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: 60

Answer

The minimum pulling force is $308.3N$.

Work Step by Step

As we can see in the photo below, in (a), the pulling force $\vec{P}$ carried out at the head of the clown gets translated to the rope tied to his feet into another force $\vec{P}$ there. In diagram (b), this pulling force $\vec{P}$, to be able to yank the clown's feet out, has to overcome the maximum static frictional force $f_s^{max}$. Therefore, $$P_{min}=f_s^{max}=\mu_sF_N$$ The normal force $F_N$ is supported here by $P$ and balance the weight of the clown, as shown in photo (b). That means $F_N=mg-P$ $$P_{min}=\mu_s(mg-P_{min})$$ $$P_{min}=0.53(890-P_{min})=471.7-0.53P_{min}$$ $$P_{min}=308.3N$$
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