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Relativistic Elastic Collisions

  1. Mar 13, 2009 #1
    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
  2. jcsd
  3. Mar 13, 2009 #2


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    Science Advisor
    Homework Helper

    Hi wam_mi! :smile:

    (have a square-root: √ and try using the X2 and X2 tags just above the Reply box :wink:)
    Nooo … start again …

    don't use T1 + mc2 … it's horrible and pointless …

    use energy = m/√(1 - v2/c2) and momentum = mv/√(1 - v2/c2) :wink:
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