Calculate Mass at Rest After Relativistic Particle Collision

[martyf]

Homework Statement

A relativistic particle with mass at rest M0 and velocity v hits another particle with mass at rest M1. the collision is perfectly inelastic. How can I calculate the mass at rest of the new particles after the collision?

Homework Equations

The Attempt at a Solution

 

[nickjer]

Conservation of momentum and total energy.

 

[Cyosis]

Easiest way to do this is using 4-momentum, $p_\mu=(\frac{E}{c},\vec{p})$. Note that 4-momentum is conserved and $p^\mu p_\mu=-m^2 c^2$ is invariant.