Question
Prove that the work done in a frictional surface is non zero in a closed path.
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Answer
Let $\mathrm{F}_f$ be the force of friction in a surface. The work done to carry a mass $m$ from a point $A$ to another point $B$ is, $-F_f$ $A B$. In the return path $B$ to $A$ also, the work done is $-F_f A B$, since the $F_f$ acts against the motion. The net work done is therefore, $-2 \mathrm{~F}_f(\mathrm{AB})$. Since friction is dependent on the nature of the surface it is dependent on path.
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