# Elastic Collision using Special Relativity

1. May 28, 2013

### sanjewierden

1. The problem statement, all variables and given/known data
I was given the following problem and I an trying to discover if it can be answered by transforming to the center of mass frame and then transforming back.

"Consider a perfectly elastic collision between a particle moving with kinetic energy 10 times its rest mass energy and an identical particle at rest. After the collision the incident particle is moving in a direction 10 degrees deflected from its original path. Find the final kinetic energies of both particles and the angle of the path of the struck particle relative to the incident direction."

3. The attempt at a solution
I started using the relationship of the rest mass energy to show
KE= ρ^2/(2m) = ((γ^2)/2)*m*v^2
so 20= (γ^2)(β^2) thus, β=sqrt(20/21) and γ=sqrt(21)

then I used conservation of momentum and conservation of momentum to try and answer the question. I tried it using a transform to the center of mass frame but I want to be sure that this is even possible. I always get confused when doing these transformations as well.

2. May 29, 2013

### Staff: Mentor

Hi. Welcome to Physics Forums.

Isn't the kinetic energy given by $KE=mc^2(\gamma -1)$, in which case γ=11?