A wedge of mass M and inclination α rests on a smooth horizontal floor. A small block of mass m is released from rest on its smooth inclined face. The magnitude of horizontal acceleration of the wedge is:
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Question

A wedge of mass M and inclination α rests on a smooth horizontal floor. A small block of mass m is released from rest on its smooth inclined face. The magnitude of horizontal acceleration of the wedge is:

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G1 Physics · Accepted Answer

Let A be the horizontal acceleration of the wedge and s be the displacement of the block relative to the wedge along the incline. Using horizontal momentum conservation, (M+m)A + m s̈ cosα = 0. Along the incline, s̈ = g sinα + A cosα. Eliminating s̈ gives A = mg sinα cosα/(M + m sin²α). Hence the magnitude is mg sinα cosα/(M + m sin²α).