Chapter 8
2. 15.7 kg m/s down
6. (a) proof
(b) r/R=M/m
(R is the radius of M's orbit)
24. (Ki-Kf)/Ki=m/(m+m_0)
26. 10.8 m/s up
30. 192.5 m/s
46. (a) -1 m/s
(b) 60 J
(c) 30 J
49. the initial speed is 83.5 mph
76. 1.19 kg

Chapter 11
10. 0.48 m
42. F_j=(8/29)Mg N;
F_l=(12.5/29)Mg N;
F_r=(8.5/29)Mg N
47. tan(theta/2) or sin(theta)/(1+cos(theta))
Chapter 12
12. 0.10058 m/s²
38200 km.
55. new minimum ground speed for orbit = 1.76 m/s
Serway Problems
12:17.  16.6 km/s
12:19.  (a) 188 GJ
(b) 103.5 kW
12:20.  0.47 GJ
12:41.  (a) v_relative = sqrt(2G(m_1+m_2)/d)
(the question should ask for relative speed
rather than relative velocity)
(b) K_1 = 1.07 x 10^32 J; K_2 = 2.67 x 10^31 J
12:48.  (a) 0.85 GJ
(b) 2.7 GJ
12:49.  proof
Chapter 13
2. T = 0.8 s; omega = 7.85 rad/s
(since v(.1 s) is not given you can't choose
between these two possible values of the phase)
6. 14.2 cm
7. THE ANSWER IN THE BACK IS INCOMPLETE.  Since no
information is given about the velocity at time
zero, the answer could be -38 mm or +38 mm.
10. f=4.98 Hz
(b) -0.05 m
(c) 2.5 m/s²
(d) 0.354 m/s
22. (a) (15.24 cm) sin(3.49 s-1 t)
(b) A=15.24 cm; omega=3.49 s-1; v_max=53.2 cm/s
30. (a) 7.06 N/m  (b) 6.26 rad/s  (c) 5.09 cm above table
40. proof
72. 4.98 taps/second