Question

A particle moving with kinetic energy $K$ makes a head on elastic collision with an identical particle at rest. Find the maximum elastic potential energy of the system during collision.

Answer 1

let the mass of the particles be m and v be its velocity. then$0.5m{v}^2$=k.
in an elastic collision, the k.e. before and after the collision remains the same and is minimum when the two particles are moving with the same speed, during collision.
applying momentum conservation
mv+0=(m+m)V
V=$\frac{v}{2}$
K.E.=$0.5\times 2m\times V^2$,put V=$\frac{v}{2}$= 0.5k (the kinetic energy when both masses are moving with same speed, at this moment k.e. is minimum and p.e. is maximum)