# Bouncing Particles on a smooth table

1. Jan 26, 2005

### Bucky

"Particles A, B and C , each of mass m, lie at rest in a straight line in the order stated. A is projected directly towards B with velocity u. The coefficient of restitution is 0.5 in each impact that follows. Show that there will be three impacts in total and find the final velocities of each particle."

I have 'an' answer for the first part:-

A and B Collide

Velocity of seperation $$= e (u_1 - u_2) =0.5(u-0) =0.5u$$
$$v_1 + v_2 = u // v_1 = u - v_2$$

$$v_2 - v_1 = e(u_1 - u_2)// v_2 - u + v_2 = 0.5u// 2v_2 = 1.5u// v_2 = 0.75u$$
$$v_1 = u - v_2 v_1 = u - 0.75u v_1 = 0.25u$$

is this the right way to do this question? the problem comes later when the moving particles hit each other.

Last edited: Jan 26, 2005