Conveyor Belt's Power: Calculating Energy and Power in a Moving System

[bakufun]

Homework Statement

Sand falls at a rate of 0.5 kg/s onto a conveyor belt which is moving at a constant speed of 2.0 m/s.

Questions:

a. Find the power expended in driving the belt!
b. Find the rate at which the sand acquires kinetic energy!
c. Account for any difference between the answer in part (a) and (b)

Homework Equations

F = m.(dv/dt) + v (dm/dt)
P = W/t = F.v

The Attempt at a Solution

For question (a), i think:
P = F.v
= [m.(dv/dt) + v (dm/dt)].v ; dv/dt = 0
= (dm/dt) . v^2
= ... W

Is it right ?

For question (b) i have no idea about the question. The question asked about speed or Power ?

Thanks a lot.

 

[truesearch]

you know that power = change in energy per second?
Can you calculate the rate of change of KE per second of the sand?

 

[bakufun]

do you mean like this ?
W = KE / t
= 0.5 m v^2 / t

m/t = 0.5 kg.
v = 2 m/s

so, W = 1 W ? is this right for question (b) ?

and

P = F.v
= [m.(dv/dt) + v (dm/dt)].v ; dv/dt = 0
= (dm/dt) . v^2
= 2 W for question (a) ?