Elastic collisions in COM frame

[joriarty]

Homework Statement

Consider an elastic collision of two particles in the centre of mass frame. Briefly explain why the speed of EACH particle after the collision is the same as before the collision.

(FYI this is exam revision so it isn't worth any marks)

The Attempt at a Solution

The centre of mass itself has the same direction, velocity, and momentum after the collision, but I do not understand why the speed of each individual particle (in the COM frame) is the same after the collision. The individual speeds certainly change from the lab frame, and given that the COM frame does not change at all after the collision, the speeds of individual particle speeds should change too, right?

 

[ehild]

The velocity of the CM is zero in the COM frame, so the total momentum of the colliding particles is also zero, both before and after the collision.

Before the collision m1v1+m2v2=0--->v2=-(m2/m1) v1

and after the collision m1u1 +m2u2 =0 --->u2=-(m2/m1) u1.

Write out the equation for conservation of energy, plug in the expressions for v2 and u2. What do you get?

ehild

 

[joriarty]

Ah I see what's going on now, thanks!