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 - General Problems - Page 136: 82

Answer

a) $r=7.00\times10^3m$ b) $a=4.50\times10^{-3}\frac{m}{s^2}$ c) $T=7.83\times10^3s$

Work Step by Step

a) $V_S=\frac{4}{3}\pi r^3=(40\times10^3m)(6\times10^3m)(6\times10^3m)$ $r=7.00\times10^{3}m$ b) $m=2.3\times10^3\frac{kg}{m^3}\times1.44\times10^{12}m^3=3.31\times10^{15}kg$ $a=\frac{(6.67\times10^{-11}\frac{Nm^2}{kg^2})(3.31\times10^{15}kg)}{(7.00\times10^{3}m)^2}=4.50\times10^{-3}\frac{m}{s^2}$ c) $T=2\pi\sqrt{\frac{r^3}{Gm}}=2\pi\sqrt{\frac{(7.00\times10^{3}m)^3}{\big(6.67\times10^{-11}\frac{Nm^2}{kg^2}\big)(3.31\times10^{15}kg)}}$ $=7.83\times10^3s$
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