# Change in potential and kinetic energy

• science_rules
In summary, the change in potential energy is related to the change in kinetic energy through the conservation of energy principle. In a system with no non-conservative forces, the sum of kinetic and potential energies remains constant, and the rate of change of potential energy is equal to the rate of change of kinetic energy.

## Homework Statement

how is the change in potential energy related to the change in kinetic energy?

## Homework Equations

i just know that for a tossed object, the KE decreases, and its PE increases until it reaches the top. Then it has potential energy at the top, and its KE increases, while its PE decreases. I am not sure how to relate the change in PE and KE though.

## The Attempt at a Solution

science_rules said:

## Homework Statement

how is the change in potential energy related to the change in kinetic energy?

## Homework Equations

i just know that for a tossed object, the KE decreases, and its PE increases until it reaches the top. Then it has potential energy at the top, and its KE increases, while its PE decreases. I am not sure how to relate the change in PE and KE though.

## The Attempt at a Solution

It very much depends whether there are any non-conservative forces acting on the system. If there are no dissipative forces acting on the system then the sum of the kinetic and potential energies is constant.

Tha rate of change of potential eenrgy = dp/dt = mg*dh/dt = mgv
Rate of change of kinetic energy = dE/dt = 1/2*m*2v*dv/dt = mgv.
So they are equal.