# Relativistic collision

1. Apr 30, 2007

### Gyroscope

1. The problem statement, all variables and given/known data
••• A particle of mass 1 MeV/c2 and kinetic
energy 2 MeV collides with a stationary particle of mass
2 MeV/c2. After the collision, the particles stick together. Find
(a) the speed of the first particle before the collision, (b) the
total energy of the first particle before the collision, (c) the ini-
tial total momentum of the system, (d) the total kinetic energy
after the collision, and (e) the mass of the system after the
collision.

I could do (a,b) and (c).

My doubts are on (d).
I know momentum must be conserved.
So,

$$p_0=(m_1'+m_2')v\gamma$$

Total energy must be conserved too:

$$E_0=(m_1'+m_2')c^2\gamma$$

If I work out these too expressions, I don't find the correct value.

What am I doing wrong.
2. Relevant equations

3. The attempt at a solution

2. Apr 30, 2007