Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 4 - Dynamics: Newton's Laws of Motion - Problems - Page 103: 39

Answer

The maximum angle for the hill where we can leave the car parked is $42^{\circ}$.

Work Step by Step

The component of the car's weight which is directed down the slope is $mg~sin(\theta)$. As long as the force of static friction is enough to oppose this weight, the car will stay on the hill without sliding down. $F_f = F_N~\mu_s = mg~cos(\theta)~\mu_s$ $mg~sin(\theta) = mg~cos(\theta)~\mu_s$ $tan(\theta) = \mu_s$ $\theta = tan^{-1}(0.90)$ $\theta = 42^{\circ}$ The maximum angle for the hill where we can leave the car parked is $42^{\circ}$.
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