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Question

A block of mass m is placed on an inclined plane which is moving with constant velocity v in horizontal direction as shown in figure. Then find out work done in ground frame by the friction in time t, if the block is at rest with respect to the inclined plane.


A
mg vt sinθ cosθ
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B
mg vt cos2θ
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C
mg vt sinθ cosθ
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D
mg vt sinθ
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Solution

The correct option is A mg vt sinθ cosθ
F.B.D of block with respect to ground.


Block is at rest with respect to wedge
f=mg sin θ
In time t the displacement of block with respect to ground d=vt

Work done by friction with respect to man A
Wf= (Component of friction force along displacement) Displacement
Wf=(mg sinθ cos(180θ))vt
Wf=mg vt cos θ sin θ

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