A simple problem of conservation of momentum

mardi 25 février 2014

Trying to understand the conservation of relativistic momentum, I thought of this problem.

It's very simple, and possibly my mistake is embarrassing so I apologize in advance :blushing:



Two particles of identical mass m and speeds v and -v in some frame S collide inelastically and they stop. The relativistic momentum in S is zero all the time.

Now, in system S' moving at -v, the initial momentum should be



p = m v' / √(1-v'2/c2) [1]



where v' is the velocity of the other particle in S'



v' = 2v / (1+v2/c2) [2]



if I substitute [2] into [1] I can get the momentum before impact as a function of v. After some manipulation I get



p = 2mv / (1 - v2/c2)



But the momentum in S' after the impact is that of a particle of mass 2m moving with speed v. So its momentum should be



p = 2mv / √(1 - v2/c2))



so - where did I go wrong?

Thank you





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