Question

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

Answer 1

This is a beautiful example where I can show you,how actually Newton's 2nd Law of motion acts.

So,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`)

In most of the cases,what happens mass of the object under consideration is fixed,so `(dm)/(dt) =0`,so we write, `F= m(dv)/(dt) = ma`

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 to maintain the constant velocity is `v (dm)/(dt) = 10 *(20/1000) = 0.2 N`