Question

A perfectly smooth sphere of mass m₁ moving with velocity v collides elastically with a similar but initially stationary sphere of mass m₂ (m₁ > m₂) and is deflected through an angle θ_L. Describe how this collision would appear in the center of mass frame of reference and show that the relation between θ_L and the angle of deflection θM, in the center of mass frame is 

tanθ_L = sinθ_M/[m₁/m₂ + cos θ_M] 

Show also that θ_L can not be greater than about 15^◦ if m₁/m₂ = 4.

Answer 1

The description of the scattering event in the CM system is shown in Fig. 7.11. 

From the velocity triangle