Question

On a smooth inclined plane of angle α is placed on in such a way that the upper wedge face is horizontal. On this horizontal face is placed a block of mass m. Find the resultant acceleration of the block in subsequent motion.

Answer 1

m will have acceleration vertically downward. Let call it a_m.

M will have acceleration along inclined plane lets call is a_M

\(\because\) m, M have no relative acceleration vertically downward,

a_M sin α = a_m   ..…(i)

Let normal force on block be N,

mg – N = m a_m

N = m(g – a_m)

From free body diagram of wedge

Answer 2

f = \(\cfrac{(M + m)gsin^2 \alpha}{m + msin^2 \alpha}\)