Power needed to keep velocity of conveyor belt constant

[diablo2121]

1. The problem statement, all variables and given/known data
A conveyor belt travels at a constant velocity v while sand is poured onto it at rate of \frac{dm}{dt}. Find the power needed to drive the conveyor belt.


2. Relevant equations
P = \frac{dW}{dt} = F*v
F = m*\frac{dv}{dt}


3. The attempt at a solution
I have the equations needed to solve the problem, but I'm confused as to how I can translate \frac{dm}{dt} into the equations.

[tiny-tim]

Hi diablo2121! :smile:
2. Relevant equations
…
F = m*\frac{dv}{dt}

Noooo … F = \frac{d(mv)}{dt} :wink:

(this is the full version of Newton's second law … f = m dv/dt is only a special case, valid only when dm/dt = 0)