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 - Focus On Concepts - Page 112: 16

Answer

(c) is the correct answer.

Work Step by Step

We have $f_k=\mu_kF_N$ In A, there are only 2 vertical forces: normal force $F_N$ and gravity force $m_{block}g$. Since there are no vertical movements, these two forces cancel each other. Therefore, $$F_N=m_{block}g$$ In B, if we call the angle $F$ makes with the horizontal $\theta$, $F$ can be translated into a vertical component: $F\sin\theta$, which points upward. Now there are 3 vertical forces: normal force $F_N$ and $F\sin\theta$ both pointing upward and gravity force $m_{block}g$ pointing downward. The upward part and downward part have to balance each other, so $$F_N+F\sin\theta=m_{block}g$$ $$F_N=m_{block}g-F\sin\theta$$ C is the opposite case of B. Again, we can translate $F$ into a vertical component: $F\sin\theta$, but now it points downward. There are 3 vertical forces: normal force $F_N$ pointing upward and $F\sin\theta$ gravity force $m_{block}g$ both pointing downward. The upward part and downward part have to balance each other, so $$F_N=m_{block}g+F\sin\theta$$ As a result, we can rank $F_N$ in ascending order: B, A, C. Since $f_k$ is directly proportional with $F_N$, $f_k$ is ranked in the same order.
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