Answers for Problem Set 14

Chapter 14

#21.
(a) W_Moon = 17 N
(b) r = 2.5 R_Earth

#23. [Text answer]
(a) Proof
(b) 1.9 h

#53. Proof

#80.
(a) No
(b) Same
(c) Yes

Delta V - Delta K = G M m [ 1/R - 3/(2 r) ], where R is the radius of the Earth and r is the distance of the satellite from the center of the Earth. The altitude of the satellite is r - R. The rotation of the Earth has been neglected.

Chapter 16

#19.
(a) Proof
(b) m = 12.47 kg
(c) M = 54.43 kg

#26. A = ( mu_s g / (4 pi² f² ) = 3.1 x 10 ^-2 m

#51.
(a) KE_tr = (1/3) k x_max² = 0.062 J
(b) KE_rot = (1/6) k x_max² = 0.031 J
(c) Proof

#71.
(a) 2 pi sqrt [(L² + 12 x² )/(12 g x) ]
(b) x/L = 1/sqrt(12)
(c) Proof, but note that x/L = 0.289 . The answer to (b) given in the back of the book is correct for x in this part of the problem.