Question

A surface is hit elastically and normally by $n$ balls per unit time, all the balls having the same mass $m$ and moving with the same velocity $u$. The force on the surface is:

• A. $mn{u}^2$
• B. $2mn{u}^2$
• C. $0.5mn{u}^2$
• D. $2mnu$

Answer 1

The correct option is D $2mnu$

Velocity of ball initially $v_i=u\hat{i}$

Since the collision is elastic, thus the ball will move with same speed but in opposite direction after collision.

Velocity of ball finally $v_f=-u\hat{i}$

Change in momentum of each ball $\Delta p=m(v_f-v_i)=-2mu\hat{i}$

Magnitude of change in momentum of each ball $|\Delta p|=2mukgm/s$

Net rate of change in momentum of balls $\frac{\Delta p}{\Delta t}=2mnu$

Force acting on the surface $F=\frac{\Delta p}{\Delta t}=2mnu$