A particle of mass m1 scatters elastically from a particle of mass m2 initially at rest as...

A particle of mass m1 scatters elastically from a particle of mass m2 initially at rest as described in Problem. Find the curve r(φ1) such that the time it takes the scattered particle to travel from the collision point to any point along the curve is a constant.

A particle of mass m1 with an initial kinetic energy T1 makes an elastic collision with a particle of mass m2 initially at rest. m1 is deflected from its original direction with a kinetic energy T′1 through an angle φ1 as in Figure 7.6.1. Letting α = m2/m1 and γ= cos φ1, show that the fractional kinetic energy lost by m1, ΔT1/T1 = (T1 − T′1)/T1 is given by