The sphere of mass m1 travels with an initial velocity upsil

The sphere of mass m_1 travels with an initial velocity upsilon_1 directed as shown and strikes the stationary sphere of mass m_2. For a given coefficient of restitution e, what condition on the mass ratio m_1/m_2 ensures that the final velocity of m_2 is greater than upsilon_1?

Solution

(i) If m = M: we get v₁ = 0 and v₂ = u₁
The two particles exchange velocities (i.e. The colliding particle comes to rest after collision while the collided particle moves off with the velocity of the colliding particle.

(ii) If m << M: we get v₁ -u₁ and v₂ = 0
m rebounds with almost the same speed, M remains stationary.

(iii) If m >> M: we get v₁ u₁ and v₂ = 2u₁
m continues with the same speed, M goes off with twice the speed of m.