Two blocks A and B are placed over each other on a horizontal smooth surface and pulled by a horizontal force F as shown. The blocks do not slip over each other :-

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Since the blocks do not slip, static friction acts between A and B. The work done by friction on A is positive, while on B it's negative. However, the total work done by friction on the A+B system is zero because their displacements are the same. Applying the work-energy theorem to the A+B system: $W_{b y F} = Δ K E$ .

$W_{b y F} + W_{b y f r} = k_{f} - k_{i} (o n A + B)$

$\displaylines W_{f ro n (A + B)} = 0$

$∴ W_{b y F} = k_{f} - k_{i} = Δ k$

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