Momentum Collisions: Mass of Resulting Object

[Gamst_12]

Homework Statement

2 objects going in opposite directions at the same (relativistic) speed crash and stick together. The second object has half the mass of the first. What is the mass of the resulting object?

Homework Equations

The Attempt at a Solution

Okay if objects momentum is p[A]+p=p[C], i assume the momentum of A is mu/\sqrt{}(1-u^{}2/c^{}2) and B is m(-u)/\sqrt{}(1-u^{}2/c^{}2)
But I am a bit confused as what to do next.

 

[Cyosis]

The second object has half the mass of the first. So replace the m with 1/2 m for the relativistic momentum of B. There are two things conserved in a relativistic collision, momentum and energy. You can write down both and start solving, however there is an easier way by using invariance equations.

<br /> -\frac{E^2}{c^2}+p^2=-m^2c^2<br />

Using this invariance equation you can easily find the mass for the composite object since you know the total energy and momentum of the system. If you have never seen this equation before perhaps it's smart to derive it!