Conservative force is a force with the property that the work is done in moving a particle between two points is independent of the path it takes. Gravity and spring forces are examples of conservative forces.

Imagine this closed path motion be divided into two motions between points A and B.

Work done for motion from A to B by conservative force along any paths are equal.

W1 = W3. 

The net work done by a conservative force is zero if a particle travels in a closed loop. Starting from point A to point B and then ending at point A via two work paths 1&2 and 3&2, the total work by the conservative force for the round trip is zero:

W=  W1 + W2 = 0 = W3 + W2 = 0

If a force is not conservative, taking different paths would lead to conflicting potential differences between the start and endpoints. Nonconservative forces transfer energy from the object in motion (just like conservative force), but they do not transfer this energy back to the potential energy of the system to regain it during reverse motion. Friction is one such nonconservative force.

Key Points

• Work done by conservative force (like Gravity or Spring force) is independent of the path it takes.

• If a particle travels in a closed-loop, the net work done by a conservative force is zero.

• Nonconservative force (like Friction) transfers the energy from the system into an energy form which can not be used by the force to transfer back to the object in motion.

Key Terms

net work done: the sum of the force acting along the path multiplied by the distance travelled

conservative force: a force with the property that the total work done in moving a particle between two points is independent of the taken path

spring force: the force exerted by the spring is always in the opposite direction to the displacement.

nonconservative force: a force for which work depends on the path.