1. d. The parallel component of $\vec{F}$ is opposite $\vec{v}$ and will cause the particle to slow down. The perpendicular component of $\vec{F}$ will cause the particle to change directions in a downward direction.

2. $T_D>T_B=T_E>T_C>T_A$. The center-directed force is $m{\omega }^{2}r$. Changing $r$ by a factor of 2 changes the tension by a factor of 2, but changing $\omega$ by a factor of 2 changes the tension by a factor of 4.

3. b. The car is moving in a circle, so there must be a net force toward the center of the circle. The circle is below the car, so the net force must point downward. This can be true only if $F_{\text{G}}>n$.

4. c. The ball does not have a “memory” of its previous motion. The velocity $\vec{v}$ is straight up at the instant the string breaks. The only force on the ball after the string breaks is the gravitational force, straight down. This is just like tossing a ball straight up.

1. 39 m

3. $4.8\text{ m}\text{/}\text{s}$

5. 0.089 N radially inward

7. $6.6\times {10}^{15}\text{rev}\text{/}\text{s}$

9. $2.01\times {10}^{20}\text{N}$

11. No

13. $v=\sqrt{{\displaystyle \frac{m_{2}rg}{m_1}}}$

15. $6.0\times {10}^{-3}\text{m}\text{/}{\text{s}}^2$

17.

1. 24.0 h

2. $0.223\text{m}\text{/}{\text{s}}^2$

3. 0 N

19. $n/F_{\text{G}}=3$

21. $20\text{ m}\text{/}\text{s}$

23.

1. $v=3.8\text{m}\text{/}\text{s}$, $a=0.95{\text{m/s}}^2$

2. $7.0\times {10}^2\text{N}$

3. $8.6\times {10}^2\text{N}$

25. $5.5\text{ m}\text{/}\text{s}$

27. 1.6 s

29. $4.2{\text{m/s}}^2$

33. 0.85 N

35. 8.6 m

37. 32 km/h

39. North Pole scale, 2.5 N

41. $34\text{ m}\text{/}\text{s}$

43. 0.79 N

45.

1. $2.9\text{ m}\text{/}\text{s}$

2. 14 N

47.

1. $2.5{\text{m/s}}^2$

2. $1.1{\text{m/s}}^2$

3. 21 N

49. 64 N

51.

1. 320 N, 1400 N

2. 5.7 s

53. 0.38 N

55.

1. $\sqrt{gL}$

2. 5.9 mph

57. 1.4 m to the right

59. 150 m

61.

1. $1.90{\text{ m/s}}^2\text{ at }21\text{°}$

2. $15.7\text{ m}\text{/}\text{s}$

63. $1.2\times {10}^2\text{ rpm}$

65.

2. 191 rpm

67. 105 m

69.

1. 130 rpm

2. 140 rpm

71. $\sqrt{gL}$