Power needed to keep velocity of conveyor belt constant

[diablo2121]

Homework Statement

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.

Homework Equations

$$P = \frac{dW}{dt} = F*v$$
$$F = m*\frac{dv}{dt}$$

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!

Homework Equations

…
$$F = m*\frac{dv}{dt}$$

Noooo … $$F = \frac{d(mv)}{dt}$$

(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)