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

AI Thread Summary
The discussion focuses on the kinetic energy changes of a conveyor belt as gravels are dropped onto it. The force required to maintain the belt's velocity is calculated as F = x * v, where x is the mass flow rate of the gravels. The power needed is derived as P = x * v^2. The rate of change in kinetic energy is expressed as 1/2 * x * v^2, highlighting that this rate differs from power. The conversation also introduces the concept of inelastic collisions in the context of the gravel's impact on the conveyor belt.
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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?
 
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Supposed I told you that dropping gravel onto a conveyor belt is an inelastic collision?
 

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