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 $\Delta t$.

• A. The average elastic force acting on the ball is $\frac{\left[m\right(u+v\left)\right]}{\Delta t}.$
• B. The average elastic force acting on the ball is $\frac{\left[2m\right(u+v\left)\right]}{\Delta t}.$ ​​​​
• 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 correct options are
B The average elastic force acting on the ball is $\frac{\left[2m\right(u+v\left)\right]}{\Delta t}.$ ​​​​
C The kinetic energy of the ball increases by 2mu (u + v)

In an elastic collision : $v_{sep}=v_{app}$
or $v^{\prime }-u=v+u$ or $v^{\prime }=v+2u$

Chnage in momentum of ball is
$|P_f-P_i|=|m(-v^{\prime })-mv|=m(v^{\prime }+v)=2mu(u+v)$
Average force is $\frac{\Delta P}{\Delta t}=\frac{2m(u+v)}{\Delta t}$
Change in $KE,K_f-K_i=\frac{1}{2}m{v}^{\prime 2}-\frac{1}{2}m{v}^2=\text{2m u (u + v)}$