# Conservative Force and Non Conservative Forces

## Conservative Force and Non Conservative Forces

The work done by the gravitational force does not depend on whether an object falls vertically or slides down a sloping incline. All that matters is the change in the object’s elevation. On the other hand, the energy loss due to friction on that incline depends on the distance the objects slides. In other words, the path makes no difference when we consider the work done by the gravitational force, but it does make a difference when we consider the energy loss due to frictional force. We can use this varying dependence on path to classify forces as either Conservative or Non – Conservative.

Of the two forces just mentioned, the Gravitational force is Conservative and the Frictional force is non – Conservative.

Conservative Force: A Conservative force is a force that acts on a particle, such that that the work done by this force in moving this particle from one point to another is independent of the path taken. To put it another way, the work done depends only on the initial and final position of the particle (relative to some coordinate system). Two examples of conservative forces are gravitational forces and elastic spring forces.Non – Conservative Forces: A non-conservative force is a force that acts on a particle (or point), such that the work done by this force in moving this particle from one point to another is dependent on the path taken. To put it another way, the work done depends on the path itself. For example, a friction force is non conservative because the work done by friction always acts in the direction of travel and therefore depends on the length L of the path taken, as shown below.

The same reasoning applies if friction is acting on a body. The work done by the friction force depends on the path travelled by that area on the body acted upon by the friction force. Thus, if a system is acted on by a non-conservative force (such as friction), and that system returns to its original position, then that system will experience a net loss of energy, due to those forces. Energy will thus not be conserved for the system. This makes sense intuitively since we know friction is a source of energy loss. This is why we always try to minimize friction in moving parts and machine components so as to minimize the energy wasted.

A comparative study between Conservative and Non – Conservative Forces: Here we will discuss about two types of forces namely Conservative and non – Conservative forces. So how do they differ? Consider following two situations as shown in the figure.In figure 1, when the mass comes to rest, the spring gets compressed by a distance “x”. The spring then comes to its normal length and mass attains a velocity “v”. This compression and elongation continues and each time with a maximum value of “x”. So we can infer that the total mechanical energy of the system (block + spring) remains constant. While in the second case also there will be compression and elongation but the minimum value will keep on decreasing. So we can say that the total mechanical energy of the system is not conserved in this case.

From our observation in the above case we can now define conservative and non-Conservative forces. A Conservative force is a force that does zero work done in a closed path. If only these forces act then the mechanical energy of the system remains conserved. Gravitational force and spring force are the examples of the Conservative force.

On the other hand non – conservative forces are those forces which cause loss of mechanical energy from the system. In the above case friction is the non – Conservative force. But as we know energy can neither created nor destroyed. Hence, these force convert mechanical energy into heat, sound, light etc. Now, Conservative force has one more property that work done by it is independent of the path taken.