Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 5 - Circular Motion; Gravitation - Problems - Page 134: 39

Answer

(a) $g = 9.72 ~m/s^2$ (b) $g = 2.43 ~m/s^2$

Work Step by Step

Let's use 6400 km as the radius of the earth. (a) At 6400 m above the Earth's surface, $r = 6.4064 \times 10^6 ~m$ $g = \frac{GM}{r^2} = \frac{(6.67 \times 10^{-11} ~N \cdot m^2/kg^2)(5.98 \times 10^{24} ~kg)}{(6.4064 \times 10^6 ~m)^2}$ $g = 9.72 ~m/s^2$ (b) At 6400 km above the Earth's surface, $r = 1.28 \times 10^7 ~m$ $g = \frac{GM}{r^2} = \frac{(6.67 \times 10^{-11} ~N \cdot m^2/kg^2)(5.98 \times 10^{24} ~kg)}{(1.28 \times 10^7 ~m)^2}$ $g = 2.43 ~m/s^2$
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