Elastic Collision in 2D between 2 Hard Spheres

  • #1

Homework Statement



By resolving the momentum equations parallel and perpendicular to the incident beam direction, show that α is related to the speed v2 of the recoiling particle by:

cos α = m2*v2/(2μ*u1) where μ=m1m2/(m1+m2)

Homework Equations



See attachment for diagram.


m1v1cosθ +m2v2 cosψ = m1u1 ( parallel equation )

m1v1sinθ + m2v2 sinΨ =0 ( perpendicular equation )

The Attempt at a Solution



expressing v1 from the perpendicular equation, then v1 was substituted into the parallel equation, and rearranging for v2 i got
cos α = m2v2/m1u1 , which is not the right thing. What am I doing wrong?
 

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