Question

A ball moving with a velocity v hits a massive wall moving towards the ball with a velocity u. An elastic impact lasts for time $\Delta$t, Then :

• A. the average elastic force acting on the ball is $\left[m\right(u+v\left)\right]/\Delta t$.
• B. the average elastic force acting on the ball is $\left[2m\right(u+v\left)\right]/\Delta t$.
• 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 average elastic force acting on the ball is $\left[2m\right(u+v\left)\right]/\Delta t$.
the kinetic energy of the ball increases by 2mu (u + v).

Given : $v_{wall}=-u$ $u_1=v$

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

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

$\frac{-v^{\prime }-(-u)}{v-(-u)}=-1$ $⟹v^{\prime }=v+2u$

Change in momentum of the ball $\Delta P=m(v+2u)-m(-v)$

$\Delta P=2m(v+u)$

Thus average elastic force acting on the ball $F=\frac{\Delta P}{\Delta t}=\frac{2m(v+u)}{\Delta t}$

Increase in kinetic energy of the ball $\Delta K.E=K.E_f-K.E_i$

$\Delta K.E=\frac{1}{2}m(v+2u{)}^2-\frac{1}{2}m{v}^2=2mu(v+u)$