A wedge with mass rests on a frictionless horizontal table top. A block with mas

Question

A wedge with mass rests on a frictionless horizontal table top. A block with mass is placed on the wedge (the figure (a)). There is no friction between the block and the wedge. The system is released from rest.
Express your answer in terms of M, m, a (alpha), and g.
A) Calculate the horizontal component of the acceleration of the wedge.
I know the answer is -gm/(M+m)tan(a)+(M/tana)
but i do not understand why
B) Calculate the horizontal component of the acceleration of the block.
C) Calculate the vertical component of the acceleration of the block.

Explanation / Answer

Draw a force diagram with the forces parallel and perpendicular to the slope. You will have three forces: F1 = Parallel and down = m g sin ? F2 = Perpendicular and down = m g cos ? F3 = Perpendicular and up (Reaction to F2) = m g cos ? The horizontal force on both the wedge and block is: F1 cos ? = m g sin ? cos ? =

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