Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 6 - Exercises and Problems - Page 107: 84


The proof is below.

Work Step by Step

We know that the force of friction is equal to the coefficient of friction times the normal force. We know that the normal force is given by $mgcos\theta$. Thus, we find: $F_f =mgcos\theta\mu $ We have to find the distance the object travels, which is: $x=\frac{\sqrt{2hR-h^2}}{cos\theta}$ We know that work is equal to force times distance, so we find: $W = mgcos\theta\mu \times \frac{\sqrt{2hR-h^2}}{cos\theta}$ $W=mg\mu \sqrt{2hR-h^2}$
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