Conservative Force

In Newtonian mechanics, the two most crucial entities that we need to consider are force and work. These two entities walk hand in hand because work is done whenever a force will act upon an object and displace it. Similarly, if work has happened, a force has been applied. Force can be of many types like frictional force, elastic force, tension force, etc. All these types of forces are responsible for doing work. However, the conservative forces act differently, even when this entity is a vector quantity. In the sections below, we will describe what a conservative force is.

What is a Conservative Force?

To know what is a conservative force, let’s consider that a body moves between points A and B. It follows three different paths – a straight path and two curved paths. The force the body is moving is conservative because, here, the body’s displacement will be similar for all three paths. Conservative forces do not depend on the path being followed, no matter what.

What is a Non-Conservative Force?

As the name suggests, non-conservative forces are the forces which depend on the path taken by the object when work is done in moving it from a starting point to an ending point by applying some kind of force. We can also say that these forces depend on the direction of the applied force and the distance between the initial as well as final points. Moreover, it should be noted that non-conservative forces can never come out to be zero, not even in the condition when the final and initial points are the same. 

Some examples of non-conservative forces are friction, tension present in a cord, and air resistance. With these forces, each of them depends on the direction of the applied force and the distance between the final and initial points. 

Conservative Versus Non-conservative Forces

Conservative and non-conservative forces are different from each other in many aspects. Some of these differences are given below. 

Properties of Conservative Forces

The properties of conservative forces are given below.

· The force will always depend on the initial and the final points or the position of the path taken and not on the path itself

· When there is a closed loop, the total work done by the conservative force would always be zero, as the initial and the final points would be the same. So, no work would be done

· The work which is done by conservative forces is always reversible

· When only conservative forces are acting on a body, we can observe that the total mechanical energy of the system is conserved. This also means that the law of conservation of energy is followed when only conservative forces are applied to a body. Moreover, we can show that the total work done by conservative forces is zero, and by this, we can prove the law of conservation of energy in a system

Properties of Non-conservative Forces

The properties of non-conservative forces are as follows:

· It is a force which is dependent on the path. This means that it depends on the final and the initial velocity of the body or the system

· Even when the initial and the final positions of the body are the same, which means it is in a closed loop, the non-conservative forces will never be zero

· The work done by non-conservative forces can never be reversible, i.e., it is always reversible

Conclusion

Whenever an external force acts on the body and causes its displacement, work is done. If the work has the same value, irrespective of the path being followed, we say that the work done is due to conservative force. Work done through the conservative forces can be positive, zero, and negative, based on the distance between the initial and final points and the force’s direction. Work done due to acceleration due to gravity or the expansion of a spring coil are a few examples of conservative forces.