Chaning Mass Kinetic Energy

[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?

 

[m2003]

I would like to clarify that power and kinetic energy are two different quantities that are related but not the same. Power is the rate at which work is done or energy is transferred, while kinetic energy is the energy an object possesses due to its motion. In this scenario, power is being calculated as the product of force and velocity, while kinetic energy is being calculated as the product of mass, velocity, and 1/2. Therefore, it is expected that the values for power and kinetic energy will be different. The rate of change in kinetic energy is also different from power, as it is the rate at which the kinetic energy of the system is changing over time. Power, on the other hand, is the rate at which work is being done. It is important to understand the difference between these quantities in order to accurately analyze and interpret the data in this scenario.