A ball A, moving with kinetic energy E, makes a head - on elastic collision with a stationary ball with mass ‘n’ times that of A. The maximum potential energy stored in the system during the colision is

Let A have mass ‘m’ and initial velocity ‘u’

${\mathrm{E}}_{\mathrm{i}}=\frac{1}{2}{\mathrm{mu}}^2=\mathrm{E}$ and momentum

P = mu = constant

The potential energy becomes maximum when the kinetic energy is minimum. This occurs when the bodies move with the same velocity.

maximum kinetic energy ${\mathrm{E}}_{\mathrm{f}}=\frac{{\mathrm{P}}^2}{2(\mathrm{m}+\mathrm{nm})}$

maximum potential energy

$=E_i-E_f=\frac{1}{2}m{u}^2-\frac{m^2{u}^2}{2m(1+n)}=\frac{nE}{n+1}$