Conservative and Non-Conservative Force

Conservative and Non-Conservative Force:

Conservative Force: When a particle is subjected to the action of other body (or bodies) so that at every point of space the particle experiences a force, the particle is said to be in a field of force. A particle near the surface of the earth experiences a force due to gravity and is said to be in a gravitation field.

To understand the meaning of a conservative force let us take an example of a ball thrown vertically up in the gravitational field of the earth. The ball after attaining certain maximum height returns to the point of projection with the same kinetic energy which it had initially. We, therefore, observe that at the completion of a round trip in a gravitational field, the kinetic energy is conserved and the ball has the same capacity to do work as it originally possessed. The gravitational force is, therefore, an example of a conservative force. Since in a round trip in the gravitational field, the total change in kinetic energy is zero, the kinetic energy-work principle shows that the total work done by the gravitational force in a round trip is also zero. This fact is taken as the basis to define a conservative force.

A conservative force is that force whose work along a round trip is zero so that at the completion of a round trip the particle returns with the same energy which it possessed initially.

Besides gravitation force, other examples of conservative forces are- elastic force, electric force, etc.

Non-Conservative Force: While discussing round the trip motion of a ball in the gravitation field above, we ignored the air resistance. The air resistance opposes both the upward as well as the downward motion of the ball and so the work done by the air resistance on each part of the journey is negative. The ball, therefore, returns to the point of projection with kinetic energy which is smaller than what it had initially. The fact that in presence of air resistance, the ball does not return with the same ability to do work shows that its energy is not conserved. In this example, the ball was under the influence of two forces- the gravitational force and the force due to air resistance. Since the energy of the ball is not conserved in a round trip, at least one of these forces must be non-conservative. Since we have already seen that the gravitational force is a conservative force, the other one i.e., the force due to air resistance must be non-conservative. On the basis of what has been said, we define a non-conservative force as follows:

A non-conservative force is that force whose work along a round trip is not zero, so that at the completion of a round trip the particle does not return with the same kinetic energy which it possessed initially.

Some well-known examples of non-conservative forces are- friction, viscous force, etc.