Question

A particle moving with kinetic energy $E$ makes an head on elastic collision with an identical particle at rest. During the collision

• A. elastic potential energy of the system is always zero
• B. maximum kinetic energy of the system is $\frac{E}{2}$
• C. maximum elastic potential energy of the system is $\frac{E}{2}$
• D. kinetic energy of the system is constant

Answer 1

Answer: (B), (C)

maximum elastic potential energy of the system is $\frac{E}{2}$
maximum kinetic energy of the system is $\frac{E}{2}$

Let mass be $m$ & initial velocity $u$

$\therefore \frac{1}{2}m{u}^2=E$

In elastic collision $K{E}_{before}=K{E}_{after}$

Since head on collision both the particles move with same speed.

$\therefore$ By conservation of momentum

$mu=2mv\therefore v=\frac{u}{2}\therefore K_{after}=\frac{1}{2}\left(2m\right)v^2=\frac{1}{2}2m(\frac{u}{2}{)}^2=\frac{1}{4}m{u}^2=\frac{E}{2}$

By conservation of Total energy

$T{E}_{Before}=T{E}_{After}E=K{E}_{After}+P{E}_{After}\therefore P{E}_{After}=E-\frac{E}{2}=\frac{E}{2}$