Mass and momentum problem in Sp.Relativity

[zimo]

Problem:
A particle with rest mass m0 and kinetic energy 3(m0)c^2 makes a complete inelastic collision with a stationary particle of rest mass 2m0. what are the velocity and rest mass of the composite particle?

I tried to approach the problem first by identifying the velocity of the first particle before collision and got v=0.968c.
Then i can't figure out why the rest mass of the composite particles is not simply 3m0, but this question is accompanied by a final answer, and it is not 3m0 for their composite rest mass.

*BTW - after that I think that momentum conservation I will have no problem to find the new velocity...

What am I missing?

 

[Hootenanny]

Problem:
A particle with rest mass m0 and kinetic energy 3(m0)c^2 makes a complete inelastic collision with a stationary particle of rest mass 2m0. what are the velocity and rest mass of the composite particle?

I tried to approach the problem first by identifying the velocity of the first particle before collision and got v=0.968c.
Then i can't figure out why the rest mass of the composite particles is not simply 3m0, but this question is accompanied by a final answer, and it is not 3m0 for their composite rest mass.

*BTW - after that I think that momentum conservation I will have no problem to find the new velocity...

What am I missing?

Remember that in relativity, mass is not a conserved quantity and in inelastic collisions kinetic energy is not conserved either. This is why the rest mass of the composite particle isn't simply the sum of the rest masses of the two constituent particles.

As you correctly say momentum is conserved in this case. However, even though kinetic energy isn't conserved in the collision, the total energy must be conserved. Using these two constraints (momentum and total energy conservation) you should be able to determine both the rest mass and velocity of the composite particle.

 

[cryptic]

Because of mass-energy equivalence both (mass and energy) should be conserved.

 

[zimo]

Thanks, now I got it right, thanks to you!

 

[Hootenanny]

Because of mass-energy equivalence both (mass and energy) should be conserved.

This is not true, in general mass itself is not a conserved quantity in relativistic collisions, as illustrated by this question. As a said previously, the total energy of the system as well as the total momentum of the system must remain constant, the masses however will vary.