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 116: 65

Answer

The coefficient of kinetic friction between the surface of the hill and the toboggan is $0.14$

Work Step by Step

As shown in the image below, the force that propels the toboggan to run downhill is $m\vec{g}\sin\theta$, with $\theta$ to be the angle of the hill. Opposing this movement is the kinetic frictional force $f_k$. Since the toboggan is in constant velocity, these 2 forces balance each other. $$mg\sin\theta=f_k=\mu_kF_N$$ The normal force $F_N$ is in opposite direction with $mg\cos\theta$. Since these two forces do not affect the movement, they balance each other, too. $$F_N=mg\cos\theta$$ Therefore, $$mg\sin\theta=\mu_k\times mg\cos\theta$$ $$\sin\theta=\mu_k\cos\theta$$ $$\mu_k=\tan\theta=\tan8^o=0.14$$
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