t. If R is measured in m3/s, and time t is measured in seconds, what are the SI units of a? A) m3 B) m3s C) m3s3 D) m3/s E) m3/s2 Answer: E Topic: Dimensional Analysis 3) Dimensional Analysis: The distance d through which a beam of length L is deflected when it is subjected to a fixed load may be described by the relationship d = RL2. What are the SI units of the constant R? A) m3 B) m2 C) m D) m-1 E) R is dimensionless Answer: D Topic: Dimensional Analysis 25 ..
4) Dimensional Analysis: The position, x, of an object is given by the equation x = A + Bt + Ct2, where t refers to time. What are the dimensions of A, B, and C? A) distance, distance, distance B) time, time, time C) distance, time, time2 D) distance, distance/time, distance/time2 E) distance/time, distance/time2, distance/time3 Answer: D Topic: Dimensional Analysis 5) Dimensional Analysis: Using dimensional analysis, which one of the following equations is dimensionally correct? In these equations, x has units of meters, t has units of seconds, v has units of meters per second, and a has units of meters per second2. A) x = v/t B) v = 2ax C) t2 = x/a D) x2 = 2av E) x = at Answer: C Topic: Dimensional Analysis 6) Dimensional Analysis: In Einstein's famous equation E = mc2, describing the relationship between matter and energy, E stands for energy, m stands for mass, and c is the speed of light in vacuum. What are the SI units of E? A) kg/s B) kg/s2 C) kg ∙ m/s2 D) s2 / (kg ∙ m) E) kg ∙ m2 / s2 Answer: E Topic: Dimensional Analysis 7) Dimensional Analysis: The kinetic energy K of an object of mass m moving with speed v is given by the formula K =
mv2. The SI unit of kinetic energy is the joule, J. Use this formula to
express the joule in terms of the fundamental SI quantities of mass, length, and time. A) J = kg ∙ m/s B) J = kg ∙ m/s2 C) J = kg2 ∙ m2/s2 D) J = kg ∙ m2/s2 Answer: D Topic: Dimensional Analysis
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8) Dimensional Analysis: The gravitational force of attraction F between two tiny masses m1 and . In the SI system, force has units of kg ∙
m2 that are separated by a distance r is F = G
m/s2 . Use the given gravitational force formula to determine the SI units of G in terms of the fundamental quantities of mass, length, and time. Answer: Topic: Dimensional Analysis 9) Dimensional Analysis: The speed v of an object falling with a constant acceleration g can be expressed in terms of g and the distance traveled from the point of release, h, as v = agbhc, where a, b, and c, are dimensionless constants. What must be the values of b and c? Answer: b = 1/2, c = 1/2 Topic: Dimensional Analysis 10) Dimensional Analysis: The period P of oscillation of a pendulum (the time interval needed to complete one full oscillation) can be expressed in terms of the mass m of the plumb bob, the length L of the string, and the acceleration due to gravity, g, as P =kmbLcgd, where k, b, c, and d are dimensionless constants. What must be the values of b, c, and d? Answer: b = 0, c = 1/2, d = -1/2 Topic: Dimensional Analysis 11) Dimensional Analysis: Newton's second law, F = ma, relates force F, mass m, and acceleration a. Use this equation to deduce the SI units of force. A) kg ∙ m/s B) s2 / (kg ∙ m) C) m/s2 D) kg ∙ m/s2 E) m2/s2 Answer: D Topic: Dimensional Analysis 1.2.7 Estimation 1) Estimation: Estimate how many pennies would you have to stack to reach from the floor to an average 8-ft ceiling. A) 2 × 103 B) 2 × 102 C) 2 × 104 D) 2 × 105 E) 2 × 106 Answer: A Topic: Estimation 27 ..
2) Estimation: Estimate the number of times the earth will rotate on its axis during a human's lifetime. A) 3 × 104 B) 3 × 105 C) 3 × 106 D) 3 × 107 E) 3 × 108 Answer: A Topic: Estimation 3) Estimation: Estimate the thickness, in meters, of an ordinary sheet of paper. A) 10-4 m B) 10-5 m C) 10-6 m D) 10-7 m E) 10-8 m Answer: A Topic: Estimation 4) Estimation: Which of the following is the most reasonable estimate of the number of characters (typed letters or numbers) in a 609-page book? Assume an average of 194 words per page and a reasonable average number of letters per word. A) 5 × 105 char B) 5 × 107 char C) 5 × 106 char D) 5 × 104 char Answer: A Topic: Estimation 5) Estimation: A marathon race is 26 mi and 385 yd long. Estimate how many strides would be required to run a marathon. Assume a reasonable value for the average number of feet/stride. A) 4.5 × 104 strides B) 4.5 × 103 strides C) 4.5 × 105 strides D) 4.5 × 106 strides Answer: A Topic: Estimation
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6) Estimation: Estimate the number of times an average person's heart beats in a lifetime. Assume the average heart rate is 69 beats/min and a life span of 75 years. A) 3 × 109 beats B) 3 × 108 beats C) 3 × 1010 beats D) 3 × 107 beats Answer: A Topic: Estimation
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College Physics, 1e (Pearson) Topic 2 Vectors 2.1 Conceptual Questions 2.1.1 Graphical Addition 1) Graphical Addition: Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum A) is equal to 2.0 m. B) could be as small as 2.0 m or as large as 12 m. C) is equal to 12 m. D) is equal to 8.6 m. Answer: B Topic: Graphical Addition 2) Graphical Addition: Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant? A) 10 mm B) 20 mm C) 40 mm D) 80 mm Answer: C Topic: Graphical Addition 3) Graphical Addition: The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors. A) True B) False Answer: B Topic: Graphical Addition 4) Graphical Addition: A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector? Answer: Between 7.0 m and 17.0 m Topic: Graphical Addition 5) Graphical Addition: If
+
=
and their magnitudes are given by A + B = C, then the
vectors and are oriented A) perpendicular relative to one other. B) parallel to each other (in the same direction). C) antiparallel to each other (in opposite directions). D) It is impossible to know from the given information. Answer: B Topic: Graphical Addition 1 ..
6) Graphical Addition: If directed in the same direction. A) True B) False Answer: A Topic: Graphical Addition
= 0, then the vectors
and
have equal magnitudes and are
7) Graphical Addition: If three vectors add to zero, they must all have equal magnitudes. A) True B) False Answer: B Topic: Graphical Addition 8) Graphical Addition: The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between these two vectors is A) 90°. B) 180°. C) 60°. D) 0°. E) 270°. Answer: D Topic: Graphical Addition 9) Graphical Addition: The sum of two vectors of fixed magnitudes has its minimum magnitude when the angle between these vectors is A) 0°. B) 90°. C) 270°. D) 180°. E) 360°. Answer: D Topic: Graphical Addition 10) Graphical Addition: Vectors and which one of the following statements?
obey the equation
A) Vectors
and
are at right angles to each other.
B) Vectors
and
point in the same direction.
C) Vectors
and
have the same magnitudes.
D) The magnitude of is the negative of the magnitude of Answer: C Topic: Graphical Addition
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+
.
= 0. These vectors satisfy
11) Graphical Addition: Consider two vectors
and
shown in the figure. The difference
-
and
shown in the figure. The difference
-
is best illustrated by
A) choice (a) B) choice (b) C) choice (c) D) choice (d) Answer: C Topic: Graphical Addition 12) Graphical Addition: Consider two vectors is best illustrated by
A) choice (a) B) choice (b) C) choice (c) D) choice (d) Answer: B Topic: Graphical Addition
3 ..
13) Graphical Addition: Refer to the figure, which shows four vectors
(a) Vector A)
+
B)
-
.
C)
-
.
+
B)
-
and
is given by
as expressed in terms of vectors
and
is given by
,
, and
.
.
(b) Vector A)
as expressed in terms of vectors
,
. .
C) - . Answer: (a) B (b) A Topic: Graphical Addition 2.1.2 Components 1) Components: If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude. A) True B) False Answer: B Topic: Components 2) Components: If a vector's components are all negative, then the magnitude of the vector is negative. A) True B) False Answer: B Topic: Components
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3) Components: The magnitude of a vector can never be less than the magnitude of any of its components. A) True B) False Answer: A Topic: Components 4) Components: The magnitude of a vector an only zero if all of its components are zero. A) True B) False Answer: A Topic: Components 5) Components: If a vector has components Ax < 0, and Ay > 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90°. B) 90° to 180°. C) 180° to 270°. D) 270° to 360°. E) It cannot be determined without additional information. Answer: B Topic: Components 6) Components: If a vector has components Ax < 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90°. B) 90° to 180°. C) 180° to 270°. D) 270° to 360°. E) It cannot be determined without additional information. Answer: C Topic: Components 7) Components: If a vector has components Ax > 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90°. B) 90° to 180°. C) 180° to 270°. D) 270° to 360°. E) It cannot be determined without additional information. Answer: D Topic: Components
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8) Components: The eastward component of vector
is equal to the westward component of
vector and their northward components are equal. Which one of the following statements must be correct for these two vectors? A) Vector
is parallel to vector
.
B) Vector
is antiparallel (in the opposite direction) to vector
C) Vector
must be perpendicular to vector
.
.
D) The magnitude of vector
must be equal to the magnitude of vector
E) The angle between vector Answer: D Topic: Components
and vector
.
must be 90°.
9) Components: Vector is along the +x-axis and vector is along the +y-axis. Which one of the following statements is correct with respect to these vectors? A) The x component of vector
is equal to the x component of vector
.
B) The y component of vector
is equal to the y component of vector
.
C) The x component of vector
is equal to the y component of vector
.
D) The y component of vector Answer: D Topic: Components
is equal to the x component of vector
.
2.2 Problems 2.2.1 Components 1) Components: A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector? Answer: 42 m/s at 31° north of west Topic: Components 2) Components: The x component of vector
is 8.7 units, and its y component is -6.5 units. The
magnitude of is closest to A) 9.9 units. B) 7.9 units. C) 8.9 units. D) 11 units. E) 12 units. Answer: D Topic: Components
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3) Components: When rolled down a mountainside at 7.0 m/s, the horizontal component of its velocity vector was 1.8 m/s. What was the angle of the mountain surface above the horizontal? A) 75° B) 57° C) 33° D) 15° Answer: A Topic: Components 4) Components: When Jeff ran up a hill at 7.0 m/s, the horizontal component of his velocity vector was 5.1 m/s. What was the vertical component of Jeff's velocity? A) 4.8 m/s B) 4.3 m/s C) 3.8 m/s D) 3.4 m/s Answer: A Topic: Components 5) Components: The x component of vector
is 5.3 units, and its y component is -2.3 units. The
angle that vector makes with the +x-axis is closest to A) 340°. B) 160°. C) 250°. D) 110°. E) 23°. Answer: A Topic: Components 6) Components: A vector in the xy-plane has an x component of -7.50 units. What must be the y component of this vector so that its magnitude is 10.0 units. (Note: There are two possible answers.) Answer: +6.6 units and -6.6 units Topic: Components
7 ..
7) Components: A displacement vector is 34.0 m in length and is directed 60.0° east of north. Selecting from the choices in the table below, what are the components of this vector?
choice 1 2 3 4 5
Northward component 29.4 m 18.2 m 22.4 m 17.0 m 25.2 m
Eastward component 17.0 m 28.1 m 11.5 m 29.4 m 18.2 m
A) choice 1 B) choice 2 C) choice 3 D) choice 4 E) choice 5 Answer: D Topic: Components 8) Components: A player throws a football 50.0 m at 61.0° north of west. What is the westward component of the displacement of the football? A) 64.7m B) 55.0 m C) 0.00 m D) 74.0 m E) 24.2 m Answer: E Topic: Components 9) Components: A vector
has components Ax = 12.0 m and Ay = 5.00 m.
(a) What is the angle that vector (b) What is the magnitude of vector Answer: (a) 22.6° (b) 13.0 m Topic: Components
makes with the +x-axis? ?
10) Components: The x and y components of a vector in a horizontal plane are 4.00 m and 3.00 m, respectively. (a) What is the magnitude of this vector? (b) What angle does this vector make with the positive +y-axis. Answer: (a) 5.00 m (b) 53.1° Topic: Components
8 ..
11) Components: A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity? A) 18.1 m/s B) 15.6 m/s C) 8.45 m/s D) 12.6 m/s E) 9.33 m/s Answer: A Topic: Components 12) Components: The magnitude of
is 5.5 m, and this vector lies in the second quadrant and
makes an angle of 34 ° with the +y-axis. The components of A) Ax = -3.1 m, Ay = 4.6 m. B) Ax = 3.1 m, Ay = -4.6 m. C) Ax = 4.6 m, Ay = -3.1 m. D) Ax = -4.6 m, Ay = 3.1 m. E) Ax = -4.6 m, Ay = -3.1 m. Answer: A Topic: Components 13) Components: The components of vectors Bx = -9.2 Cx = -4.5 By = -6.1 Cy = 4.3 The angle (less than 180°) between vectors A) 77°. B) 103°. C) 10°. D) 170°. E) 84°. Answer: A Topic: Components
and
and
are closest to:
are given as follows:
is closest to
2.2.2 Addition by Components 1) Addition by Components: A car travels 20 km west and then 20 km south. Use components to find the magnitude of its displacement vector? A) 0 km B) 20 km C) 28 km D) 40 km Answer: C Topic: Addition by Components
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9) Addition by Components: The figure shows two vectors
and
magnitudes and directions. The vector
-
(a) What is the magnitude of vector
is given by
=
, along with their
.
?
(b) What angle does vector make with the +x-axis? Answer: (a) 6.6 (b) 170° Topic: Addition by Components 10) Addition by 1. Components: Displacement vector axis. Displacement vector
is 5.5 cm long and points along the +x-
is 7.5 cm long and points at +30° to the -x-axis.
(a) Determine the x and y components of vector
.
(b) Determine the x and y components of vector . (c) Determine the x and y components of the resultant of these two vectors. (d) Determine the magnitude and direction of the resultant of these two vectors. Answer: (a) Ax = 5.5 cm, Ay = 0 cm (b) Bx = -6.5 cm, By = 3.8 cm (c) Rx = -1.0 cm, Ry = 3.8 cm (d) 3.9 cm at 75° above the -x axis Topic: Addition by Components
12 ..
11) Addition by 1. Components: Displacement vector the +x-axis. Displacement vector vector
is 75 cm long and points at 30° above
is 25 cm long and points along the -x-axis. Displacement
is 40 cm long and points at 45° below the -x-axis.
(a) Determine the x and y components of vector
.
(b) Determine the x and y components of vector
.
(c) Determine the x and y components of vector . (d) Determine the x and y components of the resultant of these three vectors. (e) Determine the magnitude and direction of the resultant of these three vectors. Answer: (a) Ax = 65 cm, Ay = 38 cm (b) Bx = -25 cm, By = 0 cm (c) Cx = -28 cm, Cy = -28 cm (d) Rx = 12 cm, Ry = 9 cm (e) 15 cm at 38° above the +x-axis Topic: Addition by Components 12) Addition by 1. Components: Vector
= 4.00 m points eastward and vector
points southward. The resultant vector + A) 5.00 m at an angle of 36.9° south of east. B) 5.00 m at an angle of 53.1° south of east. C) 5.00 m at an angle of 71.6° south of east. D) 5.00 m at an angle of 18.4° south of east. E) 5.00 m at an angle of 26.6° south of east. Answer: A Topic: Addition by Components 13) Addition by 1. Components: Vector east. Vector
= 3.00 m
is given by
has a magnitude of 6.0 m and points 30° north of
has a magnitude of 4.0 m and points 30° east of north. The resultant vector
is given by A) 0.70 m at an angle of 42° north of east. B) 14 m at an angle of 42° north of east. C) 1.1 m at an angle of 42° north of east. D) 9.7 m at an angle of 42° north of east. E) 2.0 m at an angle of 42° north of east. Answer: D Topic: Addition by Components
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+
14) Addition by 1. Components: Vector east. Vector
has a magnitude of 6.0 m and points 30° north of
has a magnitude of 4.0 m and points 30° west of north. The resultant vector
+
is given by A) 9.8 m at an angle of 64° east of north. B) 9.8 m at an angle of 26° north of east. C) 7.2 m at an angle of 26° east of north. D) 3.3 m at an angle of 26° north of east. E) 3.3 m at an angle of 64° east of north. Answer: C Topic: Addition by Components 15) Addition by 1. Components: Vector east. Vector
has a magnitude of 6.0 m and points 30° north of
has a magnitude of 4.0 m and points 30° west of south. The resultant vector
+
is given by A) 2.7 m at an angle of 8.3° south of east. B) 2.7 m at an angle of 8.3° east of south. C) 3.2 m at an angle of 8.3° east of south. D) 3.2 m at an angle of 8.3° south of east. E) 2.3 m at an angle of 8.3° south of east. Answer: D Topic: Addition by Components 16) Addition by 1. Components: Vector east. Vector
has a magnitude of 6.0 m and points 30° south of
has a magnitude of 4.0 m and points 30° west of south. The resultant vector
is given by A) 7.2 m at an angle of 64° south of east. B) 3.3 m at an angle of 64° south of east. C) 9.8 m at an angle of 26° south of east. D) 9.8 m at an angle of 64° south of east. E) 3.3 m at an angle of 26° south of east. Answer: A Topic: Addition by Components
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+
17) Addition by 1. Components: Vector
has a magnitude of 4.0 m and points 30° south of east.
Vector has a magnitude of 2.0 m and points 30° north of west. The resultant vector given by A) 10.0 m at an angle 30° south of east. B) 10.0 m at an angle 60° east of south. C) 2.0 m at an angle 60° south of east. D) 2.0 m at an angle 30° south of east. E) 1.0 m at an angle 30° east of south. Answer: D Topic: Addition by Components 18) Addition by 1. Components: Vector north. Vector
+
has a magnitude of 7.0 m and points 30° east of
has a magnitude of 5.0 m and points 30° west of south. The resultant vector
+ is given by A) 10.0 m at an angle 60° north of east. B) 10.0 m at an angle 30° east of north. C) 2.0 m at an angle 30° north of east. D) 2.0 m at an angle 60° north of east. E) 1.0 m at an angle 60° east of north Answer: D Topic: Addition by Components 19) Addition by 1. Components: Vector south. Vector
has a magnitude of 6.0 m and points 30° east of
has a magnitude of 4.0 m and points 30° west of north. The resultant vector
+ is given by A) 2.0 m at an angle of 30° north of west. B) 2.0 m at an angle of 30° east of south. C) 10.0 m at an angle of 60° north of west. D) 10.0 m at an angle of 60° east of south. E) 1.0 m at an angle of 60° north of west. Answer: B Topic: Addition by Components
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is
20) Addition by 1. Components: Vector
has a magnitude of 8.0 m and points east, vector
has a magnitude of 6.0 m and points north, and vector
has a magnitude of 5.0 m and points
west. The resultant vector + + is given by A) 2.0 m at an angle 63° north of east. B) 2.0 m at an angle 63° east of north. C) 6.7 m at an angle 63° east of north. D) 6.7 m at an angle 63° north of east. E) 3.8 m at an angle 67° north of east Answer: D Topic: Addition by Components 21) Addition by 1. Components: The figure shows three vectors and their magnitudes and relative directions. The magnitude of the resultant of the three vectors is closest to
A) 19. B) 16. C) 13. D) 10. E) 7.0. Answer: C Topic: Addition by Components
16 ..
22) Addition by 1. Components: Find the magnitude and direction of the resultant of the three force vectors, , , and , shown in the figure. These vectors have the following magnitudes: A = 5.0 lb, B = 7.9 lb, and C = 8.0 lb. Express the direction of the resultant by specifying the angle it makes with the +x-axis, with counterclockwise angles taken to be positive.
Answer: 1.6 lb, 312° Topic: Addition by Components 23) Addition by 1. Components: Two boys, Joe and Sam, who are searching for buried treasure start underneath the same tree. Joe walks 12 m east and then 12 m north, while Sam walks 15 m west and then 10 m south. Both boys then stop. Find the magnitude and direction of the vector from Sam to Joe. Express the direction of this vector by specifying the angle it makes with the west-to-east direction. Answer: 35 m at 39° north of east Topic: Addition by Components 24) Addition by 1. Components: An airplane undergoes the following displacements, all at the same altitude: First, it flies 59.0 km in a direction 30.0° east of north. Next, it flies 58.0 km due south. Finally, it flies 100 km 30.0° north of west. Use components to determine how far the airplane ends up from its starting point. A) 71.5 km B) 73.0 km C) 74.4 km D) 70.1 km E) 68.7 km Answer: A Topic: Addition by Components
17 ..
25) Addition by 1. Components: Two forces are acting on an object as shown in the figure. Assume that all the quantities shown are accurate to three significant figures.
(a) What is the magnitude of the resultant force on the object? (b) What is the direction of the resultant force? Answer: (a) 185 N (b) 77.8° above the +x-axis Topic: Addition by Components 26) Addition by 1. Components: Three forces, 1, 2, and 3, each of magnitude 70 N, all act on an object as shown in the figure. The magnitude of the resultant force acting on the object is
A) 35 N. B) 70 N. C) 140 N. D) 210 N. E) 0 N. Answer: E Topic: Addition by Components
18 ..
27) Addition by 1. Components: Three forces, 1, 2, and 3, all act on an object, as shown in the figure. The magnitudes of the forces are: F1 = 80.0 N, F2 = 60.0 N, and F3 = 40.0 N. The resultant force acting on the object is given by
A) 180 N at an angle of 60.0° with respect to +x-axis. B) 60.0 N at an angle of 90.0° with respect to +x-axis. C) 20.0 N at an angle of 34.3° with respect to +x-axis. D) 35.5 N at an angle of 34.3° with respect to +x-axis. E) 40.0 N at an angle of 60.0° with respect to +x-axis. Answer: D Topic: Addition by Components
19 ..
28) Addition by 1. Components: Four vectors, , , , and , are shown in the figure. The sum of these four vectors is a vector having magnitude and direction
A) 4.0 cm, along +x-axis. B) 4.0 cm, along -x-axis. C) 4.0 cm, along +y-axis. D) 4.0 cm, along -y-axis. E) 4.0 cm, 45° above +x-axis. Answer: D Topic: Addition by Components 29) Addition by 1. Components: Vector east; vector
has a magnitude of 8.0 m and points 30° north of
has a magnitude of 6.0 m and points 30° west of north; and vector
magnitude of 5.0 m and points 30° west of south. The resultant vector A) 2.7 m at an angle 74° north of east. B) 5.9 m at an angle 74° north of east. C) 4.8 m at an angle 74° east of north. D) 5.1 m at an angle 74° north of east. E) 2.1 m at an angle 66° east of north. Answer: D Topic: Addition by Components
20 ..
+
+
has a is given by
30) Addition by 1. Components: The figure shows three vectors, , , and , having magnitudes 7.0 cm, 6.0 cm, and 4.0 cm, respectively. Find the x and y components of the resultant of these three vectors.
Answer: -11 cm (x component), -4.5 cm (y component) Topic: Addition by Components 31) Addition by 1. Components: The figure shows four vectors, , , , and , having magnitudes 10.0 m, 8.00 m, 6.00 m, and 2.00 m, respectively. Find the magnitude of the sum of these four vectors.
Answer: 14.4 m Topic: Addition by Components
21 ..
32) Addition by 1. Components: The figure shows four vectors, , , , and , having magnitudes 12.0 m, 10.0 m, 8.0 m, and 4.0 m, respectively. The sum of these four vectors is
A) 16.4 m at an angle 77.8° with respect to +x-axis. B) 16.4 m at an angle 12.3° with respect to +x-axis. C) 19.5 m at an angle 77.8° with respect to +x-axis. D) 19.5 m at an angle 12.3° with respect to +x-axis. E) 8.20 m at an angle 77.8° with respect to +x-axis. Answer: A Topic: Addition by Components
22 ..
33) Addition by 1. Components: The figure shows four vectors,
,
,
, and
. Vectors
and each have a magnitude of 7.0 cm, and vectors and each have a magnitude of 4.0 cm. Find the x and y components of the sum of these four vectors.
Answer: 0.00 cm (x component), 4.2 cm (y component) Topic: Addition by Components 34) Addition by 1. Components: The figure shows four vectors,
,
,
, and
. Vectors
and both have a magnitude of 7.0 cm, and vectors and both have a magnitude of 4.0 cm. Find the magnitude and direction of the sum of these four vectors.
Answer: 4.2 cm along the +y-axis Topic: Addition by Components 23 ..
35) Addition by 1. Components: The figure shows three vectors,
,
, and
magnitudes. Determine the magnitude and direction of the vector given by
, along with their -
-
.
Answer: 85 m at 5.4° above the +x-axis Topic: Addition by Components 36) Addition by 1. Components: The figure shows three vectors,
,
, and
magnitudes. Determine the magnitude and direction of the vector given by
Answer: 100 m at 31° above the +x-axis Topic: Addition by Components
24 ..
, along with their +
-
.
37) Addition by 1. Components: Three vectors, , , and , have the components shown in the table. What is the magnitude of the resultant of these three vectors? x component y component 3.50 m
-4.50 m
2.00 m
0.00 m
-5.50 m
2.50 m
A) 5.50 m B) 13.0 m C) 11.1 m D) 7.00 m E) 2.00 m Answer: E Topic: Addition by Components 38) Addition by 1. Components: Three vectors, , , and , have the components shown in the table. What angle does the resultant of these three vectors make with the +x-axis? x component y component -3.5 m
4.5 m
0.00 m
-6.5 m
5.5 m
-2.5 m
A) 24° above the +x-axis B) 24° below the +x-axis C) 66° above the +x-axis D) 66° below the +x-axis Answer: D Topic: Addition by Components
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College Physics, 1e (Pearson) Topic 3 Kinematics of Motion in One Dimension 3.1 Conceptual Questions 3.1.1 Displacement 1) Displacement: Consider a deer that runs from point A to point B. The distance the deer runs can be greater than the magnitude of its displacement, but the magnitude of the displacement can never be greater than the distance it runs. A) True B) False Answer: A Topic: Displacement 2) Displacement: Which of the following quantities has units of a displacement? (There could be more than one correct choice.) A) 32 ft/s2 vertically downward B) 40 km southwest C) 9.8 m/s2 D) -120 m/s E) 186,000 mi Answer: B, E Topic: Displacement 3) Displacement: Suppose that an object travels from one point in space to another. Make a comparison between the magnitude of the displacement and the distance traveled by this object. A) The displacement is either greater than or equal to the distance traveled. B) The displacement is always equal to the distance traveled. C) The displacement is either less than or equal to the distance traveled. D) The displacement can be either greater than, smaller than, or equal to the distance traveled. Answer: C Topic: Displacement 3.1.2 Velocity 1) Velocity: Consider a car that travels between points A and B. The car's average speed can be greater than the magnitude of its average velocity, but the magnitude of its average velocity can never be greater than its average speed. A) True B) False Answer: A Topic: Velocity
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2) Velocity: Which of the following quantities has units of a velocity? (There could be more than one correct choice.) A) 40 km southwest B) -120 m/s C) 9.8 m/s2 downward D) 186,000 mi E) 9.8 m/s downward Answer: B, E Topic: Velocity 3) Velocity: When is the average velocity of an object equal to the instantaneous velocity? A) only when the velocity is increasing at a constant rate B) only when the velocity is decreasing at a constant rate C) when the velocity is constant D) always E) never Answer: C Topic: Velocity 4) Velocity: You drive 6.0 km at 50 km/h and then another 6.0 km at 90 km/h. Your average speed over the 12 km drive will be A) greater than 70 km/h. B) equal to 70 km/h. C) less than 70 km/h. D) exactly 38 km/h. E) It cannot be determined from the information given because we must also know directions traveled. Answer: C Topic: Velocity 3.1.3 Acceleration 1) Acceleration: If the velocity of an object is zero at some point, then its acceleration must also be zero at that point. A) True B) False Answer: B Topic: Acceleration 2) Acceleration: Which of the following situations is impossible? A) An object has velocity directed east and acceleration directed west. B) An object has velocity directed east and acceleration directed east. C) An object has zero velocity but non-zero acceleration. D) An object has constant non-zero acceleration and changing velocity. E) An object has constant non-zero velocity and changing acceleration. Answer: E Topic: Acceleration 2 ..
3) Acceleration: If the acceleration of an object is zero, then that object cannot be moving. A) True B) False Answer: B Topic: Acceleration 4) Acceleration: If the velocity of an object is zero, then that object cannot be accelerating. A) True B) False Answer: B Topic: Acceleration 5) Acceleration: Suppose that a car traveling to the west begins to slow down as it approaches a traffic light. Which of the following statements about its acceleration is correct? A) The acceleration is toward the east. B) Since the car is slowing down, its acceleration must be negative. C) The acceleration is zero. D) The acceleration is toward the west. Answer: A Topic: Acceleration 6) Acceleration: An auto manufacturer advertises that their car can go "from zero to sixty in eight seconds." This is a description of what characteristic of the car's motion? A) average speed B) instantaneous speed C) average acceleration D) instantaneous acceleration E) displacement Answer: C Topic: Acceleration 7) Acceleration: An object moving in the +x direction experiences an acceleration of +2.0 m/s2. This means the object A) travels 2.0 m in every second. B) is traveling at 2.0 m/s. C) is decreasing its velocity by 2.0 m/s every second. D) is increasing its velocity by 2.0 m/s every second. Answer: D Topic: Acceleration
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8) Acceleration: Suppose that a car traveling to the east (+x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration must be correct? A) Its acceleration is in the +x direction. B) Its acceleration is in the -x direction. C) Its acceleration is zero. D) Its acceleration is decreasing in magnitude as the car slows down. Answer: B Topic: Acceleration 9) Acceleration: Suppose that a car traveling to the west (-x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration must be correct? A) Its acceleration is positive. B) Its acceleration is negative. C) Its acceleration is zero. D) Its acceleration is decreasing in magnitude as the car slows down. Answer: A Topic: Acceleration 10) Acceleration: Suppose that an object is moving with a constant velocity. Which statement concerning its acceleration must be correct? A) The acceleration is constantly increasing. B) The acceleration is constantly decreasing. C) The acceleration is a constant non-zero value. D) The acceleration is equal to zero. Answer: D Topic: Acceleration 11) Acceleration: If the velocity of an object is zero at one instant, what is true about the acceleration of that object? (There could be more than one correct choice.) A) The acceleration could be positive. B) The acceleration could be negative. C) The acceleration could be zero. D) The acceleration must be zero. Answer: A, B, C Topic: Acceleration 12) Acceleration: Under what condition is average velocity equal to the average of the object's initial and final velocity? A) This can only occur if there is no acceleration. B) The acceleration is constant. C) This can occur only when the velocity is zero. D) The acceleration must be constantly increasing. E) The acceleration must be constantly decreasing. Answer: B Topic: Acceleration
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