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

Q: Consider two identical particles A and B have the same mass m in the inertial frame

R where B is at rest. The two particles collide and their trajectories after

impact are symmetrical with respect to the incident direction. Let t be the

angle between the trajectories after collision. Obtain an expression of cos t as

a function of the mass m and the kinetic energy T1 of the particle A.

2. Relevant equations

(i) Einstein Relation / Relativistic Energy Relation between energy and momentum

E^2 = (mc^2)^2 + (mod p)^2 *c^2

where E = energy

and p = momentum

(ii) Conservation of Energy: Energy before = Energy after

(iii) Conservation of Momentum: Momentum before = Momentum after

3. The attempt at a solution

Using Energy Conservation: T1 + mc^2 + mc^2 = Energy after

Using Momentum Conservation: ???

Since I do not know any velocities and I only know particle A has kinetic energy T1 and therefore total energy T1 + mc^2.... I don't know how to complete this problem.

Also I try to do momentum conservation in the x-direction

so before the impact particle A would have p(x-component)

and after the impact particle A would have p1(x-component) = p1 *cos (t/2)

and after the impact particle B would have p2 (x-component) = p2 * cos(t/2)

Please help!

Thanks a lot guys

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# Relativistic Elastic Collisions

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