How Does a Conveyor Belt's Kinetic Energy Change with Gravels?

[avonrepus]

Homework Statement

At a certain factory, gravels are dropped vertically from a machine at a rate of x (kg/s) onto a conveyor belt moving at velocity v.

a. what is the force needed to keep the belt moving at velocity v?

b. what is the power?

c. what is the rate of change in kinetic energy?

d. what is the difference between power and kinetic energy?

Homework Equations

F = dp/dt
P = F (dot product) v

The Attempt at a Solution

I got a, b, c,

a. F = dp/dt = dm/dt * v = x * v

b. P = F (dot product) v = x*v^2

c. rate of change in kinetic energy = 1/2 * dm/dt * v^2 = 1/2 *x * v^2

d. so rate of change in kinetic energy is not same as power!
what is going on?

 

[Dick]

Supposed I told you that dropping gravel onto a conveyor belt is an inelastic collision?