University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 4 - Newton's Laws of Motion - Problems - Discussion Questions - Page 124: Q4.37

Answer

The forces are the same, but the compact car experiences the larger acceleration.

Work Step by Step

The two forces mentioned in the question, $\vec{F}_{big\;on\;small}$ and $\vec{F}_{small\;on\;big}$, are always equal in magnitude and opposite in direction. This is a statement of Newton’s third law. The forces are the same, but the compact car experiences the larger acceleration. Because the 2500-kg car has 2.5 times the inertia of the 1000-kg car, and net force = ma, the smaller mass experiences an acceleration 2.5 times larger, because a = F/m. The passengers in the smaller vehicle are more likely to be injured because they are brought to rest in a smaller amount of time (due to their larger acceleration).
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