Question

Sand drops from a stationary hopper at the rate of $5kg/s$ falling on a conveyor belt moving with a constant speed of $2m/s$. What is the force required to keep the ball moving and what is the power delivered by the motor moving the belt?

Answer 1

Here mass of sand drops at a rate of $5kg/s$

$⟹\frac{dm}{dt}=5kg/s$

Velocity of conveyor belt , $v=2m/s$

Force required to keep th ball moving , $F=\frac{d}{dt}\left(mv\right)=v\frac{dm}{dt}=5\times 2=10N$

Power delivered by the motor ,$P=F\cdot v=10\times 2=20W$