Question

A ball of mass m falling vertically, collides elastically the inclined face of a wedge of mass M. If after the collision, the ball begins to move horizontally, find the angle of inclination of the wedge. Friction between all the surfaces in contact can be neglected.

Answer 1

45°

Answer 2

The problem is solved using the principles of conservation of momentum and the coefficient of restitution for an elastic collision, specifically by analyzing velocity components along the common normal and common tangent to the colliding surfaces.

1. Horizontal Momentum Conservation: As no external horizontal forces act on the ball-wedge system, the total horizontal momentum is conserved.
2. Relative Tangential Velocity Conservation: Since friction is negligible, no tangential impulse acts during the collision. Thus, the relative velocity component of the ball with respect to the wedge along the tangent to the contact surface remains unchanged.
3. Coefficient of Restitution (Normal Component): For an elastic collision, the relative speed of separation along the common normal is equal to the relative speed of approach along the common normal.

By setting up equations based on these principles and solving them, we find that the angle of inclination of the wedge must be $45^\circ$.