Question

a wedge of mass m rests on a horizontal surface. the inclination of the wedge is alpha. a ball of mass m moving horizontally with speed u hits the inclined face of the wedge inelastically and after hitting slides up the inclined face of the wedge. find the velocity of the wedge jsut after collision.

Answer 1

If M is moving to the left, then the actual trajectory is sketched as below, where aM is the acceleration of the block relative to the wedge of mass M.

Now, we look at the force diagram of the wedge and the block.

For M:     N2 sin θ=Ma1..............(1)For m:    mg−N2 cos θ=maM sin θ....................(2)               N2 sin θ=m(aM cos θ−a1)...................(3)


This is a set of simultaneous equations with 3 unknowns. We

If M is moving to the left, then the actual trajectory is sketched as below, where aM is the acceleration of the block relative to the wedge of mass M.

Now, we look at the force diagram of the wedge and the block.

For M:     N2 sin θ=Ma1..............(1)For m:    mg−N2 cos θ=maM sin θ....................(2)               N2 sin θ=m(aM cos θ−a1)...................(3)

This is a set of simultaneous equations with 3 unknowns. We obtain,

a1=mg sin θ cos θM+m sin2 θ and aM=(M+m)g sin θM+m sin2 θ