## Physics (10th Edition)

Published by Wiley

# Chapter 6 - Work and Energy - Problems - Page 166: 10

#### Answer

The work done by the pushing force $P$ is $+1120J$. The work done by kinetic friction $f_k$ is $-943.25J$. The work done by the $mg$ and $F_N$ is $0$.

#### Work Step by Step

The four forces that act on the box are the pushing force $P$, kinetic friction $f_k$, gravitational force $mg$ and normal force $F_N$ Since there is no vertical displacement, the work done by $mg$ and $F_N$ is 0. 1) Pushing force $P$ $P=160N$, $s=7m$, the angle $\vec{P}$ makes with the box's displacement $\theta=0^o$. The work done by $P$ is $$W=Ps=+1120J$$ 2) Kinetic friction $f_k$ We have $f_k=\mu_kF_N=\mu_kmg$ (since there is no vertical acceleration) So, $f_k=0.25\times55\times9.8=134.75N$ $f_k$ opposes the motion, so the angle $\vec{f}_k$ makes with $\vec{s}$ is $\theta=180^o$ The work done by $f_k$ is $$W=(f_k\cos180)s=-943.25J$$

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