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

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SUMMARY

The discussion focuses on determining potential energy when force is defined as f(r,t) = (k/r^2) * exp(-alpha*t), where k and alpha are positive constants, r is the particle's position, and t is time. It concludes that this force is non-conservative due to its time dependence, which complicates the application of traditional energy conservation principles. Instead, it suggests that using the force directly may be more practical for calculations, especially when the time scale of motion is small compared to the rate of potential change.

PREREQUISITES
  • Understanding of classical mechanics and force concepts
  • Familiarity with potential energy and conservative forces
  • Knowledge of time-dependent functions in physics
  • Basic grasp of exponential functions and their applications
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  • Explore the concept of pseudo potentials in time-varying systems
  • Study the implications of non-conservative forces on energy conservation
  • Investigate the mathematical treatment of time-dependent forces
  • Learn about the applications of force in dynamic systems analysis
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Physicists, engineering students, and anyone interested in advanced mechanics, particularly those dealing with time-dependent forces and their implications on potential energy.

swapnilp
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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 ?
 
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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.
 
swapnilp said:
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.
 
Last edited:
With a highly time dependent force like the one you have there the concept of energy is not exactly defined or useful.
 

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