Question

Potential energy is not defined for which of the following forces?

• A. Gravitational force
• B. Restoring force
• C. Friction
• D. Electrostatic force

Hint:

For conservative forces, potential energy is defined. Non-conservative forces, like friction, do not have a well-defined potential energy function.

Answer 1

The Correct Option is C

Potential energy is applicable solely to conservative forces. A force is considered conservative if the work it performs on a particle traversing between two points remains invariant to the displacement path. This relationship is mathematically expressed as \( dU = - \mathbf{F}_{ci} \cdot d\mathbf{r} \), where \( \mathbf{F}_{ci} \) denotes a conservative force and \( d\mathbf{r} \) represents the displacement vector.Examples of conservative forces and their associated potential energies include:- Gravitational force, for which potential energy is \( U = -\frac{GMm}{r} \).- Restoring forces, such as those described by Hooke's law for springs.- Electrostatic force, with potential energy given by \( U = \frac{kQq}{r} \).Conversely, friction is a non-conservative force. The work done by friction is path-dependent and results in energy dissipation (e.g., as heat), precluding the definition of potential energy for it.Consequently, friction is the correct answer.