Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 4 - Forces and Newton's Laws of Motion - Problems - Page 117: 84

Answer

(a) $T=1.09\times10^4N$ (b) $T=544N$

Work Step by Step

The tension $T$ in the coupling is the force that pulls the cars and causes it to have acceleration. If we take $\sum M$ to be the total mass of all the cars behind a specific coupling, according to Newton's 2nd Law, $$T=\sum Ma$$ (a) The coupling between 30th and 31st cars pulls 20 cars behind it, which has the total mass $$\sum M=20\times6.8\times10^3=1.36\times10^5kg$$ Therefore, $$T=(1.36\times10^5kg)\times(8\times10^{-2}m/s^2)=1.09\times10^4N$$ (b) The coupling between 49th and 50th cars pulls only 1 car behind it, which has the total mass $$\sum M=6.8\times10^3kg$$ Therefore, $$T=6.8\times10^3kg\times8\times10^{-2}m/s^2=544N$$
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