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# Conservative Force

A conservative force is one in which the final displacement of the object (in the direction of force) determines its work, such as gravity between Earth and another mass. A conservative force does the same amount of work regardless of the path it follows to achieve the same displacement, and when the path is closed, that work is zero. Therefore, it is only possible to define stored energy as potential energy for conservative forces. Friction and other non-conservative forces that depend on other factors, such as velocity, are dissipative and cannot be represented by potential energy.

## Conservative forces and potential energy

Forces are responsible for doing work, and some forces, such as weight, are special. Like a spring's restoring force, conservative force effects work not by the path taken during the motion but on its starting point or ending point. Just as we defined potential energy (PE) for the gravitational force, you can do the same for any conservative force. For example, when you rotate the key in a toy or the key-wind watch, you work against its spring and store energy within it. (We assume that the spring has no frictional force and no thermal energy is produced by the spring.) The stored energy in the spring can be recovered as work, and it can be termed as potential energy. In fact, this characteristic is due to the fact that springs are conservative by nature. Therefore, the conservative force stored in the spring remains in the form of potential energy.

## What is a Conservative Force?

Conservative forces conserve energy, as their name suggests. The law of conservation of energy applies to them. When a particle is moved from one point to another, a conservative force is said to have been applied to it if it is independent of the particle's path. Conservative forces only depend on the initial and final positions of the particle. Examples of conservation forces include gravitational force and elastic spring force. Let us understand the concept better with the help of the following example.

## A particle is subjected to gravitational force.

A particle is subject to a gravitational force of magnitude mg, where 'g' represents the acceleration of gravity and 'm' represents the mass of the substance. Let's assume the particle moves from point A to point B, and Δh gives its vertical displacement. Let' assume the body falls to Earth in a curve under the influence of other forces. Nevertheless, the force of gravity is not affected by the curved path taken by the body. Therefore, it can be treated as an independent entity. There is only the vertical displacement of the body that influences the gravity force.

The total work done by gravity on the body is given as follows:

Wg=mgΔh

Where,

'm' is the mass of the body

'g' is the acceleration due to gravity

'Δh' is the difference between the final position (at point B) and the initial position (at point A)

Using the above expression, we can easily find out how gravity affects the particle regardless of the path taken by the particle. Accordingly, it has been concluded that gravitational force is independent of the path taken by the particle but is dependent only on the initial and final positions. As a result, it can be considered conservative in nature.

## Properties of Conservative Forces

Conservative forces have the following characteristics.

• When the force is solely influenced by the start and end positions of a body, regardless of the path taken.
• A conservative force cannot do any work on a closed path.
• Any conservative force does reversible work.

## How do you define non-conservative force?

For a non-conservative force, the work done depends on the length of the path taken. Friction, for example, is a non-conservative force. A force is defined as a non-conservative force if it produces a change in mechanical energy. Mechanical energy is nothing more than the sum of the potential and kinetic energy of the body. In work done by a non-conservative force, mechanical energy is either added or removed. Friction causes loss of energy in terms of thermal energy when it is used to perform work. The energy lost cannot be recovered completely.

## Characteristics of non-conservative forces

Its characteristics are opposite to those of conservative forces. They are as follows:

• It depends on the initial and final velocity because it is path-dependent.
• The work done by a non-conservative force is not zero, even on a closed path.
• Non-conservative forces lead to irreversible work done.
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