The present exam will have the same types of components as our first exam. Don't forget to bring

- A calculator
- (if you wish) one page of formulas or other information from Chapters 1-8.

The number of questions is rather large; use them to find out your weaknesses rather than your strengths (do the opposite on the exam: answer the easier ones first, so you can build on success).

A solution key is available, and here you can find students' questions and answers.

**CHAPTER 5**

4. A horizontal force of 100 N is applied to move a 45-kg cart across a 9.0-m level surface. What work is done by the 100-N force?

a. 405 J

b. 500 J

c. 900 J

d. 4 500 J

5. I use a rope 2.00 m long to swing a 10.0-kg weight around my head. The tension in the rope is 20.0 N. In half a revolution how much work is done by the rope on the weight?

a. 40.0 J

b. 126 J

c. 251 J

d. 0

6. The work done by static friction can be:

a. positive.

b. negative.

c. zero.

d. Any of the above.

13. A golf ball hits a wall and bounces back at 3/4 the original speed. What part of the original kinetic energy of the ball did it lose in the collision?

a. 1/4

b. 3/8

c. 7/16

d. 9/16

14. If both mass and velocity of a ball are tripled, the kinetic energy is increased by a factor of:

a. 3.

b. 6.

c. 9.

d. 27.

16. If during a given physical process the only force acting on an object is friction, which of the following must be assumed in regard to the object's kinetic energy?

a. decreases

b. increases

c. remains constant

d. cannot tell from the information given

17. A very light cart holding a 300-N box is moved at constant velocity across a 15-m level surface. What is the net work done in the process?

a. zero

b. 1/20 J

c. 20 J

d. 2 000 J

18. A 7.00-kg bowling ball falls from a 2.00-m shelf. Just before hitting the floor, what will be its kinetic energy? (g = 9.80 m/s2 and assume air resistance is negligible)

a. 14.0 J

b. 19.6 J

c. 29.4 J

d. 137 J

20. What is the minimum amount of energy required for an 80 kg climber carrying a 20 kg pack to climb Mt. Everest, 8 850 m high?

a. 8.67 MJ

b. 4.16 MJ

c. 2.47 MJ

d. 1.00 MJ

21. A professional skier reaches a speed of 56 m/s on a 30° ski slope. Ignoring friction, what was the minimum distance along the slope the skier would have had to travel, starting from rest?

a. 110 m

b. 160 m

c. 320 m

d. 640 m

22. As an object is lowered into a deep hole in the surface of the earth, which of the following must be assumed in regard to its potential energy?

a. increase

b. decrease

c. remain constant

d. cannot tell from the information given

23. When an object is dropped from a tower, what is the effect of the air resistance as it falls?

a. does positive work

b. increases the object's kinetic energy

c. increases the object's potential energy

d. None of the above choices are valid.

25. A 15.0-kg crate, initially at rest, slides down a ramp 2.0 m long and inclined at an angle of 20° with the horizontal. If there is no friction between ramp surface and crate, what is the kinetic energy of the crate at the bottom of the ramp? (g = 9.8 m/s2)

a. 220 J

b. 690 J

c. 10 J

d. 100 J

26. A 10.0-kg box starts at rest and slides 3.5 m down a ramp inclined at an angle of 10 with the horizontal. If there is no friction between the ramp surface and crate, what is the velocity of the crate at the bottom of the ramp? (g = 9.8 m/s2)

a. 6.1 m/s

b. 3.5 m/s

c. 10.7 m/s

d. 8.3 m/s

28. A simple pendulum, 1.00 m in length, is released from rest when the support string is at an angle of 35.0° from the vertical. What is the speed of the suspended mass at the bottom of the swing? (g = 9.80 m/s2 and ignore air resistance)

a. 0.67 m/s

b. 0.94 m/s

c. 1.33 m/s

d. 1.88 m/s

29. A simple pendulum, 2.0 m in length, is released with a push when the support string is at an angle of 25° from the vertical. If the initial speed of the suspended mass is 1.2 m/s when at the release point, what is its speed at the bottom of the swing? (g = 9.8 m/s2)

a. 2.3 m/s

b. 2.6 m/s

c. 2.0 m/s

d. 0.5 m/s

30. A simple pendulum, 2.0 m in length, is released by a push when the support string is at an angle of 25° from the vertical. If the initial speed of the suspended mass is 1.2 m/s when at the release point, to what maximum angle will it move in the second half of its swing?

a. 37

b. 30

c. 27

d. 21

31. A hill is 100 m long and makes an angle of 12° with the horizontal. As a 50-kg jogger runs up the hill, how much work does gravity do on the jogger?

a. 49 000 J

b. 10 000 J

c. -10 000 J

d. zero

32. A 2.00-kg ball has zero kinetic and potential energy. Ernie drops the ball into a 10.0-m-deep well. Just before the ball hits the bottom, the sum of its kinetic and potential energy is:

a. zero.

b. 196 J.

c. -196 J.

d. 392 J.

33. A 2.00-kg ball has zero potential and kinetic energy. Maria drops the ball into a 10.0-m-deep well. After the ball comes to a stop in the mud, the sum of its potential and kinetic energy is:

a. zero.

b. 196 J.

c. -196 J.

d. 392 J.

34. Two blocks are released from the top of a building. One falls straight down while the other slides down a smooth ramp. If all friction is ignored, which one is moving faster when it reaches the bottom?

a. The block that went straight down.

b. The block that went down the ramp.

c. They both will have the same speed.

d. Insufficient information to work the problem.

40. A 2 000 kg ore car rolls 50.0 m down a frictionless 10.0° incline. If there is a horizontal spring at the end of the incline, what spring constant is required to stop the ore car in a distance of 1.00 m?

a. 340 kN/m

b. 681 kN/m

c. 980 kN/m

d. 1 960 kN/m

41. An amount of work equal to 1.5 J is required to compress the spring in a spring gun. What is the "launch speed" of a 15 g marble?

a. 14 m/s

b. 15 m/s

c. 18 m/s

d. 21 m/s

43. By how much is the energy stored in a Hooke's law spring increased when its stretch is increased from 8.00 cm to 16.0 cm?

a. 100%

b. 200%

c. 300 %

d. The correct answer is not given.

46. A Hooke's law spring is mounted horizontally over a frictionless surface. The spring is then compressed a distance d and is used to launch a mass m along the frictionless surface. What compression of the spring would result in the mass attaining double the kinetic energy received in the above situation?

a. 1.41 d

b. 1.73 d

c. 2.00 d

d. 4.00 d

47. A Hooke's law spring is mounted horizontally over a frictionless surface. The spring is then compressed a distance d and is used to launch a mass m along the frictionless surface. What compression of the spring would result in the mass attaining double the speed received in the above situation?

a. 1.41 d

b. 1.73 d

c. 2.00 d

d. 4.00 d

49. Adisa pulls a 40-N crate up a 5.0-m long inclined plane at a constant velocity. If the plane is inclined at an angle of 37° to the horizontal and there is a constant force of friction of 10 N between the crate and the surface, what is the net change in potential energy of the crate?

a. 120 J

b. -120 J

c. 200 J

d. -200 J

50. A 20-N crate starting at rest slides down a rough 5.0-m long ramp, inclined at 25° with the horizontal. 20 J of energy is lost to friction. What will be the speed of the crate at the bottom of the incline?

a. 0.98 m/s

b. 1.9 m/s

c. 3.2 m/s

d. 4.7 m/s

52. A pile driver drives a post into the ground. The mass of the pile driver is 2 500 kg and it is dropped through a height of 8.0 m on each stroke. If the resisting force of the ground is 4.0 × 10^{6} N, how far is the post driven in on each stroke?

a. 4.9 cm

b. 9.8 cm

c. 16 cm

d. 49 cm

55. A girl and her bicycle have a total mass of 40 kg. At the top of the hill her speed is 5.0 m/s. The hill is 10 m high and 100 m long. If the force of friction as she rides down the hill is 20 N, what is her speed at the bottom?

a. 5.0 m/s

b. 10 m/s

c. 11 m/s

d. She stops before she reaches the bottom.

56. I drop a 60-g golf ball from 2.0 m high. It rebounds to 1.5 m. How much energy is lost?

a. 0.29 J

b. 0.50 J

c. 0.88 J

d. 1.0 J

57. A parachutist of mass 50.0 kg jumps out of an airplane at a height of 1 000 m. The parachute deploys, and she lands on the ground with a speed of 5.0 m/s. How much energy was lost to air friction during this jump?

a. 49 400 J

b. 98 700 J

c. 198 000 J

d. 489 000 J

58. A Hooke's law spring is compressed a distance d and is used to launch a mass m vertically to a height h above its starting position. Under the same compression d, the spring is now used to launch a mass of 2m. How high does this second mass rise?

a. h

b. h/2

c. h/1.41

d. h/4

59. A Hooke's law spring is compressed a distance d and is used to launch a mass m vertically to a height h above its starting position. Under double the compression, the spring is now used to launch the mass. How high does the mass now rise above its starting position?

a. 2 h

b. 1.41 h

c. 3 h

d. 4 h

60. A Hooke's law spring is compressed a distance d and is used to launch a particle of mass m vertically to a height h above its starting position. Under double the compression, the spring is now used to launch a particle of mass 2 m. How high does the second mass rise above its starting position?

a. h

b. 2 h

c. 3 h

d. 4 h

61. The quantity of work equal to one joule is also equivalent to which of the following?

a. watt

b. watt/s

c. watt·s

d. watt/s²

64. A 60 kg woman runs up a flight of stairs having a rise of 4.0 m in a time of 4.2 s. What average power did she supply?

a. 380 W

b. 560 W

c. 620 W

d. 670 W

66. Yuri, a Russian weightlifter, is able to lift 250 kg 2.00 m in 2.00 s. What is his power output?

a. 500 W

b. 2.45 kW

c. 4.90 kW

d. 9.80 kW

68. A speed boat requires 80 kW to move at a constant speed of 15 m/s. What is the resistive force of the water at this speed?

a. 2 700 N

b. 5 300 N

c. 6 500 N

d. 7 700 N

72. A 100-W light bulb is left on for 10.0 hours. Over this period of time, how much energy was used by the bulb?

a. 1 000 J

b. 3 600 J

c. 3 600 000 J

d. 1.34 hp

**CHAPTER 6**

4. A 0.12-kg ball is moving at 6 m/s when it is hit by a bat, causing it to reverse direction and have a speed of 14 m/s. What is the change in the magnitude of the momentum of the ball?

a. 0.39 kg m/s

b. 0.42 kg m/s

c. 1.3 kg m/s

d. 2.4 kg m/s

5. The impulse experienced by a body is equivalent to its change in:

a. velocity.

b. kinetic energy.

c. momentum.

d. None of the above choices are valid.

7. Alex throws a 0.15-kg rubber ball down onto the floor. The ball's speed just before impact is 6.5 m/s, and just after is 3.5 m/s. What is the magnitude of the ball's change in momentum?

a. 0.09 kg m/s

b. 1.5 kg m/s

c. 4.3 kg m/s

d. 126 kg m/s

12. A ball with original momentum +4.0 kg m/s hits a wall and bounces straight back without losing any kinetic energy. The change in momentum of the ball is:

a. 0.

b. -4.0 kg m/s.

c. 8.0 kg m/s.

d. -8.0 kg m/s.

14. A car wash nozzle directs a steady stream of water at 1.5 kg/s, with a speed of 30 m/s, against a car window. What force does the water exert on the glass? Assume the water does not splash back.

a. 11 N

b. 45 N

c. 110 N

d. 440 N

16. A 75-kg swimmer dives horizontally off a 500-kg raft. If the diver's speed immediately after leaving the raft is 4 m/s, what is the corresponding raft speed?

a. 0.2 m/s

b. 0.5 m/s

c. 0.6 m/s

d. 4.0 m/s

17. A cannon of mass 1 500 kg fires a 10-kg shell with a velocity of 200 m/s at an angle of 45 above the horizontal. Find the recoil velocity of the cannon across the level ground.

a. 1.33 m/s

b. 0.94 m/s

c. 2.41 m/s

d. 1.94 m/s

18. The law of conservation of momentum is applicable to systems made up of objects described by which of the following?

a. macroscopic

b. microscopic

c. interacting through friction

d. All the above choices are valid.

22. A uranium nucleus (mass 238 units) at rest decays into a helium nucleus (mass 4.0 units) and a thorium nucleus (mass 234 units). If the speed of the helium nucleus is 6.0 105 m/s, what is the speed of the thorium nucleus?

a. 1.0 x 104 m/s

b. 3.0 104 m/s

c. 3.6 104 m/s

d. 4.1 104 m/s

23. If the momentum of an object is tripled, its kinetic energy will change by what factor?

a. zero

b. one-third

c. three

d. nine

24. The kinetic energy of an object is quadrupled. Its momentum will change by what factor?

a. zero

b. two

c. eight

d. four

25. A moderate force will break an egg. However, an egg dropped on the road usually breaks, while one dropped on the grass usually doesn't break. This is because for the egg dropped on the grass:

a. the change in momentum is greater.

b. the change in momentum is less.

c. the time interval for stopping is greater.

d. the time interval for stopping is less.

26. A 70-kg man is standing in a 20-kg boat. The man steps to the right thinking he is stepping out onto the dock. However, the following will actually happen (ignore the friction of the water or air on the boat or the man):

a. The man only moves a short distance to the right while the boat moves a larger distance to the left.

b. The man actually stays still while the boat moves toward the left.

c. The boat doesn't move and the man moves to the right.

d. None of the above.

27. A lump of clay is thrown at a wall. A rubber ball of identical mass is thrown with the same speed toward the same wall. Which statement is true?

a. The clay experiences a greater change in momentum than the ball.

b. The ball experiences a greater change in momentum than the clay.

c. The clay and the ball experience the same change in momentum.

d. It is not possible to know which object has the greater change in momentum.

28. A high diver of mass 70 kg jumps off a board 10 m above the water. If, 1.0 s after entering the water his downward motion is stopped, what average upward force did the water exert?

a. 100 N

b. 686 N

c. 980 N

d. No answer is correct.

29. Object 1 has twice the mass of Object 2. Both objects have the same kinetic energy. Which of the following statements is true?

a. Both objects can have the same magnitude of momentum.

b. Object 1 has a momentum of greater magnitude than Object 2.

c. The magnitude of the momentum of Object 2 is four times that of Object 1.

d. All the statements are false.

30. Object 1 has twice the mass of Object 2. Each of the objects has the same magnitude of momentum. Which of the following statements is true?

a. Both objects can have the same kinetic energy.

b. One object has 0.707 times the kinetic energy of the other.

c. One object has twice the kinetic energy of the other.

d. One object has 4 times the kinetic energy of the other.

32. A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s. If the block had been originally at rest and is free to move, what is its resulting speed?

a. 9 m/s

b. 18 m/s

c. 90 m/s

d. 900 m/s

35. An object of mass m moving at speed v_{0} strikes and object of mass 2m which had been at rest. The first object bounces backward along its initial path at speed v_{0}. Is this collision elastic, and if not, what is the change in kinetic energy of the system?

a. The collision is elastic.

b. The kinetic energy decreases by mv2.

c. The kinetic energy decreases by ½mv2.

d. The kinetic energy increases by mv2.

38. During a snowball fight two balls with masses of 0.4 and 0.6 kg, respectively, are thrown in such a manner that they meet head on and combine to form a single mass. The magnitude of initial velocity for each is 15 m/s. What is the speed of the 1.0-kg mass immediately after collision?

a. zero

b. 3 m/s

c. 6 m/s

d. 9 m/s

39. A 2 500 kg truck moving at 10.00 m/s strikes a car waiting at a traffic light, hooking bumpers. The two continue to move together at 7.00 m/s. What was the mass of the struck car?

a. 1 730 kg

b. 1 550 kg

c. 1 200 kg

d. 1 070 kg

40. A billiard ball collides in an elastic head on collision with a second stationary identical ball. After the collision which of the following conditions applies to the first ball?

a. maintains the same velocity as before

b. has one half its initial velocity

c. comes to rest

d. moves in the opposite direction

41. A billiard ball collides in an elastic head on collision with a second identical ball. What is the kinetic energy of the system after the collision compared to that before collision?

a. the same as

b. one fourth

c. twice

d. four times

42. In a two body collision, if the momentum of the system is conserved, then which of the following best describes the kinetic energy after the collision?

a. must be less

b. must also be conserved

c. may also be conserved

d. is doubled in value

43. In a two body collision, if the kinetic energy of the system is conserved, then which of the following best describes the momentum after the collision?

a. must be less

b. must also be conserved

c. may also be conserved

d. is doubled in value

48. Two billiard balls have velocities of 2.0 m/s and 1.0 m/s when they meet in an elastic head on collision. What is the final velocity of the first ball after collision?

a. -2.0 m/s

b. -1.0 m/s

c. -0.5 m/s

d. +1.0 m/s

49. Two objects, one less massive than the other, collide elastically and bounce back after the collision. If the two originally had velocities that were equal in size but opposite in direction, then which one will be moving faster after the collision?

a. The less massive one.

b. The more massive one.

c. The speeds will be the same after the collision.

d. There is no way to be sure without the actual masses.

60. Two identical 7-kg bowling balls roll toward each other. The one on the left is moving at +4 m/s while the one on the right is moving at −4 m/s. What is the velocity of each ball after they collide elastically?

a. Neither is moving.

b. -4 m/s, +4 m/s

c. +4 m/s, -4 m/s

d. -14 m/s, +14 m/s

62. A 5-kg object is moving to the right at 4 m/s and collides with a 4-kg object moving to the left at 5 m/s. The objects collide and stick together. After the collision, the combined object:

a. has the same kinetic energy that the system had before the collision.

b. has more kinetic energy than the system had before the collision.

c. has no kinetic energy.

d. has less momentum than the system had before the collision.

67. When a collision is perfectly inelastic, then:

a. all the kinetic energy is conserved.

b. all the kinetic energy is gone.

c. the participants stick together.

d. the total momentum is zero.

**CHAPTER** 7

3. A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s. What is the wheel's average angular acceleration?

a. 9.6 rad/s²

b. 4.8 rad/s²

c. 1.6 rad/s²

d. 0.33 rad/s²

4. What is the angular speed about the rotational axis of the Earth for a person standing on the surface?

a. 7.3 × 10^{-5} rad/s

b. 3.6 × 10^{-5} rad/s

c. 6.28 × 10^{-5} rad/s

d. 3.14 × 10^{-5} rad/s

12. Starting from rest, a wheel undergoes constant angular acceleration for a period of time T. At which of the following times does the average angular acceleration equal the instantaneous angular acceleration?

a. 0.50 T

b. 0.67 T

c. 0.71 T

d. all of the above

13. A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 4.9 rad. What is its average angular acceleration?

a. 0.10 rad/s²

b. 0.05 rad/s²

c. 1.8 rad/s²

d. 0.60 rad/s²

16. A ventilation fan has blades 0.25 m in radius rotating at 20 rpm. What is the tangential speed of each blade tip?

a. 0.02 m/s

b. 0.52 m/s

c. 5.0 m/s

d. 20 m/s

18. A point on the rim of a 0.30-m-radius rotating wheel has a tangential speed of 4.0 m/s. What is the tangential speed of a point 0.20 m from the center of the same wheel?

a. 1.0 m/s

b. 1.3 m/s

c. 2.7 m/s

d. 8.0 m/s

20. The end of the cutting cord on a gas-powered weed cutter is 0.15 m in length. If the motor rotates at the rate of 20 rev/s, what is the tangential speed of the end of the cord?

a. 628 m/s

b. 25 m/s

c. 19 m/s

d. 63 m/s

21. A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s?

a. 3.0 rev/s

b. 1.5 rev/s

c. 0.48 rev/s

d. 0.24 rev/s

22. Consider a point on a bicycle wheel as the wheel makes exactly four complete revolutions about a fixed axis. Compare the linear and angular displacement of the point.

a. Both are zero.

b. Only the angular displacement is zero.

c. Only the linear displacement is zero.

d. Neither is zero.

23. Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular velocities of the point.

a. Both are constant.

b. Only the angular velocity is constant.

c. Only the linear velocity is constant.

d. Neither is constant.

24. Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular accelerations of the point.

a. Both are zero.

b. Only the angular acceleration is zero.

c. Only the linear acceleration is zero.

d. Neither is zero.

29. A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum speed can the mass have if the string is not to break?

a. 370 m/s

b. 22 m/s

c. 19 m/s

d. 29 m/s

37. A 0.400-kg object is swung in a circular path and in a vertical plane on a 0.500-m-length string. If the angular speed at the bottom is 8.00 rad/s, what is the tension in the string when the object is at the bottom of the circle?

a. 5.60 N

b. 10.5 N

c. 16.7 N

d. 19.6 N

39. A car* rounds an unbanked curve with a radius of 52 m at a speed of 12 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s²)

a. 0.18

b. 0.30

c. 0.28

d. 0.37

*The original problem specified the car's mass as 1 500 kg, but that is not needed (why?)

41. At what speed will a car round a 52-m-radius curve, banked at a 45° angle, if no friction is required between the road and tires to prevent the car from slipping? (g = 9.8 m/s2)

a. 27 m/s

b. 17 m/s

c. 23 m/s

d. 35 m/s

43. Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed. The direction for the acceleration for this point at that moment is:

a. upward.

b. down toward the ground.

c. forward.

d. at that moment the acceleration is zero.

45. What angular speed (in revolutions/second) is needed for a centrifuge to produce an acceleration of 1 000 g at a radius arm of 15.0 cm?

a. 40.7 rev/s

b. 75.4 rev/s

c. 81.4 rev/s

d. 151 rev/s

47. A cylindrical space colony 8 km in diameter and 30 km long has been proposed as living quarters for future space explorers. Such a habitat would have cities, land and lakes on the inside surface and air and clouds in the center. All this would be held in place by the rotation of the cylinder about the long axis. How fast would such a cylinder have to rotate to produce a 1-g gravitational field at the walls of the cylinder?

a. 0.05 rad/s

b. 0.10 rad/s

c. 0.15 rad/s

d. 0.20 rad/s

48. The Earth is 93 million miles (mi) from the Sun and its period of revolution is 1 year = 3.15 × 10^{7} s. What is the acceleration of the Earth in its orbit about the Sun?

a. 18.6 mi/s²

b. 9.3 ´ 10-3 mi/s²

c. 13.6 ´ 10-6 mi/s²

d. 3.7 ´ 10-6 mi/s²

49. A wheel is rotated about a horizontal axle at a constant angular speed. Next it is rotated in the opposite direction with the same angular speed. The acceleration at a point on the top of the wheel in the second case as compared to the acceleration in the first case:

a. is in the same direction.

b. is in the opposite direction.

c. is upward.

d. is tangential to the wheel.

53. An Earth satellite is orbiting at a distance from the Earth's surface equal to one Earth radius (4 000 miles). At this location, the acceleration due to gravity is what factor times the value of g at the Earth's surface?

a. There is no acceleration since the satellite is in orbit.

b. 2

c. 1/2

d. 1/4

60. A careful photographic survey of Jupiter's moon Io by the spacecraft Voyager 1 showed active volcanoes spewing liquid sulfur to heights of 70 km above the surface of this moon. If the value of g on Io is 2.0 m/s², estimate the speed with which the liquid sulfur left the volcano.

a. 260 m/s

b. 530 m/s

c. 790 m/s

d. 970 m/s

**CHAPTER 8**

3. A rod of length L is pivoted about its left end and has a force F applied perpendicular to the other end. The force F is now removed and another force F' is applied at the midpoint of the rod. If F' is at an angle of 30° with respect to the rod, what is its magnitude if the resulting torque is the same as when F was applied?

a. F

b. 2F

c. 3F

d. 4F

4. Two children seat themselves on a seesaw. The one on the left has a weight of 400 N while the one on the right weighs 300 N. The fulcrum is at the midpoint of the seesaw. If the child on the left is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced, what is the torque provided by the weight of the child on the right?

a. 600 N·m

b. 450 N·m

c. -600 N·m

d. -450 N·m

6. A bucket of water with total mass 23 kg is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder. What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible, that cylinder turns on frictionless bearings, and that g = 9.8 m/s2.)

a. 45 N

b. 68 N

c. 90 N

d. 135 N

11. Tasha has mass 20 kg and wants to use a 4.0-m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. How far is she from the support point?

a. 2.0 m

b. 1.0 m

c. 0.67 m

d. 0.33 m

12. An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall. If the ladder has a mass of 20 kg and it makes an angle of 60° with the ground, find the force of friction of the ground on the foot of the ladder.

a. 7.8 x 102 N

b. 2.0 x 102 N

c. 50 N

d. 1.7 x 102 N

18. A uniform, horizontal beam of length 6.0 m and weight 120 N is attached at one end to a wall by a pin connection (so that it may rotate). A cable attached to the wall above the pin supports the opposite end. The cable makes an angle of 60° with the horizontal. What is the tension in the cable needed to maintain the beam in equilibrium?

a. 35 N

b. 69 N

c. 60 N

d. 120 N

21. A 4.2-kg mass is placed at (3.0, 4.0) m. Where can an 8.4-kg mass be placed so that the moment of inertia about the z-axis is zero?

a. (-3.0, -4.0) m

b. (-6.0, -8.0) m

c. (-1.5, -2.0) m

d. There is no position giving this result.

25. If a net torque is applied to an object, that object will experience:

a. a constant angular speed.

b. an angular acceleration.

c. a constant moment of inertia.

d. an increasing moment of inertia.

as I wrote in response to a student's inquiry: (b) is the approved answer. But it's not unique: it talks about an
object, and from the possible answers one must contemplate that it may
have a changing moment of inertia. (They should have said: a rigid
body; even then (c) would of course be correct) The torque really causes
an change in the angular momentum. If the moment of inertia increases at
the same rate, the angular speed could be constant, there would be no
angular acceleration. So all answers can be correct!

34. A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.12 kg×m². If the bucket is raised to the top of the well and released, what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope's mass is negligible, that cylinder turns on frictionless bearings and that g = 9.8 m/s2.)

a. 3.2 m/s²

b. 6.3 m/s²

c. 7.4 m/s²

d. 9.8 m/s²

35. A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well. The bucket is raised to the top of the well and released. The bucket is moving with a speed of 8.0 m/s upon hitting the water surface in the well. What is the angular speed of the cylinder at this instant?

a. 39 rad/s

b. 79 rad/s

c. 120 rad/s

d. 160 rad/s

38. A solid cylinder (I = MR²/2) has a string wrapped around it many times. When I release the cylinder, holding on to the string, the cylinder falls and spins as the string unwinds. What is the downward acceleration of the cylinder as it falls?

a. 0

b. 4.9 m/s²

c. 6.5 m/s²

d. 9.8 m/s²

39. A 40-kg boy is standing on the edge of a stationary 30-kg platform that is free to rotate. The boy tries to walk around the platform in a counterclockwise direction. As he does:

a. the platform doesn't rotate.

b. the platform rotates in a clockwise direction just fast enough so that the boy remains
stationary relative to the ground.

c. the platform rotates in a clockwise direction while the boy goes around in a
counterclockwise direction relative to the ground.

d. both go around with equal angular velocities but in opposite directions.

40. A rod of length L is hinged at one end. The moment of inertia as the rod rotates around that hinge is ML²/3. Suppose a 2.00-m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released?

a. 3.70 rad/s²

b. 7.35 rad/s²

c. 2.45 rad/s²

d. 4.90 rad/s²

45. The total kinetic energy of a baseball thrown with a spinning motion is a function of:

a. its linear speed but not rotational speed.

b. its rotational speed but not linear speed.

c. both linear and rotational speeds.

d. neither linear nor rotational speed.

47. A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well. The moment of inertia of the cylinder and crank is 0.12 kg×m². The bucket is raised to the top of the well and released to fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 8.0 m/s?

a. 2.1 × 10³ J

b. 1.5 × 10³ J

c. 0.70 × 10³ J

d. 0.40 × 10³ J

48. A solid sphere of mass 4.0 kg and radius 0.12 m is at rest at the top of a ramp inclined 15°. It rolls to the bottom without slipping. The upper end of the ramp is 1.2 m higher than the lower end. Find the sphere's total kinetic energy when it reaches the bottom.

a. 70 J

b. 47 J

c. 18 J

d. 8.8 J

49. A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15°, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = 0.4MR² for a solid sphere and g = 9.8 m/s²)

a. 4.7 m/s

b. 4.1 m/s

c. 3.4 m/s

d. 2.4 m/s

57. An initially installed flywheel can store 10^{6} J of kinetic energy when rotating at 300 rad/s. It is replaced by another flywheel of the same size but made of a lighter and stronger material. If its mass is half that of the original and it is now capable of achieving a rotational speed of 600 rad/s, what maximum energy can be stored?

a. 40 × 10^{5} J

b. 20 × 10^{5} J

c. 10 × 10^{5} J

d. 5.0 × 10^{5} J

61. An object of radius R and moment of inertia I rolls down an incline of height H after starting from rest. Its total kinetic energy at the bottom of the incline:

a. is gR/I.

b. is I/gH.

c. is 0.5 Ig/H.

d. cannot be found from the given information alone.

62. A uniform solid sphere rolls down an incline of height 3 m after starting from rest. In order to calculate its speed at the bottom of the incline, one needs to know:

a. the mass of the sphere.

b. the radius of the sphere.

c. the mass and the radius of the sphere.

d. no more than is given in the problem.

64. A solid disk of radius R rolls down an incline in time T. The center of the disk is removed up to a radius of R/2. The remaining portion of the disk with its center gone is again rolled down the same incline. The time it takes is:

a. T.

b. more than T.

c. less than T.

d. requires more information than given in the problem to figure out.

67. A figure skater with arms initially extended starts spinning on the ice at 3 rad/s. She then pulls her arms in close to her body. Which of the following results?

a. a smaller rotational rate

b. a greater rotational rate

c. a greater angular momentum

d. a smaller angular momentum

75. A tetherball is attached to a pole with a 2.0-m rope. It is circling at 0.20 rev/s. As the rope wraps around the pole it shortens. How long is the rope when the ball is moving at 5.0 m/s?

a. 1.8 m

b. 1.5 m

c. 1.2 m

d. 1.0 m

The author of this problem wants you to do it by angular momentum conservation. But when a string wraps about a pole, there *is* a torque, since the string is tangent to the pole, does not go through its center. Instead, energy is conserved (where would the increased KE come from!), so the problem makes no sense -- the speed will always be the same as the initial speed, 2.5 m/s.

77. An object with mass m and moment of inertia I is spinning with an angular momentum L. Its kinetic energy is:

a. 0.5 I²/L.

b. 0.5 L²/I.

c. 0.5 L²/m.

d. 0.5 I²/m.