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

Question

A wedge with mass M rests on a frictionless horizontal table top. A block with mass m is placed on the wedge (the figure (Figure 1) (a)). There is no friction between the block and the wedge. The system is released from rest.

a. Calculate the x component of the acceleration of the wedge. Express your answer in terms of M, m, , and constant g.

b. Calculate the x component of the acceleration of the block. Express your answer in terms of M, m, , and constant g.

c. Calculate the y component of the acceleration of the block. Express your answer in terms of M, m, , and constant g.

Explanation / Answer

a) a = acceleration of the wedge

a' = acceleration of the block relative to the wedge

for M: Nsin = Ma

for m: mgsin = m(a' - acos)

mgcos - N = masin

solve N, a and a' from above 3 eqautions and get

a = mgsincos/(M + msin2)

a' = (M + m)gsin/(M + msin2)

b) horizontal component of the acceleration of the block = a'cos- a = Mgsin/(M + msin2)

c) vertical component of the acceleration of the block = a'sin =(M + m)gsin2/(M + msin2)

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