University Physics Volume 1

# Chapter 7

7.1

No, only its magnitude can be constant; its direction must change, to be always opposite the relative displacement along the surface.

7.2

No, it’s only approximately constant near Earth’s surface.

7.3

$W = 35 J W = 35 J$

7.4

a. The spring force is the opposite direction to a compression (as it is for an extension), so the work it does is negative. b. The work done depends on the square of the displacement, which is the same for $x=±6cmx=±6cm$, so the magnitude is 0.54 J.

7.5

a. the car; b. the truck

7.6

against

7.7

$3 m/s 3 m/s$

7.8

980 W

### Conceptual Questions

1 .

When you push on the wall, this “feels” like work; however, there is no displacement so there is no physical work. Energy is consumed, but no energy is transferred.

3 .

If you continue to push on a wall without breaking through the wall, you continue to exert a force with no displacement, so no work is done.

5 .

The total displacement of the ball is zero, so no work is done.

7 .

Both require the same gravitational work, but the stairs allow Tarzan to take this work over a longer time interval and hence gradually exert his energy, rather than dramatically by climbing a vine.

9 .

The first particle has a kinetic energy of $4(12mv2)4(12mv2)$ whereas the second particle has a kinetic energy of $2(12mv2),2(12mv2),$ so the first particle has twice the kinetic energy of the second particle.

11 .

The mower would gain energy if $−90°<θ<90°.−90°<θ<90°.$ It would lose energy if $90°<θ<270°.90°<θ<270°.$ The mower may also lose energy due to friction with the grass while pushing; however, we are not concerned with that energy loss for this problem.

13 .

The second marble has twice the kinetic energy of the first because kinetic energy is directly proportional to mass, like the work done by gravity.

15 .

Unless the environment is nearly frictionless, you are doing some positive work on the environment to cancel out the frictional work against you, resulting in zero total work producing a constant velocity.

17 .

Appliances are rated in terms of the energy consumed in a relatively small time interval. It does not matter how long the appliance is on, only the rate of change of energy per unit time.

19 .

The spark occurs over a relatively short time span, thereby delivering a very low amount of energy to your body.

21 .

If the force is antiparallel or points in an opposite direction to the velocity, the power expended can be negative.

### Problems

23 .

3.00 J

25 .

a. 593 kJ; b. –589 kJ; c. 0 J

27 .

3.14 kJ

29 .

a. –700 J; b. 0 J; c. 700 J; d. 38.6 N; e. 0 J

31 .

100 J

33 .

a. 2.45 J; b. – 2.45 J; c. 0 J

35 .

a. 2.22 kJ; b. −2.22 kJ; c. 0 J

37 .

18.6 kJ

39 .

a. 2.32 kN; b. 22.0 kJ

41 .

835 N

43 .

257 J

45 .

a. 1.47 m/s; b. answers may vary

47 .

a. 772 kJ; b. 4.0 kJ; c. $1.8×10−16J1.8×10−16J$

49 .

a. 2.6 kJ; b. 640 J

51 .

2.72 kN

53 .

102 N

55 .

2.8 m/s

57 .

$W ( bullet ) = 20 × W ( crate ) W ( bullet ) = 20 × W ( crate )$

59 .

12.8 kN

61 .

0.25

63 .

a. 24 m/s, −4.8 m/s2; b. 29.4 m

65 .

310 m/s

67 .

a. 40; b. 8 million

69 .

\$149

71 .

a. 208 W; b. 141 s

73 .

a. 3.20 s; b. 4.04 s

75 .

a. 224 s; b. 24.8 MW; c. 49.7 kN

77 .

a. 1.57 kW; b. 6.28 kW

79 .

$6.83 μW 6.83 μW$

81 .

a. 8.51 J; b. 8.51 W

83 .

1.7 kW

85 .

$15 N · m 15 N · m$

87 .

$39 N · m 39 N · m$

89 .

a. $208N·m208N·m$; b. $240N·m240N·m$

91 .

a. $−0.5N·m−0.5N·m$; b. $−0.83N·m−0.83N·m$

93 .

a. 10. J; b. –10. J; c. 380 N/m

95 .

160 J/s

97 .

a. 10 N; b. 20 W

### Challenge Problems

99 .

If crate goes up: a. 3.46 kJ; b. −1.89 kJ; c. −1.57 kJ; d. 0; If crate goes down: a. −0.39 kJ; b. −1.18 kJ; c. 1.57 kJ; d. 0

101 .

8.0 J

103 .

35.7 J

105 .

24.3 J

107 .

a. 40 hp; b. 39.8 MJ, independent of speed; c. 80 hp, 79.6 MJ at 30 m/s; d. If air resistance is proportional to speed, the car gets about 22 mpg at 34 mph and half that at twice the speed, closer to actual driving experience.

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