Queens College, CUNY - PHYSICS 152

Chapter 7—Conservation of Energy

MULTIPLE CHOICE

1)Any change of the energy of a system occurs because of

1. 1. energy transfer across the boundaries of the system.
   2. combustion of fuels within the system.
   3. radioactive decay of elements within the system.
   4. all of the above.
   5. only (b) and (c) above.

2. A 0.60-kg object is suspended from the ceiling at the end of a 2.0-m string. When pulled to the side and released, it has a speed of 4.0 m/s at the lowest point of its path. What maximum angle does the string make with the vertical as the object swings up?

a.   61?

b.    54?

c.   69?

d.    77?

e.   47?

3. A pendulum is made by letting a 2.0-kg object swing at the end of a string that has a length of 1.5 m. The maximum angle the string makes with the vertical as the pendulum swings is 30?. What is the speed of the object at the lowest point in its trajectory?
   1. 2.0 m/s
   2. 2.2 m/s
   3. 2.5 m/s
   4. 2.7 m/s
   5. 3.1 m/s

4. A 2.0-kg mass swings at the end of a light string (length = 3.0 m). Its speed at the lowest point on its circular path is 6.0 m/s. What is its kinetic energy at an instant when the string makes an angle of 50? with the vertical?
   1. 21 J
   2. 15 J
   3. 28 J
   4. 36 J
   5. 23 J

5. A 2.5-kg object suspended from the ceiling by a string that has a length of 2.5 m is released from rest with the string 40? below the horizontal position. What is the tension in the string at the instant when the object passes through its lowest position?
   1. 11 N
   2. 25 N
   3. 42 N
   4. 18 N

1. 5. 32 N

6. A certain pendulum consists of a 1.5-kg mass swinging at the end of a string (length = 2.0 m). At the lowest point in the swing the tension in the string is equal to 20 N. To what maximum height above this lowest point will the mass rise during its oscillation?
   1. 77 cm
   2. 50 cm
   3. 63 cm
   4. 36 cm
   5. 95 cm

7. A 0.80-kg object tied to the end of a 2.0-m string swings as a pendulum. At the lowest point of its swing, the object has a kinetic energy of 10 J. Determine the speed of the object at the instant when the string makes an angle of 50? with the vertical.
   1. 5.6 m/s
   2. 4.4 m/s
   3. 3.3 m/s
   4. 5.0 m/s
   5. 6.1 m/s

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)?

1. 1. 12 J
   2. ?12 J
   3. 20 J
   4. ?20 J
   5. 32 J

9. A 1.2-kg mass is projected from ground level with a velocity of 30 m/s at some unknown angle above the horizontal. A short time after being projected, the mass barely clears a 16-m tall fence. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass as it clears the fence?

10. A 2.0-kg mass is projected from the edge of the top of a 20-m tall building with a velocity of 24 m/s at some unknown angle above the horizontal. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass just before it strikes the ground?
    1. 0.18 kJ
    2. 0.97 kJ
    3. 0.89 kJ
    4. 0.26 kJ
    5. 0.40 kJ

11. The equation below is the solution to a physics problem:

.

The most likely physical situation it describes is

1. 1. a 2.30 kg cart rolling up a 30? incline.
   2. a 2.30 kg cart rolling down a 30? incline.
   3. a 2.30 kg cart rolling up a 60? incline.
   4. a 2.30 kg cart rolling down a 60? incline.
   5. a 2.30 kg cart rolling down a 90? incline.

12. A skier weighing 0.70 kN goes over a frictionless circular hill as shown. If the skier's speed at point A is 9.2 m/s, what is his speed at the top of the hill (point B)?

1. 1. 3.1 m/s
   2. 6.2 m/s
   3. 5.2 m/s
   4. 4.1 m/s
   5. 6.5 m/s

13. A skier weighing 0.80 kN comes down a frictionless ski run that is circular (R = 30 m) at the bottom, as shown. If her speed is 12 m/s at point A, what is her speed at the bottom of the hill (point B)?

14. A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. The upper end is depressed 20 cm, and a 4.0-kg block is placed on top of the depressed spring. The system is then released from rest. How far above the point of release will the block rise?
    1. 46 cm
    2. 36 cm
    3. 41 cm
    4. 31 cm
    5. 20 cm

15. A spring (k = 200 N/m) is suspended with its upper end supported from a ceiling. With the spring hanging in its equilibrium configuration, an object (mass = 2.0 kg) is attached to the lower end and released from rest. What is the speed of the object after it has fallen 4.0 cm?
    1. 90 cm/s
    2. 79 cm/s
    3. 96 cm/s
    4. 83 cm/s
    5. 57 cm/s

16. A 2.0-kg block sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 200 N/m) which has its other end fixed. If the block has a speed of 4.0 m/s as it passes through the equilibrium position, what is its speed when it is 20 cm from the equilibrium position?
    1. 2.6 m/s
    2. 3.1 m/s
    3. 3.5 m/s
    4. 1.9 m/s
    5. 2.3 m/s

17. A block (mass = 4.0 kg) sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 100 N/m) which has its other end fixed. If the maximum distance the block slides from the equilibrium position is equal to 20 cm, what is the speed of the block at an instant when it is a distance of 16 cm from the equilibrium position?
    1. 71 cm/s
    2. 60 cm/s
    3. 80 cm/s
    4. 87 cm/s
    5. 57 cm/s

18. A 1.0-kg block is released from rest at the top of a frictionless incline that makes an angle of 37? with the horizontal. An unknown distance down the incline from the point of release, there is a spring with k = 200 N/m. It is observed that the mass is brought momentarily to rest after compressing the spring

0.20 m. How far does the mass slide from the point of release until it is brought momentarily to rest? a. 0.98 m

b.   0.68 m

c.   0.82 m

d.   0.55 m

e.   0.20 m

19. A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed?

1. 1. 2.2 m/s
   2. 2.5 m/s
   3. 1.9 m/s
   4. 1.5 m/s
   5. 3.6 m/s

20. A spring (k = 600 N/m) is at the bottom of a frictionless plane that makes an angle of 30? with the horizontal. The upper end of the spring is depressed 0.10 m, and a 2.0-kg block is placed against the depressed spring. The system is then released from rest. What is the kinetic energy of the block at the instant it has traveled 0.10 m and the spring has returned to its uncompressed length?

21. A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. A 2.0-kg block that is initially 0.40 m above the upper end of the spring is dropped from rest onto the spring. What is the kinetic energy of the block at the instant it has fallen 0.50 m (compressing the spring 0.10 m)?
    1. 5.3 J
    2. 6.8 J
    3. 6.3 J
    4. 5.8 J
    5. 6.5 J

22. A large spring is used to stop the cars after they come down the last hill of a roller coaster. The cars start at rest at the top of the hill and are caught by a mechanism at the instant their velocities at the bottom are zero. Compare the compression of the spring, x_A, for a fully loaded car with that, x_B, for a lightly loaded car when m_A = 2m_B.

a.

x_A =    x_B.

2. x_A = x_B.
3. x_A = x_B.
4. x_A = 2 x_B.
5. x_A = 4 x_B.

23. A small lead sphere of mass m is hung from a spring of spring constant k. The gravitational potential energy of the system equals zero at the equilibrium position of the spring before the weight is attached.

The total mechanical energy of the system when the mass is hanging at rest is

1. 1. ?kx². b.

? kx².

c.   0. d.

+ kx².

e.   +kx².

24. A pendulum bob has potential energy U₀ when held taut in a horizontal position. The bob falls until it is 30? away from the horizontal position, when it has potential energy U_A. It continues to fall until the string is vertical, when it has potential energy U_B. Compare its potential energies at O, A, and B.

1. 1. U₀ = U_A = U_B.
   2. U_A ? U_B = 2U₀.
   3. U_A ? U_B = U₀ ? U_A.
   4. U₀ = U_B = 2U_A.
   5. U₀ ? U_A = 2(U_A ? U_B).

25. A spring with spring constant k = 800 N/m is compressed 12 cm from its equilibrium position. A spring with spring constant k = 400 N/m has the same elastic potential energy as the first spring when its extension is

a.   0.060 m.

b.   0.085 m.

c.   0.12 m.

d.   0.17 m.

e.   0.24 m.

26. A spring with spring constant k = 800 N/m is extended 12 cm from its equilibrium position. A spring with 6.0 cm extension from equilibrium will have the same potential energy as the first spring if its spring constant is

a.   200 N/m.

b.   400 N/m.

c.   800 N/m.

d.   1 600 N/m.

e.   3 200 N/m.

27. Identical masses m are attached to identical springs of spring constant k suspended from the ceiling. With both masses hanging in their equilibrium positions, mass A is pulled down 10 cm and released while mass B is pushed up 10 cm and released. Which statement is correct?
    1. Mass A will travel a smaller distance to its highest point than mass B will travel to its lowest point.
    2. Mass A will travel a greater distance to its highest point than mass B will travel to its lowest point.
    3. Masses A and B will travel equal distances between their highest and lowest points.
    4. More work was done on mass A by the extending force than on mass B by the compressing force.
    5. The total work done on mass A by the extending force was equal to the total work done on mass B by the compressing force.

28. The solution to a problem is the equation below. Which description best fits this solution?

1. 1. A vertical spring compressed 0.120 m shoots a 2.00 kg mass 2.90 cm above the equilibrium position of the spring.
   2. A vertical spring stretched 0.120 m shoots a 2.00 kg mass 9.10 cm above the equilibrium position of the spring.
   3. A vertical spring compressed 0.120 m shoots a 2.00 kg mass 12.0 cm above the equilibrium position of the spring.
   4. A vertical spring compressed 0.120 m shoots a 2.00 kg mass 14.9 cm above the equilibrium position of the spring.
   5. A 2.00 kg mass has fallen 0.820 m and compressed the upper end of a vertical spring 12.0 cm below the equilibrium position.

29. The same force F is applied horizontally to bodies 1, 2, 3 and 4, of masses m, 2m, 3m and 4m, initially at rest and on a frictionless surface, until each body has traveled distance d. The correct listing of the magnitudes of the velocities of the bodies, v₁, v₂, v₃, and v₄ is

a.

.

b. v₄ = v₂ > v₃ = v₁. c.

.

d. v₁ = 2v₂ = 3v₃ = 4v₄.

e.

.

30. Two masses, M_A and M_B, with M_B = 2M_A, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen equal distances, we find that

31. Two masses, M_A and M_B, with M_B = 2M_A, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen for equal times, we find that
    1. K_B = K_A.
    2. K_B = 2K_A.
    3. K_B = 4K_A.
    4. K_A = 2K_B.
    5. K_A = 4K_B.

32. A 2.0-kg block slides down a fixed, rough curved track. The block has a speed of 5.0 m/s after its height above a horizontal surface has decreased by 1.8 m. Assume the block starts from rest. What is the change in mechanical energy of the block caused by the force of friction during this descent?
    1. ?14 J
    2. ?12 J
    3. ?10 J
    4. ?16 J
    5. ?25 J

33. A 1.5-kg block sliding on a rough horizontal surface is attached to one end of a horizontal spring (k = 200 N/m) which has its other end fixed. If this system is displaced 20 cm horizontally from the equilibrium position and released from rest, the block first reaches the equilibrium position with a speed of 2.0 m/s. What is the coefficient of kinetic friction between the block and the horizontal surface on which it slides?

a.   0.34

b.   0.24

c.   0.13

d.   0.44

e.   0.17

34. A 0.75-kg sphere is released from rest and is moving 5.0 m/s after falling 2.0 m in a viscous medium. What is the change in mechanical energy caused by the force the viscous medium exerts on the sphere during this descent?

a.   ?6.1 J

b. ?4.6 J

c.   ?5.3 J

d. ?6.8 J

e.   ?2.7 J

35. A 12-kg projectile is launched with an initial vertical speed of 20 m/s. It rises to a maximum height of 18 m above the launch point. What is the change in mechanical energy caused by the dissipative (air) resistive force on the projectile during this ascent?

a.   ?0.64 kJ

b. ?0.40 kJ

c.   ?0.52 kJ

d. ?0.28 kJ

e.   ?0.76 kJ

36. A 10-kg object is dropped from rest. After falling a distance of 50 m, it has a speed of 26 m/s. What is the change in mechanical energy caused by the dissipative (air) resistive force on the object during this descent?
    1. ?1.3 kJ
    2. ?1.5 kJ
    3. ?1.8 kJ
    4. ?2.0 kJ
    5. ?2.3 kJ

37. The block shown is released from rest when the spring is stretched a distance d. If k = 50 N/m, m =

0.50 kg, d = 10 cm, and the coefficient of kinetic friction between the block and the horizontal surface is equal to 0.25, determine the speed of the block when it first passes through the position for which the spring is unstretched.

38. A 2.0-kg block sliding on a rough horizontal surface is attached to one end of a horizontal spring (k = 250 N/m) which has its other end fixed. The block passes through the equilibrium position with a speed of 2.6 m/s and first comes to rest at a displacement of 0.20 m from equilibrium. What is the coefficient of kinetic friction between the block and the horizontal surface?

a.   0.32

b.   0.45

c.   0.58

d.   0.19

e.   0.26

39. In a given frictionless displacement of a particle, its kinetic energy increases by 25 J while its potential energy decreases by 10 J. Determine the work of the nonconservative forces acting on the particle during this displacement.
    1. ?15 J

b.   +35 J

c.   +15 J

4. ?35 J

e.   +55 J

40. A particle is acted upon by only two forces, one conservative and one nonconservative and neither being a force of friction, as it moves from point A to point B. The kinetic energies of the particle at points A and B are equal if
    1. the sum of the works of the two forces is zero.
    2. the work of the conservative force is equal to the work of the nonconservative force.
    3. the work of the conservative force is zero.
    4. the work of the nonconservative force is zero.
    5. None of the above.

41. A 1.2-kg mass is projected down a rough circular track (radius = 2.0 m) as shown. The speed of the mass at point A is 3.2 m/s, and at point B, it is 6.0 m/s. What is the change in mechanical energy done on the system between A and B by the force of friction?

a.   ?8.9 J

b. ?7.3 J

c.   ?8.1 J

d. ?6.6 J

5. ?24 J

42. A 1.2-kg mass is projected up a rough circular track (radius = 0.80 m) as shown. The speed of the mass at point A is 8.4 m/s, and at point B, it is 5.6 m/s. What is the change in mechanical energy between A and B caused by the force of friction?

a.   ?2.7 J

b. ?8.8 J

c.   ?4.7 J

d. ?6.7 J

e.   ?19 J

43. A 3.0-kg mass is dropped from the edge of a 50-m tall building with an initial speed of zero. The mass strikes the ground with a downward velocity of 25 m/s. Find the change in mechanical energy of the mass caused by air resistance between the point where it is dropped and the point where it strikes the ground?

a.   ?0.46 kJ

b. ?0.53 kJ

c.   ?0.61 kJ

d. ?0.38 kJ

e.   ?0.81 kJ

44. A 2.0-kg mass is projected vertically upward from ground level with an initial speed of 30 m/s. The mass rises to a maximum height of 35 m above ground level. What is the change in mechanical energy of the mass caused by air resistance between the point of projection and the point of maximum height? a.    ?0.21 kJ

b. ?0.47 kJ

c.   ?0.40 kJ

d. ?0.34 kJ

e.   ?0.69 kJ

45. A 25-kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 2.0 cm toward its equilibrium position, its kinetic energy is 12 J. What is the change in mechanical energy caused by the frictional force on the block as it moves the 2.0 cm?

a.   ?4.0 J

b. ?3.5 J

c.   ?2.4 J

d. ?2.9 J

e.   ?15 J

46. The two masses in the figure are released from rest. After the 3.0-kg mass has fallen 1.5 m, it is moving with a speed of 3.8 m/s. What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0 kg mass?

1. 1. ?12 J
   2. ?17 J
   3. ?20 J

d. ?8.0 J

e.   ?28 J

47. A 2.0-kg block is projected down a plane that makes an angle of 20? with the horizontal with an initial kinetic energy of 2.0 J. If the coefficient of kinetic friction between the block and plane is 0.40, how far will the block slide down the plane before coming to rest?
    1. 3.0 m
    2. 1.8 m

c.   0.30 m

4. 1.0 m
5. 1.3 m

48. Objects A and B, of mass M and 2M respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value ?_k. At the highest point,
    1. K_A = Fd = K_B.
    2. K_A = (F ? ?_kMg cos?)d; K_B = (F ? 2?_kMg cos?)d.
    3. K_A = (F ? Mg sin?)d; K_B = (F ? 2Mg sin?)d.
    4. K_A = (F ? Mg sin? ? ?_kMg cos?)d; K_B = (F ? Mg sin? ? ?_kMg cos?)d.
    5. K_A = (F ? Mg sin? ? ?_kMg cos?)d; K_B = (F ? 2Mg sin? ? 2?_kMg cos?)d.   
49. As an object moves from point A to point B only two forces act on it: one force is nonconservative and does ?30 J of work, the other force is conservative and does +50 J of work. Between A and B,

1. 1. the kinetic energy of object increases, mechanical energy decreases.
   2. the kinetic energy of object decreases, mechanical energy decreases.
   3. the kinetic energy of object decreases, mechanical energy increases.
   4. the kinetic energy of object increases, mechanical energy increases.
   5. None of the above.

50. As an object moves from point A to point B only two forces act on it: one force is conservative and does ?70 J of work, the other force is nonconservative and does +50 J of work. Between A and B,
    1. the kinetic energy of object increases, mechanical energy increases.
    2. the kinetic energy of object decreases, mechanical energy increases.
    3. the kinetic energy of object decreases, mechanical energy decreases.
    4. the kinetic energy of object increases, mechanical energy decreases.
    5. None of the above.

51. An astronaut tosses a ball out in space where gravitational forces may be neglected. What will happen to the ball?
    1. It will stop as soon as the force the astronaut gave it is used up.
    2. It will stop when the energy the astronaut gave it runs out.
    3. It will stop after a short time because there is no gravity to keep it moving.
    4. It will move in a circle like a boomerang.
    5. It will be slowed down very gradually by collisions with molecules in space.     
52. Objects A and B, of mass M and 2M respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value ?_k. At the highest point,
    1. K_A > K_B.
    2. K_A = K_B.
    3. K_A < K_B.
    4. The work done by F on A is greater than the work done by F on B.
    5. The work done by F on A is less than the work done by F on B.   
53. The equation below describes a physical situation:

Which description best fits the equation?

1. 1. A 1.70 kg block slows down while sliding down a frictionless plane inclined at a 30? angle.
   2. A 1.70 kg block slows down while sliding down a plane with ?_k = 0.320, with the plane inclined at a 30? angle.
   3. A 1.70 kg block speeds up while sliding up a frictionless plane inclined at a 30? angle.
   4. A 1.70 kg block speeds up while sliding down a plane with ?_k = 0.320, with the plane

inclined at a 30? angle.

1. 5. A 1.70 kg block slides over the top of an inclined plane and then descends on the other side. Both planes, inclined at a 30? angle, have ?_k = 0.320.

54. A spring with spring constant 800 N/m compressed 0.200 m is released and projects a 0.800 kg mass along a frictionless surface. The mass reaches a surface area where ?_k = 0.400 and comes to a stop. The following student solution contains at least one error. What is the error?

54. 1. The elastic potential energy is equal only to the kinetic energy on the right, and is never equal to the internal thermal energy.
    2. The elastic potential energy is equal only to the internal thermal energy on the right, and is never equal to the kinetic energy.
    3. The elastic potential energy is equal to either the kinetic energy or the internal thermal energy on the right, but not to their sum, depending on the part of the problem being done.
    4. Elastic potential energy cannot end up as internal energy change caused by friction.
    5. Change in mechanical energy by friction cannot end up as elastic potential energy.                    
55. As a result of friction between internal parts of an isolated system
    1. the total mechanical energy of the system increases.
    2. the total mechanical energy of the system decreases.
    3. the total mechanical energy of the system remains the same.
    4. the potential energy of the system increases but the kinetic energy remains the same.
    5. the kinetic energy of the system increases but the potential energy of the system remains the same.

56. A 3.50 kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the same direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is

a.   5.6.

b.   22.0.

c.   32.9.

d.   54.8.

e.   76.8.

57. A 3.50 kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the opposite direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is

a.   5.6.

b.   22.0.

c.   32.9.

d.   54.8.

e.   76.8.

58. An all-terrain vehicle of 2 000 kg mass moves up a 15.0? slope at a constant velocity of 6.00 m/s. The rate of change of gravitational potential energy with time is

a.   5.25 kW.

b.   24.8 kW.

c.   30.4 kW.

4. 118 kW.
5. 439 kW.

59. A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would have used at least     J of energy.

a.   746

b.  3.43 ? 10⁵

c.   3.73 ? 10⁵

d.  7.46 ? 10⁵

e.   2.61 ? 10⁷

60. 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  seconds.
    1. 1

b.   460

c.   500

d. 1 000

e.   35 000

61. A champion athlete can produce one horsepower (746 W) for a short period of time. The number of 16 cm high steps a 70 kg athlete could ascend in one minute while expending one horsepower is
    1. 4.
    2. 7.

c.   65.

d. 408.

e.   4 567.

62. Jane and Jake are looking at what happens to body 1 of mass m and body 2 of mass 2m, initially at rest, when equal forces are applied separately to the two bodies. Jake says that equal forces applied for equal times do equal amounts of work on the two bodies. Jane says that the two forces do equal amounts of work only if the two bodies move equal distances in the direction of the forces. Which one, if either, is correct?
    1. Jake, because the speed of body 1 is half the speed of body 2, but m₁v₁ = m₂v₂.
    2. Jane, because work does not depend on mass, only on force times distance.
    3. Jake, because all bodies travel equal distances when equal forces are applied for equal times.

62. 4. Jane, because it takes the same time for all bodies to travel equal distances when equal forces are involved.
    5. Neither, because we can't compare the amounts of work done on bodies of different mass.
63. A 6.0-kg block slides along a horizontal surface. If µ_k = 0.20 for the block and surface, at what rate is the friction force changing the mechanical energy of the block at an instant when its speed is 4.0 m/s?
    1. ?59 W
    2. ?47 W
    3. ?71 W
    4. ?82 W

e.   +71 W

64. At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30? above the horizontal?

a.   +39 W

2. ?78 W
3. ?39 W

d.   +78 W

e.   +25 W

65. A 2.0-kg block slides down a plane (inclined at 40? with the horizontal) at a constant speed of 5.0 m/s. At what rate is the gravitational force on the block doing work?

a.   +98 W

b.   +63 W

c.   zero

d.   +75 W

e.   ?75 W

66. The speed of a 4.0-kg object is given by v = (2t) m/s, where t is in s. At what rate is the resultant force on this object doing work at t = 1 s?
    1. 48 W
    2. 40 W
    3. 32 W
    4. 56 W
    5. 16 W

67. A 3.0-kg block is on a frictionless horizontal surface. The block is at rest when, at t = 0, a force (magnitude P = 2.0 N) acting at an angle of 22? above the horizontal is applied to the block. At what rate is the force P doing work at t = 2.0 s?
    1. 2.3 W
    2. 2.0 W
    3. 1.4 W
    4. 1.7 W
    5. 1.2 W

68. A 1.6-kg block slides down a plane (inclined at 25? with the horizontal) at a constant speed of 2.0 m/s. At what rate is the frictional force changing the mechanical energy of the block?

a.   +28 W

b.   +13 W

3. ?13 W
4. ?28 W

e.   +6.5 W

69. A 3.0-kg block is on a horizontal surface. The block is at rest when, at t = 0, a force (magnitude P = 12 N) acting parallel to the surface is applied to the block causing it to accelerate. The coefficient of kinetic friction between the block and the surface is 0.20. At what rate is the force P doing work on the block at t = 2.0 s?
    1. 54 W
    2. 49 W
    3. 44 W
    4. 59 W
    5. 24 W

70. Starting from rest at t = 0, a 5.0-kg block is pulled across a horizontal surface by a constant horizontal force having a magnitude of 12 N. If the coefficient of friction between the block and the surface is 0.20, at what rate is the 12-N force doing work at t = 5.0 s?
    1. 0.13 kW
    2. 0.14 kW
    3. 0.12 kW
    4. 26 W
    5. 12 W

71. Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are F_A and F_B, while the power supplied is respectively P_A and P_B. Which statement is correct?

1. 1. F_B = F_A; P_B = P_A.
   2. F_B = F_A; P_B = 2 P_A.
   3. F_B = 2 F_A; P_B = P_A.
   4. F_B = 2 F_A; P_B = 2 P_A.
   5. P_A = F_A; P_B = F_B.

PROBLEM

72. A surprising demonstration involves dropping an egg from a third-floor window to land on a foam- rubber pad 2 in (5 cm) thick without breaking. If a 56-gram egg falls 12 m, and the foam pad stops the egg in 6.25 ms, by how much is the pad compressed?

73. An automobile (m = 1.00 ? 10³ kg) is driven into a brick wall in a safety test. The bumper behaves like a spring (k = 5.00 ? 10⁶ N/m), and is observed to compress a distance of 3.16 cm as the car is brought to rest. What was the initial speed of the automobile?

74. An archer pulls her bow string back 0.40 m by exerting a force that increases uniformly from zero to 240 N. What is the equivalent spring constant of the bow, and how much work is done in pulling the bow?

75. An ore car of mass 4 000 kg starts from rest and rolls downhill on tracks from a mine. A spring with k

= 400 000 N/m is located at the end of the tracks. At the spring's maximum compression, the car is at an elevation 10 m lower than its elevation at the starting point. How much is the spring compressed in stopping the ore car? Ignore friction.

76. The mat of a trampoline is held by 32 springs, each having a spring constant of 5 000 N/m. A person with a mass of 40.0 kg jumps from a platform 1.93 m high onto the trampoline. Determine the stretch of each of the springs.