# 3 Body Collision

1. Jul 11, 2008

### Littlepig

Hi.
I'm having some problem solving this problem: Consider a 3 body elastic collision; 3 bodies on 1 axe; both have known initial velocity≠0 and mass≠0, Particle 2 is between of 1 and 3 so that v1>0 and (v2 >0 or v2<0) and v3<0.
Now, can I calculate the final velocity of all particles without assumptions??

Energy and momentum conservation only gives 2 equations for 3 variables.

However, if one make an assumption(like final velocity of 1 is equal final velocity of 2), one can solve it. This leads to my second question: assuming mass of 2 >> mass 1 and mass 2>> mass 3, can you suggest one assumption physically plausible in a way that final velocity of 2≠0 ? (particles have no special configuration, like rectangles or circles)

I was thinking of having some fraction of final velocity of 1 as final velocity of 2, but I'm not sure if it is plausible nor what fraction should i use use...xD

Littlepig

2. Jul 12, 2008

### BobMonahon

Think of the particles at point of collision: P1,P2,P3.
Now think of them as a system of [P1] and [P2,P3] - that is, a two-body problem.

The technique for solving the two-body problem is to convert to the Center-of-mass-at-rest frame of reference. In that COM/rest frame, total momentum is zero.

The only possible solution for the velocities after collision, if total momentum is zero, is that they reverse - that is [P1] has +v coming in, and -v going out. For two-body problem, you can prove this.

So you can solve 1/3rd of the problem: Convert to COM-at-rest frame, reverse the velocity of P1, and then convert back to the Lab frame.

Do you see that the same logic will hold for P3? And that then the same holds for P2?

Regards, BobM