Question

A ball of mass $m$ moving with a velocity $v$ strikes a wall moving toward the ball with a velocity $u$. An elastic impact lasts for $t$ sec. Then the mean elastic force acting on the ball is:

• A. $\frac{2mv}{t}$
• B. $\frac{2m(v+u)}{t}$
• C. $\frac{2m(v+2u)}{t}$
• D. $\frac{m(2v+u)}{t}$

Answer 1

Answer: (B)

$\frac{2m(v+u)}{t}$

Here, the ball moves towards the wall in positive direction and hence
relative speed of the ball $=(v+u)$
While the ball bounces it moves in the opposite direction and speed after rebouncing $=-(v+u)$
And to find the net elastic force we need to add these two forces,

$F=m\frac{\Delta v}{\Delta t}=\frac{m}{t}\left[\right(v+u)-[-(v+u)\left]\right]$

Net elastic force $F=\frac{2m}{t}(v+u)$