Conveyor Belt's Power

bakufun

1. The problem statement, all variables and given/known data
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)


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


3. 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) ?