Question

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

• A. Coulomb's force
• B. Gravitational force
• C. Frictional force
• D. Restoring force

Hint:

A key characteristic of conservative forces is that the work they do is path-independent, and they allow for the definition of a potential energy. Non-conservative forces, like friction, result in energy dissipation, and their work depends on the path taken.

Answer 1

The Correct Option is C

To identify the force not expressible in terms of potential energy, we examine the properties of each listed force:

1. Coulomb's Force: This is the electrostatic force between charged particles. It is a conservative force and can be represented by potential energy, \( U = \frac{k \cdot q_1 \cdot q_2}{r} \), where \( k \) is Coulomb’s constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the separation distance.
2. Gravitational Force: This force, exerted by masses, is also conservative. Its potential energy is given by \( U = -\frac{G \cdot m_1 \cdot m_2}{r} \), where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between their centers.
3. Restoring Force: This force, like that in springs governed by Hooke's law, acts to return a system to equilibrium. It is conservative, with potential energy \( U = \frac{1}{2} k x^2 \), where \( k \) is the spring constant and \( x \) is the displacement.
4. Frictional Force: This force opposes motion and is non-conservative. Due to its energy-dissipating nature (converting mechanical energy to heat), it cannot be defined by potential energy. It depends on velocity and hinders motion irreversibly.

Thus, frictional force is the force that cannot be expressed in terms of potential energy.

Conclusion: Frictional force is a non-conservative force and is the correct identification.