Change in potential and kinetic energy

[science_rules]

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

 

[Hootenanny]

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.

 

[rl.bhat]

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.