1. a. Kinetic energy depends linearly on the mass but on the square of the velocity. A factor of 2 change in velocity is more significant than a factor of 2 change in mass.

2. Positive. The force (gravity) and the displacement are in the same direction. The rock gains kinetic energy.

3. Positive. Each puck experiences a force in the direction of motion, which is a positive amount of work. The net force is zero, but the total work is not zero because the pucks have different displacements.

4. c. The upward tension force is opposite the displacement, so it does negative work. The downward gravitational force is parallel to the displacement, so it does positive work.

5. c. $W=F\left(\text{Δ}r\right)\text{cos}\theta$. The 10 N force at $90\text{°}$ does no work at all. Because $\text{cos}60\text{°}={\displaystyle \frac{1}{2}}$, the 8 N force does less work than the 6 N force.

6. Zero. The road does exert a forward force on the car, but the point of application does not move because the tires are not skidding on the road. The car’s increasing kinetic energy is a transformation of chemical energy to kinetic energy, not a transfer of energy from the road to the car.

7. $k{}_1>k{}_2>k{}_3$. The spring constant is the slope of the force-versus-displacement-graph.

8. Positive. At each end, the spring exerts a force in the direction of the block’s displacement and thus does positive work. This is also seen from the fact that both blocks gain kinetic energy.

9. $P{}_B>P{}_A=P{}_C>P{}_D$. The work done is $mg\text{Δ}y$, so the power output is $mg\text{Δ}y/\text{Δ}t$. Runner B does the same work as runner A, but in less time. The ratio $m/\text{Δ}t$ is the same for runners A and C. Runner D does twice the work of A but takes more than twice as long.

1. 112 km/h

3. 2.0

5.

1. 5.3 J

2. 0 J

7. 0 J

9.

1. $-26\text{kJ}$

2. 26 kJ

11.

1. 6

2. 0

13. $125\text{°}$

15.

1. $-7.7$

2. $-20$

3. $-13$

17. $-390\text{J}$

19. $W=1.25\times {10}^4\text{J,}\vec{T}{}_1=-7.92\times {10}^3\text{J,}\vec{T}{}_2=-4.58\times {10}^3\text{J}$

21. $8.0\text{ m}\text{/}\text{s}$, $10\text{ m}\text{/}\text{s}$, $11\text{ m}\text{/}\text{s}$

23. $\frac{1}{3}q{d}^3$

25. 38 N

27.

1. $3.9\times {10}^2\text{N}\text{/}\text{m}$

2. 17.5 cm

29. 0.31 m

31.

1. $6.9\times {10}^5\text{J}$

2. No

33. 0.037

35.

1. 0.57 kJ, $-0.20\text{kJ}$, 0.0 J

2. 39 J

37.

1. $9.80\times {10}^5\text{J}$

2. $1.96\times {10}^4\text{W}$

39.

1. $10\times {10}^1\text{N}$

2. 0.42 kW, 0.83 kW, 1.3 kW

41. Runner: $P_{\text{avg}}=1.2\text{kW}\text{;}$ greyhound: $P_{\text{avg}}=2.0\text{kW}$

43.

1. $-9.8\times {10}^4\text{J}$

2. $1.1\times {10}^5\text{J}$

3. $1.1\times {10}^4\text{J}$

45. $3.27\text{ m}\text{/}\text{s}$

47. 13 kN

49.

1. $2.2\text{ m}\text{/}\text{s}$

2. 0.0058

51.

1. 2.9 J

2. 3.6%

53.

1. $G{m}_1{m}_2\left({\displaystyle \frac{x_2-x_1}{x_1{x}_2}}\right)g$

2. $2.1\times {10}^5\text{m}\text{/}\text{s}$

55. 16 N/m

57.

1. $mg\text{cos}\left(\theta \right)$

2. $mgR$

59. $L_1+L_2+({\displaystyle \frac{m_1+m_2}{k_1}}+{\displaystyle \frac{m_2}{k_2}})g$

61. $2.5\times {10}^5\text{kg}\text{/}\text{s}$

63.

1. 95 W

2. $3.8\times {10}^2\text{W}$

3. $3.2\times {10}^2\text{cal}$

65. $1.2\times {10}^8\text{ly}$

71. 24 W