Question

Sand is deposited at a uniform rate of 20g/s and with negligible kinetic energy unto an empty convegor belt moving horizontally at a constant speed of 10m/s. Calculate the power required to maintain the constant velocity?

Answer 1

`2 W`

Explanation:

From Newton's 2nd Law of motion,

Force is defined as rate of change in momentum,

i,e `F=(dP)/(dt) = (d(mv))/(dt) = m (dv)/(dt) + v (dm)/(dt)` (as momentum `P=mv`)

But,see here, `(dm)/(dt)` is not equals zero,rather `(dv)/(dt)=0` as the belt is moving with constant velocity.

so,here,required amount of force(`F`) to maintain the constant velocity is `v (dm)/(dt) = 10 *(20/1000) = 0.2 N`

So,power required to be supplied to keep on the belt moving with constant speed is `F*v=0.2*10=2 W`