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

A particle of mass m whose total energy is twice its rest energy collides with an identical particle at rest. If they stick together, what is the mass of the resulting composite particle? What is its velocity?

2. Relevant equations

E = (gamma)mc^2

p = (gamma)mu

3. The attempt at a solution

The total energy of the first particle is twice its rest energy, or

E_{total} = (gamma)mc^2

= 2mc^2

or [tex]\gamma[/tex] = 2.

Using this, I find that the velocity of particle 1 is:

u = (sqrt{3})/{2}

Using this is both momentum and energy conservation equations yields the two comparable equations:

m_{final} = (gamma 1)m{1} / (gamma final)

and

m_{final} = sqrt{3}m{1}c / (gamma final) u{final}

Solving this, I get:

u_{final} = c

and

m_{final} = 0

The two answers in relation to each other seem alright, but what is happening here? Is this saying that the particles completely annihilated each other? What is special about the initial conditions that makes this happen?

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# Relativistic Collision of Particles

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