Question

A sphere impinges elastically on a wall at an angle a (Fig.). The mass of the sphere is m, its speed before and after the collision has the same value v, and the angle of incidence is equal to the angle of rebound. Find the magnitude and direction of the change in momentum of the sphere.

Answer 1

Answer: 2mv sin a. The vector change in momentum is directed away from the wall.

Explanation:

The vector OA (Fig.) represents the momentum of the ball before the collision; the vector OB, that after the collision. The vector AB represents the change in the momentum of the

ball. If vectors OA and OB are resolved into components perpendicular and parallel to the wall then, since the angles a are the same and the magnitudes of vectors OA and OB are equal, it obviously follows that the change in momentum is due only to the change in direction of the components perpendicular to the wall, and is equal to 2 my sinα.