Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 5 - Dynamics of Uniform Circular Motion - Problems - Page 139: 37



Work Step by Step

1) Find the centripetal acceleration $a_c$ of the satellite Since the centripetal force of a satellite is the same as its gravitational force, the centripetal acceleration is similar to the gravitational acceleration: $a_c=g$ To find $g$, we have the formula $$g=G\frac{M_E}{r^2}$$ We have $G=6.67\times10^{-11}Nm^2/kg^2$, $M_E=5.98\times10^{24}kg$ and radius $r$ is given to be $6.7\times10^6m$. Therefore, $$a_c=g=8.885m/s^2$$ 2) The plane has the same $a_c=8.885m/s^2$ and its radius of flying path $r=15m$. Its speed needs to be $$v^2=a_cr=133.275m^2/s^2$$ $$v=11.54m/s$$
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