Question

In the figure shown, a ball of mass m collides perpendicularly on a
smooth stationary wedge of mass M, kept on a smooth horizontal
plane. If the coefficient of restitution of collision is e, then determine
the velocity of the wedge after collision.​

Answer 1

Answer:

$v_w=\frac{(1+e)mv_osin(\theta)}{M+msin^2(\theta)}$

Explanation:

1) Let

$v_w$ : Final Velocity of Wedge

$v_b$ Final velocity of ball

Initial velocity of wedge is 0 and that of ball is $v_o$

2) There is no external force along x-direction .

Linear momentum along x is conserved .

$mv_osin(\theta)=Mv_w-mv_bsin(\theta)--(1)$

And coefficient of restitution is given as :

$e=\frac{v_{sep}}{v_{app}}=\frac{v_b+v_wsin(\theta)}{v_o} \\ \\=> ev_o=v_b+v_wsin(\theta)----(2)$

3) We two equations and two variables ,

On Solving (1) and (2) ,

we get

$v_w=\frac{(1+e)mv_osin(\theta)}{M+msin^2(\theta)}$