Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 22 - Electric Charges and Forces - Exercises and Problems - Page 626: 57


$v = 7.3~m/s$

Work Step by Step

We can find the net force on the spaceship due to electric charges and the gravitational force: $F = \vert \frac{kq_1~q_2}{r^2} \vert+\frac{G~m_1~m_2}{r^2}$ $F = \frac{(9.0\times 10^9~N~m^2/C^2)(4400~C)(1.2~C)}{(3.75\times 10^6~m)^2} + \frac{(6.67\times 10^{-11}~N~m^2/kg^2)(3.3\times 10^5~kg)(8.7\times 10^{17}~kg)}{(3.75\times 10^6~m)^2}$ $F = 4.74~N$ We can find the required speed: $F = \frac{mv^2}{r}$ $v^2 = \frac{F~r}{m}$ $v = \sqrt{\frac{F~r}{m}}$ $v = \sqrt{\frac{(4.74~N)(3.75\times 10^6~m)}{3.3\times 10^5~kg}}$ $v = 7.3~m/s$
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