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Conservative and Non-conservative Forces

What are Conservative and Non-conservative Forces

A conservative force is a force in which the work done in moving a particle from one position to another depends on the initial and final positions and not on the path. It follows the law of conservation of energy. The sum of the potential and kinetic energies remains unchanged as the path progresses. The total work done by a conservative force around a closed path is zero.

An example of conservative force is the gravitational force of attraction between the Sun and the Earth.

Conservative Force

Unlike conservative force, a non-conservative force is one in which the work done depends on the path taken in going from initial to final positions. It does not follow the law of conservation of energy. There is energy loss, mostly as heat, as the path progresses. The total mechanical energy in the final position is not the same as that in the initial position.

An example of a non-conservative force is the friction between the wheel and the road during driving.

Non Conservative Force

Conservative vs. Non-conservative Forces

The following table compares and contrasts the properties and examples of conservative and non-conservative forces.

Conservative ForceNon-conservative Force
Work done isIndependent on the pathDependent on the path
Work done around a close path isZeroNon zero
Law of conservation of energyObeysDoes not obey
Loss of mechanical energy (potential + kinetic)NoYes
Reversible or irreversibleReversibleIrreversible
TypesGravitational force, spring force, electric force, a magnetic forceFriction, air resistance, viscosity, and fluid friction
ExampleThe force that holds the electrons in an atomThe resistance to a ship sailing in water
Conservative and Non-Conservative Forces

Conservative and Non-conservative Forces: Types and Examples

Conservative Force Types

1. Gravitational Force: Example – The attractive force between the Earth and Moon.

2. Spring Force: Example – The force with which a spring balance weighs fruits.

3. Electrostatic Force: Example – The force that holds the electrons in an atom.

4. Magnetic Force: Example – The force with which a bar magnet pulls iron nails.

Non-conservative Force Types

1. Friction: ExampleThe force that resists a box sliding on a floor.

2. Air resistance: Example – The resistance offered by air when a ball falls through it.

3. Fluid Friction: Example – The resistance offered by water to a submarine.

4. Viscosity: Example – Spreading honey over bread.

Work Done by a Conservative Force

There is stored energy associated with the conservative force. It is known as potential energy. The difference in the stored energy when the object moves from one position to another is the work done to move the object.

Suppose an object of mass m is lifted to a height h from the surface of the Earth. Then, the potential energies are:

At ground: PE1 = 0

At a height above the surface: PE2 = mgh

Therefore, the work done W is given by the change in potential energy.

W = PE2 – PE1 = mgh – 0 = mgh

FAQ

Q1. What happens to the potential energy when a conservative force does work on a body?

Ans. When a conservative force does positive work on a body, the potential energy decreases.

Article was last reviewed on Monday, February 15, 2021

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