# Conservative force & Non-Conservative force

Last updated on April 13th, 2023 at 04:17 pm

Often we hear these two terms as we discuss Work and Force in our physics class – conservative force and Non-conservative force. Here we will talk about these two and define them. Also, we will differentiate them and list examples for each of these forces for better understanding. So let’s start.

Forces are either conservative or nonconservative.

Some forces, such as gravity and elastic forces, act within systems without affecting the mechanical energy of the system. When such forces operate, energy is conserved. These are called conservative forces. Other forces, such as friction, and forces applied from outside a system, cause the energy of the system to change so that energy is not conserved for that system. These are known as non-conservative forces.

## Conservative force

A force is called a conservative force if work done by it or against it depends only on the starting and ending points of a motion and not on the path taken.

In other words, A force is conservative if the work done by the force in displacing a particle from one point to another is independent of the path followed by the particle and depends only on the endpoints.

Another definition of conservative force: A force is conservative when it does no work on an object moving around a closed path, starting and finishing at the same point. Hence a force is conservative if the work done by the force in moving a particle around any closed path is zero.

A conservative force results in stored or potential energy. example: gravitational force.

### What is conservative force?

A force is conservative if the work done by the force in displacing a particle from one point to another is independent of the path followed by the particle and depends only on the endpoints. Hence a force is conservative if the work done by the force in moving a particle around any closed path is zero.

### Conservative force examples

The gravitational force is our first example of a conservative force. The other two examples are the elastic force of a spring and the electrical force of electrically charged particles.

### gravitational force a conservative force – why?

When we lift an object of some mass to a height against the gravitational force then the work done against the gravitational force doesn’t depend on whether we lift the object walking the stairs or by using the elevator.

The final (or end) point and the starting (initial) point are all that matter to calculate the work done. Hence gravitational force is an example of a conservative force.

### spring force a conservative force – Explain with potential energy concept

When we wind up a toy or an old-fashioned manual watch, we do work against its spring and store energy in it. (We consider these springs as ideal, in that we assume there is no friction and no production of thermal energy.) This stored energy is the potential energy stored in the spring which is recoverable as work.
A conservative force results in stored or potential energy. This proves that the spring force is conservative.

## Non-conservative force

A non-conservative force is one for which work depends on the path taken. For a closed path, the total work done by a nonconservative force is not zero.

### Non-conservative force examples

Friction is a good example of a nonconservative force. Air resistance is another nonconservative force. There is no potential energy associated with nonconservative forces. Work done by a nonconservative force adds or removes mechanical energy from a system.

### friction or frictional force a nonconservative force – why?

Work done against friction depends on the length of the path between the starting and ending points. Because of this dependence on the path, there is no potential energy associated with frictional forces. Friction creates thermal energy that dissipates, removing energy from the system.

Because thermal energy is being radiated out of the system, the system is, by definition, a non-isolated system.

Furthermore, even if the thermal energy is retained or captured, it cannot be fully converted back to work, so it is lost or not recoverable in that sense as well. The amount of work done by friction will cause the mechanical energy of the system to change. Hence, friction is a nonconservative force.

## Difference between conservative and non-conservative force

• A force is called a conservative force if work done by it or against it depends only on the starting and ending points of a motion and not on the path taken. A conservative force results in stored or potential energy.
• A non-conservative force is one for which work depends on the path taken. There is no potential energy associated with nonconservative forces. Work done by a non-conservative force adds or removes mechanical energy from a system.
• Conservative force does no work on an object moving around a closed path, starting and finishing at the same point. (i.e. total work done =0)
• But For a closed path, the total work done by a nonconservative force is not zero.

Take away

So here we have defined conservative and non-conservative forces with examples. Also, we have discussed the differences between them. If you find this post useful please share this post.