# Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath

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2 1. A constant force F is applied to a body of mass m that initially is headed east at velocity v 0 until its velocity becomes v 0. The total time of travel is 2t. The total distance the body travels in that time is: (NOT the total displacement, but the total distance, ie, what would the odometer read?). a) 1 F 2 m t2 a) 2(v 0 t b) F m t2 b) F m t2 c) v 0 t 1 F 2 m t2 c) v 0 t 1 F 2 d) v 0 t + 1 F 2 m t2 d) v 0 t + 1 F 2 e) 2(v 0 t + 1 F 2 m t2 ) e) 1 F 2 m t2 Solution m t2 F m t2 ) m t2 During the first segment of the trip, the body accelerates from v 0 to 0 m s with an acceleration a = F m. During the second segment, the body accelerates from 0 m s acceleration a = F. m to v 0 with an The motions are identical because the magnitude of the changes in velocity are the same and accelerations are identical. The motions are just in opposite directions. During the second segment, the body travels a distance x = 1 2 F m t2 During the first segment, the body goes the same distance, but in the positive direction. The length of the path (not the displacement) that the body has traveled is 1 F 2 m t2 + 1 F 2 m t2 = F m t2 2

3 2. In the figure shown, the coefficient of kinetic friction between the block and the incline is The incline is 40 degrees above the horizon. What is the magnitude of the acceleration of the suspended block as it falls? Disregard any pulley mass or friction in the pulley. a) 3.4 m/s 2 a) 3.9 m/s 2 b) 3.7 m/s 2 b) 4.2 m/s 2 c) 4.2 m/s 2 c) 3.4 m/s 2 d) 3.9 m/s 2 d) 3.7 m/s 2 e) 5.4 m/s 2 e) 5.4 m/s 2 3

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5 3. 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 a) 30 N b) 20 N b) 44 N c) 44 N c) 0 N d) 0 N d) 39 N e) 30 N e) 20 N 5

6 4. 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 a) 21 N b) 11 N b) 16 N c) 16 N c) 26 N d) 26 N d) 36 N e) 36 N e) 11 N 6

7 5. 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 a) 2.2 J b) 1.0 J b) 1.6 J c) 2.2 J c) 2.7 J d) 1.6 J d) 3.2 J e) 3.2 J e) 1.0 J 7

8 6. 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. code 101 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. code 102 a) It is meaningless to compare the amount of work because the forces were so different. b) More work was done on A than on B. c) The amount of work is the same for both. d) Work was done on B, but no work was done on A because the wall did not move. e) More work was done on A than on B. 8

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10 7. 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 reach the summit in how many seconds? a) 1 a) 1 b) 460 b) 460 c) 500 c) 500 d) 1000 d) 1000 e) e) KE i + W muscles on bike body system = KE f + U g,f W = mgh To find the time it will take to do this work: W ( 1s 1s ) = mgh( ) = 460s 746J 746J 10

11 8. 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 (K B K A )? a) 12 J a) -20 J b) -12 J b) -12 J c) 20 J c) 32 J d) -20 J d) 20 J e) 32 J e) 12 J 11

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13 9. 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 a) 2.1 m/s b) 1.1 m/s b) 1.1 m/s c) 1.5 m/s c) 1.3 m/s d) 1.3 m/s d) 1.5 m/s e) 2.1 m/s e) 1.7 m/s 13

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15 10. A 10-g bullet moving 1000 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 a) 37 cm b) 66 cm b) 56 cm c) 56 cm c) 78 cm d) 46 cm d) 46 cm e) 37 cm e) 66 cm 15

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17 11. 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 of 5.0 m/s 2. What is the moment of inertia of the wheel? a) kg m 2 a) kg m 2 b) kg m 2 b) kg m 2 c) kg m 2 c) kg m 2 d) kg m 2 d) kg m 2 e) kg m 2 e) kg m 2 17

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19 12. A cylindrical shell rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is a) (5/7)g sin θ a) (5/7)g sin θ b) (1/2)g sin θ b) (3/5)g sin θ c) (3/5)g sin θ c) (4/5)g sin θ d) (2/3)g sin θ d) (1/2)g sin θ e) (4/5)g sin θ e) (2/3)g sin θ 19

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21 13. 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 a) all take the same time b) spherical shell b) spherical shell c) solid cylinder c) solid cylinder d) cylindrical shell d) solid sphere e) all take the same time e) cylindrical shell 21

22 14. An ice skater with rotational inertia I o is spinning with angular speed ω o. She pulls her arms in, decreasing her rotational inertia to I o /3. Her angular speed becomes: a) ω o /3 b) ω o / 3 a) ω o b) 3ω o c) ω o c) 3ω o d) 3ω o d) ω o /3 e) 3ω o e) ω o / 3 22

23 15. A uniform plank is 12 ft long and weighs 20 lb. It is balanced on a sawhorse at its center. An additional 40 lb weight is now placed on the left end of the plank. To keep the plank balanced, it must be moved what distance to the right? ( In English units, g= 32 ft/s 2 ). a) 4 ft a) 1 ft b) 3 ft b) 4 ft c) 2 ft c) 2 ft d) 3.43 ft d) 3.43 ft e) 1 ft e) 3 ft 23

24 16. 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 = 5. What is its angular momentum (in kg m 2 /s) relative to the origin? a) -30 k a) 15 k b) 30 k b) 45 k c) -15 k c) -30 k d) 15 k d) 30 k e) 45 k e) -15 k 24

25 17. What is the gravitational force on a 20-kg satellite circling the Earth (radius = m, mass = kg) with a period of 5.0 h? a) 88 N a) 36 N b) 55 N b) 88 N c) 36 N c) 55 N d) 98 N d) 18 N e) 18 N e) 98 N 25

26 18. Five moles of an ideal gas expands isothermally at 100 degrees Celsius to five times its initial volume. Find the heat flow into the system. a) J a) J b) J b) J c) J c) J d) J d) J e) J e) J 26

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28 19. 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) a) GmM/(6R) b) GmM/(3R) b) GmM/(3R) c) GmM/(4R) c) GmM/(4R) d) GmM/(6R) d) GmM/(2R) e) 3GmM/(4R) e) 3GmM/(4R) 28

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30 20. Planet Zero has a mass of kg and a radius of m. A 10-kg space probe is launched vertically from the surface of Zero with an initial kinetic energy of J. What maximum distance from the center of Zero is achieved by the probe? a) m a) m b) m b) m c) m c) m d) m d) m e) m e) m 30

31 21. 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 a) +8.0 a) -5.0 b) -8.0 b) -14 c) -14 c) +14 d) +14 d) +8.0 e) -5.0 e)

32 22. 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 a) 140 b) 140 b) 264 c) 86 c) 172 d) 440 d) 86 e) 172 e)

33 23. Organ pipe X (open at one end) is half as long as organ pipe Y (open at both ends) as shown. The ratio of their fundamental frequencies f X : f Y is: a) 1:1 a) 4:1 b) 1:2 b) 1:4 c) 2:1 c) 1:2 d) 1:4 d) 2:1 e) 4:1 e) 1:1 33

34 24. A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only when the displacement is a) zero a) A/2 b) A/4 b) A/4 c) A/ 2 c) anywhere between -A and +A d) A/2 d) zero e) anywhere between -A and +A e) A/ 2 34

35 25. Two strings are respectively 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings? a) 0.800, 0.670, a) 4.00, 2.00, 1.00 b) 1.33, 1.00, b) 1.33, 1.00, c) 2.00, 1.00, c) 0.800, 0.670, d) 2.00, 1.33, 1.00 d) 2.00, 1.00, e) 4.00, 2.00, 1.00 e) 2.00, 1.33, 1.00 When we look at standing waves on a string, the ends of the string which are tied to a certain position (and hence cannot move) must be nodes of the standing wave. Similarly, the ends of the string which are free to move must be antinodes of the standing wave. We must find the 3 standing waves from the possibilities above that give either nodes or antinodes at the ends of both of the strings. 35

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37 26. A gas expands from A to B as shown in the graph. Calculate the work (in joules) done by the gas. (1 atm= N/m 2.) a) 12 a) 24 b) 24 b) c) c) d) d) e) e) 12 37

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