Forest UCM Energy TimeDepPE

Time dependent force.

What happens if you have a time dependent force that still manages to satisfy

[math]\vec \nabla \times \vec F = 0[/math]?

Because of the above, and Stoke's Theorem , you would be able to find a close loop where zero work is done at some given time.

If we consider the work energy theorem

[math]\Delta T = W = \int \vec F \cdot d \vec r[/math]

The for a potential defined as

[math]U(r,t) = - \int \vec {F}(r,t) \cdot d \vec r[/math]

you would be left with

[math]\Delta T = - U(r,t) [/math]

Forest_UCM_Energy#Time_Dependent_PE