Answers to even questions in Chapter 8.   Notify me of any disagreement.

2.  The torque applied to the root about point A is 0.642 N m (CCW).

4.  The torque exerted by the fish is 168 N m (CW).

6.  The center of gravity of the system is at +1.00 m on the y-axis.

8.  The fourth mass should be placed at (-1.5m, -1.5m).

10. The mass of the meter stick is 139 g.

12. The tensions in the ropes are 333 N and 567 N.

14. a) See solution.
    b) The tension in the wire would be 343 N.
    c) The maximum distance the bear can walk is 5.14 m.

16. a) The tension in the cable is 400 N.
    b) The forces exerted on the beam by the wall are 346 N (h) and 0 N (v).

18. The magnitude of F_t is 724 N,
	and F_s is 716 N at 8.75 deg below horizontal.

20. a) The forces exerted by the Earth are 267 N (h) and 1300 N (v).
    b) The coefficient of static friction is 0.324.

22. The tension in the supporting cable is 1465 N, 
	and the reaction forces are 1328 N (h) and 2581 N (v).

24. The minimum distance for an additional weight is x = 2.8 m.

26. The torque required about the x-axis is 149 N m,
	about the y-axis it is 66.0 N m and about the z-axis it is 215 N m.

28. a) The force of the fish on the line is 34 N.
    b) In 0.50 s, 33 cm of the line unwinds.

30. The angular acceleration of the pulley is 24 rad/s^2.

32. The coefficient of kinetic friction is 0.524.

34. a) Newton's second law for the cylinder is: m g - T = m a .
    b) The net torque about the center of the cylinder is T r N m.
    c) See solution.

36. The moment of inertia of the propeller is 0.150 kg m^2.

38. a) The kinetic energy stored in the flywheel is 1.37*10^8 J.
    b) The flywheel could run for 5.11 hr before needing replenishment.

40. a) The angular speed at the bottom of the hill is 36 rad/s.

42. a) The angular momentum of the Earth about its axis is 9.74*10^(37) J s.
    b) For the Earth in orbit about the Sun, it is 2.66*10^(40) J s.

44. The speed of Halley's comet when it is furtherest from the Sun is 0.91 km/s.

46. The final angular speed of the system is 6.73 rad/s.

48. The work done on the puck is 5.99*10^(-2) J.

50. a) Omega equals I_1/(I_1+I_2)*omega_0.
    b) The ratio of final to initial kinetic energy is I_1/(I_1+I_2) < 1.

52. See solution.

54. a) The tension in the rope is 46.8 N.
    b) The moment of inertia of the wheel is 0.234 kg m^2.
    c) The angular speed of the wheel after 2.00 s is 40.0 rad/s.

56. T_1 = 11.2 N, T_2 = 1.39 N and F = 7.23 N.

58. a) The center of gravity remains stationary.
    b) The child ends up 5.55 m from the pier.
    c) The child remains 0.45 m from the turtle.

60. a) The acceleration of the masses is 3.12 m/s^2.
    b) T_1 is 26.7 N and T_2 is 9.36 N.

62. a) The angular momentum relative to the center of mass is 7.20*10^(-3) J s.
    b) The angular velocity about the center of mass is 9.47 rad/s.

64. a) The angular momentum of the system is d M v.
    b) The rotational energy of the system is M v^2.
    c) The new angular momentum of the system is d M v.
    d) Their new speeds are v_2 = 2 v.
    e) The new rotational energy of the system is 4 M v^2.
    f) The astronomers did work equal to 3 M v^2.

66. The 1000-kg mass accelerates at 1.41 m/s^2.

68. The length of the day would increase by 7.5*10^(-11) s.

70. a) The tension in each cord is M m g/(M + 4 m).
    b) The acceleration of each mass is 4 m g/(M + 4 m).

72. See solution.