College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 26 - Conceptual Questions - Page 1008: 2


The acceleration is less than $\frac{F}{m}$

Work Step by Step

We can write an expression for the relativistic mass of an object when it is moving at speed $v$: $m_{rel} = \frac{m}{\sqrt{1-\frac{v^2}{c^2}}}$ We can find an expression for the acceleration: $F = m_{rel}~a$ $a = \frac{F}{m_{rel}}$ $a = \frac{F}{\frac{m}{\sqrt{1-\frac{v^2}{c^2}}}}$ $a = \frac{F~\sqrt{1-\frac{v^2}{c^2}}}{m} \lt \frac{F}{m}$ The acceleration is less than $\frac{F}{m}$.
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