A wedge of mass $\displaystyle M$ rests with a rough face in contact with a horizontal table and with another face which is smooth inclined at an angle $\displaystyle \alpha$ to the table. The angle of friction between the wedge and the table is $\displaystyle \epsilon$. A particle of mass $\displaystyle m$ slides down the smooth face. Find the condition that the wedge may move ; and prove that, if it moves, its acceleration is:

$\displaystyle \frac{m\cos \alpha \sin (\alpha - \epsilon) - M\sin \epsilon}{M\cos \epsilon + m\sin \alpha \sin (\alpha - \epsilon)}g$