Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 9 - Exercises and Problems - Page 164: 36


a) The ratio is 3. b) $v_{2f}=2v_{1i}$

Work Step by Step

We know the following equation for elastic collisions: $v_{1f}=\frac{m_1-m_2}{m_1+m_2}v_{1i}+\frac{2m_2}{m_1+m_2}v_{2i}$ $m_1$ ends up at rest, $v_{1f}$, and $v_{1i}=-v_{2i}$, so it follows: $\frac{m_1-m_2}{m_1+m_2}=\frac{2m_2}{m_1+m_2}$ $m_1-m_2=2m_2$ $m_1=3m_2$ Thus, the ratio is 3. b) We use the mass ratio to find the final speed of the second particle: $v_{2f}=\frac{4m_2}{2m_2}v_{1i}=2v_{1i}$
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