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 9 - Impulse and Momentum - Exercises and Problems - Page 243: 56

Answer

$3\;\rm m/s$

Work Step by Step

We can use the conservation of momentum to find the speed of the 30-ton car. $$p_i=p_f$$ The two cars initially were at rest, so $p_i=0$ $$p_f=m_1v_1+m_2v_2=0\tag 1$$ where $m_1$ is the 30-ton car and $m_2$ is the 90-ton car. Since the speed of $m_1$ is 4 m/s relative to $m_2$, so $$v_1=v_2+4$$ Solving for $v_2$ since we need to find $v_1$; $$v_2=v_1-4$$ Plugging into (1); $$m_1v_1+m_2(v_1-4)=m_1v_1+m_2 v_1-4m_2 =0$$ Solving for $v_1$; $$v_1=\dfrac{4m_2}{m_1+m_2}$$ Plugging the known; $$v_1=\dfrac{4\times 90\times 10^3}{(30+90)\times 10^3}=\color{red}{\bf 3}\;\rm m/s$$ This means that the speed of the 30-ton car relative to the ground is 3 m/s.
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