Conservative and Non conservative forces

Introduction

We know from the law of conservation of energy in a closed system, that is a system which is isolated from its surroundings, the total energy of a system is always conserved.” The conservative force obeys the law of conservation of energy. Conservative and non – conservative forces are the two types of forces.

Non-conservative forces are the forces for which work done depends on the body’s particular path.

Conservative Force

A conservative force is one where the work done in moving a particle from one point to another depends on the starting and ending positions and not the path. Conservative force follows the law of conservation of energy. The sum of potential energy and kinetic energy remains unchanged over the course of the path. The total work done around a closed path by a conservative force is zero.

Conservative forces and potential energy

Forces are responsible for work done, and some forces, like weight, are special. Like the restoring force of a spring, the effects of the conservative force do not act according to the distance covered during the movement, but rather at their start and end point. As we defined the potential energy (PE) for the gravitational force, you can do the same for other conservative forces. For example, when you rotate the key of a toy or wind-up clock, you work against the spring and store energy in it. (We assume the spring has no frictional force and the spring does not generate thermal energy.) The energy stored in the spring can be recovered as work and called potential energy. In fact, this characteristic is because of the fact that the nature of spring is conservative. 

Gravitational Force Acted on a Particle

A particle is subjected to a gravitational force having magnitude equals to mg, where “g” is the acceleration due to gravity and “m” is the mass of the substance. Suppose the particle moves from point A to point B, and h represents its vertical displacement. Suppose the body falls to the earth in a curve under the influence of other forces. However, gravity is not affected by the curved path that the body follows. Therefore, it can be considered as an independent entity. The vertical displacement of the body affects gravitational force.

Total work done is given by

w=mgh

Here,

W = work done by the body

m = mass of body

g = gravitational acceleration

h= change in displacement of body

Characteristics of Conservative Force

1. Force depends on the start and end positions of a body rather than the path taken by the body.
2. Work done in a closed path is zero for conservative force.

The work which is done by the conservative force is reversible.

Examples of Conservative Force

There are many examples of conservative forces, some of which are given here.

1. Gravitational Force
2. Electrostatic Force
3. Electric force
4. Magnetic Force

Gravitational Force

Each body in the universe with a mass attracts other bodies with a force known as a gravitational force, so that gravity is a study of interaction between two bodies having masses.

The gravitational force is a central force, which depends on the position of the mass of a test body to the mass of the source body and it always acts along the line which joins the centres of the two masses.

Electric Force

Electric force is defined as the force of repulsion or force of attraction between two charged bodies.

Non – Conservative Force

For a non – conservative force, the work done depends on the distance travelled. For example, friction is a non-conservative force. A force is a non-conservative force when it generates a change in mechanical energy. Mechanical energy is the sum of the body’s potential and kinetic energy. When work is done by a non-conservative force, mechanical energy is added or removed. Friction causes energy losses in the form of thermal energy when work is done on it.

Characteristics Non – Conservative force

There are many characteristics of non-conservative force which are almost opposite of conservative force. 

1. Non – Conservative Force depends on the initial velocity and final velocity as it is path-dependent.
2. Even on a closed path, the work done is not zero by a non-conservative force.
3. Non-conservative force is responsible for irreversible work done.

Conclusion

A conservative force is one where the work done in moving a particle from one point to another depends on the starting and ending positions and not the path.

Conservative force follows the law of conservation of energy.

Total work done by a conservative force is given by

w=mgh

There are many examples of conservative forces, some of which are given here.

1. Gravitational Force
2. Electrostatic Force
3. Electric force
4. Magnetic Force

Non-conservative forces are the forces for which work done or kinetic energy depends on other factors like speed or the body’s particular path.