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.
(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
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)
Thanks a lot guys