Finding the potential energy if force depends on both position and time

[swapnilp]

How to find potential energy if force depends on both position of particle and time ?

Suppose force is : f(r,t) = (k/r^2) * exp(-alpha*t),
k, alpha = positive constants,
r = position of the particle from force-centre
t = time

Is this force a conservative or non-conservative ?

 

[Cutter Ketch]

A time varying potential is generally not considered conservative. However, if the time scale of the interesting motion is small compared to the rate the potential is changing, you can call this a pseudo potential. Over a short time scale the energy will approximately only depend only on position.

 

[A.T.]

Is this force a conservative or non-conservative ?

The question is rather how useful the concept of a potential is here. You don't have the usual energy conservation over time. Depending on what you want to compute, using the force itself might be simpler.

 

[HomogenousCow]

With a highly time dependent force like the one you have there the concept of energy is not exactly defined or useful.