A wedge is placed on the smooth surface of a fixed incline having inclination `theta` with the horizontal. The vertical wall of the wedge has height h and there is a small block A on the edge of the horizontal surface of the wedge. Mass of the wedge and the small block are M and m respectively.
(a) Find the acceleration of the wedge if friction between block A and the wedge is large enough to prevent slipping between the two.
(b) Find friction force between the block and the wedge in the above case. Also find the normal force between the two.
(c) Assuming there is no friction between the block and the wedge, calculate the time in which the block will hit the incline.

Answer

(a) `g "sin"theta`
(b) `f = (1)/(2) mg "sin"2theta`
`N = "mg"cos^(2)theta`
(c) `t = sqrt((2h(M + m sin^(2)theta)/((M+m) g sin^(2)theta))`