(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle having a [tex]3m[/tex] rest mass is moving with velocity [tex]v[/tex] towards another particle, which is at rest and having a rest mass of [tex]m[/tex]. After the collision, two new particle are formed, each having a rest mass of [tex]2.5m[/tex]

I'm required to find the minimum velocity for which such a process occurs.

2. The attempt at a solution

(1) conservation of energy:

[tex] \gamma \cdot 3mc^{2} + mc^{2} = 2 \sqrt{p^{2}c^{2}+(2.5m)^{2}c^{4}} [/tex]

(2) conservation of momentum:

[tex] \gamma \cdot 3mv = 2p [/tex]

solving these two equations with [tex]\gamma = \frac{1}{\sqrt{1-v^{2}/c^{2}}} [/tex], we get:

[tex] v = \frac {\sqrt{21}}{5} c [/tex]

This answer is correct, but I have several questions regarding my own solution (LOL):

1) why is the energy of both particles equal?

2) why is equation no.(2) correct? in other words, why is the momentum of the new particles equal? and why is it assumed that they both will move along the same direction that the 3m particle has moved?

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# Relativistic dynamics problem

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