Question

A sphere of mass $m$ slides with velocity $\nu$ on a frictionless surface towards a smooth inclined wall as shown in Fig. If the collision with the wall is perfectly elastic, find (a) the impulse imparted by the wall on the sphere, (b) the impulse imparted by the floor on the sphere.

Answer 1

As the collision is elastic, so the sphere will rebound with the same speed after collision.

$J_{1}cos\theta =J_2$ (i)

$-m\nu +J_{1}sin\theta =m\nu$ (ii)

Solving Eqs. (i) and (ii), we get

$J_2=2m\nu cot\theta$

$J_1=2m\nu cosec\theta$