University of the Philippines College of Science

Physics 71 Set A Third Long Exam First Semester AY 2011-2012

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Physics 71/Third Long Exam A

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Instructions: Choose the letter of the best otherwise. Useful constants: h 3 i −11 m G = 6.67 × 10 kg·s2 g near surface of the Earth = 9.81 m/s2 Mass of Sun = 1.99 × 1030 [kg] Mass of Earth = 5.97 × 1024 [kg] Radius of Earth = 6.38 × 106 [m]

1st Sem AY 2011-2012

answer. Ignore air resistance unless stated

3 Density of water = 1000 kg/m Density of seawater = 1030 kg/m3 Atmosphere pressure = 1 [atm] = 101325 [Pa]

1. Center of Gravity Which of the following statements is always TRUE about the center of gravity? (a) It is located within the object. (b)It is the object’s center of mass. (c) It is at the object’s geometric center. (d)The torque due to weight about this point is zero. 2. Non-uniform beam I. The figure shows two configurations in which a beam (mass = 45.0 [kg], length = 4.00 [m]) of nonuniform mass distribution is in static equilibrium. How far is the center of gravity of the beam from its left end? (a) 0.667 [m] (b)1.00 [m] (c) 1.50 [m]

(d)1.67 [m] (e)2.50 [m]

3. In Equilibrium Which of the following situations satisfy the conditions for static equilibrium? I. A stationary rod pivoted at one end. II. A bowling ball rolls without slipping at a constant non-zero speed along a horizontal alley. III. A cable wrapped around a cylinder that can rotate about its axis, unwinds without slipping at a constant speed. (a) I only (b)II only (c) III only

(d)I and III only (e)II and III only

Physics 71/Third Long Exam A

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4. Equilibrium A 5.00 [kg] uniform rod, of length 2.00 [m], is placed on top of a weighing scale on one end and hung with a rope at the other end such that it is in static equilibrium as shown in the figure. What is the reading on the weighing scale? (a) 9.81 [N] (b)19.6 [N] (c)24.5 [N]

1st Sem AY 2011-2012

(d)49.1 [N]

5. Wiring Three different wires, I, II, and III, with lengths L, 2L, and 3L and cross-section areas 3A, 2A, and A respectively, are stretched with the same amount of force F. All wires are stretched by a length of L/20. Which wire has the greatest Young’s Modulus if the stress is less than the proportional limit? (a) I (b)II (c)III 6. YM 1. An string of length L and cross sectional area A is stretched by some tensile force small enough such that Hooke’s law is obeyed. What is the proportionality constant between the magnitude of the tensile force F to the elongation ∆L of the string? (Y is Young’s Modulus) (a) Y (b)YA (c)YA/L (d)YL (e)YL/A 7. Scallop A scallop forces open its shell with an elastic material called abductin whose 6 2 Young’s modulus is about 2.0 × 10 N/m 2 . If this piece of abductin is 3.0 [mm] thick and has a cross-sectional area of 0.50 cm , how much potential energy does it store when compressed to 1.0 [cm] assuming the stress is less than the proportional limit? (a) 0.017 [J] (b)0.025 [J] (c)0.050 [J] (d)0.100 [J] (e)0.150 [J] 8. Gravitational Force I. Consider two point masses each of mass m at positions x = a and x = −a. At which point is the magnitude of the net gravitational force on a test particle the greatest?

(a) I and III

(b)II

(c)III

(d)IV

(e)V

Physics 71/Third Long Exam A

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1st Sem AY 2011-2012

9. Force. An unknown object with mass of 75.5 [kg] is located at a height of 6.35 × 103 [m] from the surface of the Earth. What is the magnitude of the gravitational force on the object due to the Earth? (d)7.46 × 108 [N]

(a)737 [N] (b)4.71 × 109 [N] (c)1.16 × 10−4 [N]

(e)741 [N]

10. Gundam 00 In the year 3000, humans were able to build a 500. [km] space elevator in an attempt to harness solar energy better. A space elevator employee of mass 100 [kg] tries to weigh himself at a height 500. [km] above the ground. What percentage of his weight on the Earth’s surface does he measure? (a) 86.0%

(b)92.7%

(c)100%

(d)108%

(e)116%

11. Launch Consider a planet that is thrice as massive and with radius twice that of Earth. At what minimum speed should an artificial object be launched so that it reaches a height equal to Earth’s radius? (a)5.59 × 103 [m/s] (b)7.90 × 103 [m/s]

(c)1.12 × 104 [m/s] (d)6.24 × 104 [m/s]

12. Grazing orbit. What is the speed of a satellite in circular orbit at a height r = rE = 6.38 × 106 [m] above the surface of the planet Earth? (d)7.90 × 103 ms (a)2.53 × 103 ms (b)3.95 × 103 ms (e)1.12 × 104 ms (c)5.59 × 103 ms 13. Elliptical Orbit. A body traces an elliptical path with the Sun at one of its foci. At which point is the body fastest? (a) I (b)II (c) III (d)IV (e) The speed of the body at any point in its path is constant.

Physics 71/Third Long Exam A

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1st Sem AY 2011-2012

14. Kepler Which of the following statements is/are FALSE? I. The angular momentum of Earth about the Sun is constant at all points in the orbit. II. Earth travels faster at aphelion than at perihelion. III. Mercury (with a semi-major axis of 57.9×106 [km]) has a shorter orbital period than the Earth (with a semi-major axis of 149×106 [km]. (a) I only

(b)II only

(c)III only

(d)I and II only (e)I and III only

15. Lift works A hydraulic lift is used to jack a 980-[kg] car 12 [cm] off the floor. The diameter of the output piston is 18 [cm] and the input force is 250 N. If the input piston moves 13 [cm] uniformly in 1.0 [s] each stroke, how high does the car moves up in each stroke? (a) 2.3 [mm] (b)3.1 [mm] (c) 3.4 [mm] (d)4.7 [mm] (e) 9.2 [mm] h

kg m3

16. Cube. A solid box with a uniform density of 2500 h i (ρ = 1000 mkg3 ). Which of the following is TRUE?

i

is completely immersed in water

I. The volume of the water displaced by the box is equal to the volume of the box. II. The buoyant force on the object is less than the weight of the box. III. The weight of the box is less than the weight of the water displaced by the box. (a) I only (b)II only (c) III only

(d)I and II only (e)I, II and III

17. Ball in water. A spherical h i ball with a radius of 0.300 [m] is in equilibrium floating in seawater ρ = 1030 mkg3 . If 1/8 of the volume of the ball is immersed in the water, what is the buoyant force on the ball? (a) 116 [N]

(b)143 [N]

(c)291 [N]

(d)999 [N]

(e)1142 [N]

Physics 71/Third Long Exam A

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1st Sem AY 2011-2012

18. Buoy. A cube of density ρc , mass m and volume V is floating in seawater of density ρs . What is the magnitude of the buoyant force on the cube? (a)ρs V g (b)(ρc − ρs )V g (c)(ρc + ρs )V g

(d) 21 (ρc + ρs )V g (e)mg

19. Capital L Liter. Water streams out of a faucet of opening radius 0.75 [cm] at a rate 3of 1.0 s . What is the speed of the water stream as it leaves the faucet? (1 [mL] = 1 cm ) (a)5.7 ms (b)4.2 ms (c)1.8 ms (d)0.32 ms (e)0.18 ms 20. Volume Flow Rate. Water is flowing in a pipe with a varying area. At 2cross-sectional the front end, the cross sectional area of the pipe is 0.070 m and the magnitude of the fluid velocity is 3.50 [m/s]. What is the volume flow rate if the cross-sectional area doubled at the other end? h i h 3i h 3i m m m3 m (c)1.75 s (e)3.50 ms (a) 0.245 s (b)0.245 s (d)1.75 s 21. Green. A stream of water passes through a garden hose horizontally at speed v and from a certain height h above the ground. The water reaches the ground at range R. If you pinch the hose such that the hole radius becomes halved, what will be the range of the water stream? (a)4R (b)2R (c)R (d)R/2 (e)R/4 22. Flow. Water flows through a pipe as shown in the figure. The pipe has a circular cross-section throughout. The radius of the pipe narrows from 0.40 [m](point A) to 0.20 [m](point B). mAt point A, the fluid is moving at 0.10 s . What is the magnitude of the pressure difference between points A and B? (a) 100 [Pa] (b)75 [Pa] (c) 50 [Pa]

(d)25 [Pa] (e)15 [Pa]

23. SHM. The position of an object undergoing simple harmonic motion is described by the equation x = A sin(ωt). Which of the following is TRUE? (v and a are the velocity and acceleration of the object along the x-axis, respectively.) (a)vx = −ωx (b)vx = ωx (c)ax = −ω 2 x

(d)The period of the motion is 1/ω. (e)The total kinetic energy of the object is constant.

Physics 71/Third Long Exam A

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1st Sem AY 2011-2012

24. Punching bag. A punching bag suspended from the ceiling oscillates about the vertical in simple harmonic motion. If the punching bag is released from rest at a small angle from the vertical, it swings to the other side for 0.50 [s] before momentarily coming to rest. What is the frequency of oscillation of the punching bag? (a) 4.0 [Hz]

(b)2.0 [Hz]

(c)1.0 [Hz]

(d)0.5 [Hz]

25. Spring. The motion of a 12.5 [kg] mass on an ideal spring as a function of time is shown in the figure. If the spring moves in a simple harmonic motion, what is its force constant? N N (a)123 m (d)1.97 × 103 m N N (b)247 m (e)157 m N (c)39.3 m 26. Oscillating spring. A small box of mass m is hung on a vertical spring with spring constant k. From equilibrium, the mass is stretched by some distance ∆x0 and released from rest at t = 0. On which quantities below does the total mechanical energy of the spring-mass system at some time t depend? I. ∆x0 II. k III. position of the small box at time t (a) I only (b)II only (c) III only

(d)I and II only (e)I, II and III

27. Two springs. Two ideal horizontal spring-mass systems A and B have the same amplitudes and periods of oscillation. If the mass in system A is four times that of system B, how much total energy does system A (EA ) have compared to system B (EB )? (a)EA = 4EB (b)EA = 2EB (c)EA = EB

(d)EA = (1/2)EB (e)EA = (1/4)EB

Physics 71/Third Long Exam A

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1st Sem AY 2011-2012

28. Simple pendulum. A 0.15 [m] simple pendulum is displaced 2.2◦ with respect to the vertical and is released from rest. The time it takes to reach its maximum speed is 0.19 [s]. If the angle is changed to 1.1◦ , how long will the pendulum reach the maximum speed? (a)0.19 [s] (b)0.10 [s] (c)0.38 [s] (d)0.036 [s] (e)0.44 [s] 29. Spring-mass in honey. A horizontal spring-mass (spring constant k, mass m) system is immersed in a tank of viscous honey. The spring was stretched by a distance s and the mass is released from rest. The spring goes back to its unstretched position with oscillations of diminishing amplitude. Which of the following can be concluded about the spring-mass system from these observations? (a) It is critically damped. (b)It is overdamped.

(c)It is underdamped. (d)It is undamped.

30. Damping N ba? An object with mass 2.00 [kg] oscillates on a spring with force constant 512 m . If the period of oscillation is 0.393 [s], what type of oscillation is manifested? (a) Overdamped (b)Undamped (c)Critically damped 31. Wave Speed. What is the speed of propagation of a transverse wave that has a frequency of 4.0 [Hz] and wavelength of 2.0 [m]? (a) 0.50 ms (b)1.0 ms (c)2.0 ms (d)8.0 ms 32. Thin wire. A thin 75 [cm] long wire has one end tied to a nail and the other end is attached to a screw that can be adjusted m to vary the tension in the wire. A transverse wave propagating at a speed of 29.1 s is produced if the screw is adjusted in such a way that the tension in the wire is 18.6 [N]. What is the mass of the thin wire? (a) 11.7 [g] (b)16.5 [g] (c)21.8 [g] (d)29.3 [g] (e)34.1 [g] 33. Wangwang. A stationary ambulance siren emits sound waves that radiate uniformly in all directions. W At a distance of 25.0 [m] from the ambulance, the intensity of the sound is 0.350 m2 . What will be the intensity of the sound at a distance of 12.0 [m] from the ambulance? (a)1.52 mW2 (b)0.729 mW2 (c)0.0806 mW2 (d)0.168 mW2 34. Algebra. Two transverse waves, y1 = A1 cos(kx + ωt) and y2 = A2 cos(kx + ωt) interfere with each other. What is the frequency of the resultant wave? (b)ω (c)2ω (d)ω + k (e)2(ω + k) (a) 21 ω

Physics 71/Third Long Exam A

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1st Sem AY 2011-2012

35. Sound Energy A student measured that a siren’s sound intensity 4.3 [m] from the source 2 is 0.026 W/m . How much sound energy does the siren emit in one hour if its power output remains constant? (a)3.6 × 102 [J] (b)5.1 × 103 [J] (c)1.1 × 104 [J] (d)2.2 × 104 [J] (e)6.0 × 104 [J] 36. Overtones. Which of the following frequencies does not belong to the harmonic frequencies of a certain string vibrating at the fundamental frequency 214 [Hz]? (a) 428 [Hz] (b)749 [Hz] (c)1284 [Hz] (d)2568 [Hz] 37. Harmonics. A 1.25 [m] long rope is stretched and tied at both ends with m a tension that produces transverse standing waves with speed of propagation 35.0 s . What is the wavelength of the second harmonic? (a) 2.50 [m] (b)1.77 [m] (c)1.25 [m] (d)0.884 [m] (e)0.625 [m] 38. Five Nodes. A standing wave is produced on a string of length L fixed at both ends. If five nodes (including both ends of the string) are produced by the wave, what is its wavelength? (a) 2L (b)L (c)2L/3 (d)L/2 (e)2L/5 39. Run. A fire siren at rest is emitting sound waves of frequency 500 [Hz]. How fast are you running away from the siren if you detect a frequency of 498 [Hz]? (a) 0.688 ms (b)1.38 ms (c)2.75 ms (d)343 ms (e)687 ms 40. Siren. An ambulance siren is releasing a sound with a frequency of 400 [Hz]. It approaches you at constant speed while you are at rest. Which of the following can be a possible value of frequency that you will hear at the instances the ambulance is near you? (a) 100 [Hz] (b)200 [Hz] (c)400 [Hz] (d)500 [Hz] 41. U-tube. Each end of a U-tube is connected to a gas container. The left end is connected to Gas 1 while the right end is connected to Gas 2. Theh U-tube coni 3 kg tains water (ρ = 1.0 × 10 m3 ) and oil h i 2 kg (ρ = 9.20 × 10 m3 ), as shown. The oil column is 0.150 [m]high, and the height difference h is 0.100 [m]. If the pressure of gas 1 is P1 and that of gas 2 is P2 , what is P1 − P2 ?

Physics 71/Third Long Exam A

(a) 39.2 [Pa]

(b)451 [Pa]

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(c)491 [Pa]

(d)863 [Pa]

1st Sem AY 2011-2012

(e)903 [Pa]

42. Hose there. An incompressible, nonviscous fluid flows nonturbulently through a horizontal hose. If it speeds up with constant non-zero acceleration, which of the following figures best describes the shape of the hose?

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