Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 36 - Relativity - Conceptual Questions - Page 1097: 10

Answer

$p_A \gt p_B$

Work Step by Step

We can write an expression for the momentum of particle A: $p_A = \gamma_A~m_A~v_a$ We can write an expression for the momentum of particle B: $p_B = \gamma_B~m_B~v_B$ $p_B = \gamma_B~(2m_A)~(v_A/2)$ $p_B = \gamma_B~m_A~v_A$ In general: $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ As $v$ increases, the value of $\gamma$ also increases. Therefore, $\gamma_A \gt \gamma_B$, since $v_A \gt v_B$ Then, $p_A \gt p_B$, since $\gamma_A \gt \gamma_B$
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