Question

A sphere of mass $m$ moving with velocity $v$ strikes elastically with a wall moving towards the sphere with a velocity $u$. If the mass of the wall is infinitely large, the work done by the wall during collision will be

• A. $mu(u+v)$
• B. $2mu(u+v)$
• C. $2mv(u+v)$
• D. $2m(u+v)$

Answer 1

Answer: (A)

$mu(u+v)$

It is given that $v_w=-u$ and $u_1=v$

let speed of ball after collision be $v^{\prime }$

$e=\frac{\text{velocity of seperation}}{\text{velocity of approach}}$

$e=\frac{v_{wall}+v^{\prime }}{u_1-v_{wall}}$

$1=\frac{-u+v^{\prime }}{v+u}$

$v^{\prime }=v+2u$

work done by wall $=$ change in kinetic energy of ball

$W=\Delta KE$

$W=\frac{1}{2}m{v}^{\prime 2}-\frac{1}{2}m{u}_1^2$

$W=\frac{1}{2}m(v+2u{)}^2-\frac{1}{2}m{v}^2$

$W=mu(u+v)$