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Collision Mechanics and Differential Cross Section

  1. Jan 13, 2014 #1
    1. The problem statement, all variables and given/known data
    The problem concerns the collision of a particle on a rigid, fixed disk of radius R. The coefficient of friction is zero, and the coefficient of restitution is 0 < ε < 1, such that vperpendicular, final = εvperpendicular, initial .
    A) Show that tanαincident = εtanαfinal (completed)
    Where α is the angle from the velocity vector to the normal vector

    B) Write a program to numerically solve for the differential cross section (main problem)


    2. Relevant equations
    impact parameter : b
    Scattering angle : θ
    differential cross section : dσ/dΩ = (b/sinθ)|db/dθ|

    3. The attempt at a solution
    I honestly do not know where to start here. I solved this problem for hard-sphere scattering but now solving for the impact parameter, b, leads to a dependence on α, which vanished in the hard-sphere case. Any tips on getting this started would be appreciated.
     
  2. jcsd
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