Question
Prove that the work done in a frictional surface is non zero in a closed path.

Answer

Let Ff 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, -Ff AB. In the return path B to A also, the work done is -Ff AB, since the Ff acts against the motion. The net work done is therefore, -2Ff (AB). Since friction is dependent on the nature of the surface it is dependent on path.

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