Question

A ball of mass $m$ moving with a velocity $v$ hits a massive wall of mass $\text{M}$ $(M>>m)$ moving towards the ball with a velocity $u$. The elastic impact lasts for a time $\Delta t.$

• A. The average elastic force acting on the ball is $\frac{m(u+v)}{\Delta t}$
• B. The average elastic force acting on the ball is $\frac{2m(u+v)}{\Delta t}$
• C. The kinetic energy of the ball increases by $2mu(u+v)$
• D. The kinetic energy of the ball remains the same after the collision.

Answer 1

Answer: (B), (C)

The kinetic energy of the ball increases by $2mu(u+v)$

In an elastic collision
$v_{sep}=v_{app}$
or v' - u = v + u
or v' = v + 2u
change in momentum of ball is $|p_f-p_i|$
$=|m\left({-v}^{\prime }\right)-mv|$
$=m(v^{\prime }+v)$
$=2m(u+v)$
average force = $\frac{\Delta p}{\Delta t}=\frac{2m(u+v)}{\Delta t}$
change in KE = $K_f-K_i=\frac{1}{2}m{v}^{\prime 2}-\frac{1}{2}m{v}^2$
= $2mu(u+v)$