Which one of the following forces cannot be expressed in terms of potential energy?

<p>The correct answer is:</p> <p>$\textbf{Option A: Frictional force}$</p> <p>Here's why:</p> <p><strong>Conservative vs. Non-Conservative Forces:</strong></p> <p><p><strong>Conservative Forces:</strong> These are forces for which the work done is independent of the path taken; they only depend on the initial and final positions. For conservative forces, you can define a potential energy function. Examples include Coulomb’s force, gravitational force, and the restoring force of a spring.</p></p> <p><p><strong>Non-Conservative Forces:</strong> These forces depend on the path taken and usually result in energy dissipation (often as heat). Friction is a typical example, and hence, it cannot be described solely by a potential energy function.</p></p> <p><strong>Example Explanations:</strong></p> <p><p><strong>Coulomb’s Force:</strong> It is a conservative force because the work done in moving a charge in an electric field only depends on the difference in electric potential between two points.</p></p> <p><p><strong>Gravitational Force:</strong> It is also conservative. The potential energy associated with gravitational force is given by gravitational potential energy, for example, $U = mgh$ near the Earth’s surface.</p></p> <p><p><strong>Restoring Force:</strong> For a spring, the force is given by Hooke’s law: $F = -kx$ and the corresponding potential energy is $U = \frac{1}{2}kx^2.$ This is a conservative force.</p></p> <p>Since friction is a non-conservative force that dissipates energy, it cannot be expressed in terms of potential energy.</p> <p>Therefore, the correct answer is Option A: Frictional force.</p>