Question

A moving body of mass m makes a head on elastic collision with another body of mass $2$m which is initially at rest. Find the fraction of kinetic energy lost by the colliding particle after collision.

Answer 1

By kinetic energy conservation law,

$\frac{1}{2}{m}_1{u_1}^2+\frac{1}{2}{m}_2{u_2}^2=\frac{1}{2}{m}_1{v_1}^2+\frac{1}{2}{m}_2{v_2}^2$

$v_1=\left(\frac{m_1-m_2}{m_1+m_2}\right)u_1+\left(\frac{2m_2{u}_2}{m_1+m_2}\right)$

$u_2=0,$

$v_1=u_1\left(\frac{m-2m}{m+2m}\right)=-\frac{u_1}{3}\frac{m}{s}$

$=\frac{\frac{1}{2}{m}_1{u_1}^2-\frac{1}{2}{m}_1{v_1}^2}{\frac{1}{2}m{u_1}^2}=1-\frac{{v_1}^2}{{u_1}^2}=1-\frac{-\frac{u_1}{3}}{{u_1}^2}=\frac{8}{9}$