Conservative Forces – Definition, Formula, Examples

Conservative Force is a type of force which is independent of path taken to do a work. This means when an when force applied in moving an object from one position to another is the same irrespective of the path taken, it is called conservative force. A force is a push or pull acting on an object. In our surroundings, several forces exist. Conservative forces include magnetic force, gravitational force, etc.

In this article, we will learn in detail about conservative force, its definition, formula, and examples. We will also compare conservative and non-conservative forces.

What is a Conservative Force?

Conservative force is a type of force with the special property that the total work done on a moving object is not dependent upon the path travelled. Conservative force is dependent upon the initial and final points of the path covered. When an object is moving in a closed loop, the total work done by the conservative force is zero. Because in a closed loop or circular path, if a particle completes a complete move, it means it came to the initial point. So the initial point and final point are the same in this case. Thus, the work done is zero by the conservative force. This force is not dependent on the path that is covered by an object. The conservative force follows the theories of the law of conservation of energy and the conservation of kinetic energy.

Examples of Conservative Forces

Electrostatic force, gravitational force, magnetic force etc. are the examples of the conservative forces. Force due to a spring and electrostatic force are also the examples of conservation force.

Properties of Conservative Force

The properties of Conservative force is mentioned below:

• It is Independent of the path covered by a particle
• It is fully dependent upon the final and initial position of the particle.
• Work done will remain zero in the closed loop or circular path.
• This force is reversible.

Work Done by a Conservative Force

The total work done by a conservative force is referred as the work done by an object when a conservative force acting upon the object. To calculate the work done by a conservative force, we have to find out the magnitude of the force and the displacement of the body. Once we find out the magnitude of the force and the displacement of object, then multiply the magnitude of the force by the travelled distance of the object. The final value after multiplication is the total work done by the force.

The equation to calculate the total work done by a conservation force is ,

W = F × d

where

• W = work done,
• F = Force acting on the object,
• d = the distance between the force and the object.

Note:

• Work done by conservative force on a system is given by the change in the potential energy of the system
• Work done by conservative force is equal to the negative change in the potential energy.
• Work done by conservative force is positive when potential energy of the body decreases and kinetic energy of the body increases

Gravitational Force is a Conservative Force

The work done against gravity is always conserved, so it is an example of Conservative force. Let us discuss the gravitational force as an example of Conservative force.

Let us suppose, an object or a particle at height “h” from the ground, is thrown vertically, then the work done against gravity on this object is,

W₁ = -mgh

When the same object falls down from the same height “h”, the work done on that object is,

W₂ = mgh

Thus the total work done on that object is,

W = W₁ + W₂

W = -mgh + mgh = 0.

Hence, the total work done for an object moves from the ground to a height ‘h’ and falling back to the ground from that height ‘h’ is equal to zero. It means that the work done is zero and it is conserved. This example shows that gravitational force is a type of conservative force.

Conservative Force Formula

The formula of a conservative force is given as

F_c = – dU/ds

where,

• F_c = conservative force
• U = Potential energy
• s = position

Conservative Force and Potential Energy

A conservative force is a force that only depends on the initial and final position of the moving path and not dependent on the total path travelled.

Potential energy is a type energy that depends a system’s position, shape, or configuration. It is a stored type energy which is completely recoverable.

Potential energy is denoted as P_E and it is defined for any conservative forces. During the work done by a conservative force, the object reach the final configuration. Conservative force depends on the final configuration and that configuration adds potential energy.

For a conservative force, the mechanical energy is the sum of kinetic energy and potential energy. When a conservative force acts on a body, the total mechanical energy remains constant. It defined that the conservative force obeys the law of mechanical energy.

KE_i + PE_i = KE_f + PE_f = Constant

Conservative and Non-Conservative Forces

In contrast to conservative forces, non-conservative force are the force that depends on the path covered by a body. Non conservative force is also depends on the final and initial position of the body.

Examples of non-conservative forces include Air Resistance, Tension in the cord, Hands Rubbing and Friction are the examples of Non-conservative force.

By rubbing hands together, a significant quantity of heat energy is generated. This is because of friction, which opposes the force used to rub the hands together. The frictional force opposes the motion and removes the energy generated by the applied force into heat energy. The transformation of physical energy to thermal energy involves the presence of an opposing force.

Properties of the Non-Conservative Force

The followings are the important properties of the Non-conservative force –

• It is Dependent of the path covered by a body.
• It is Dependent upon the path travelled by the body.
• Work done will always remain a positive.
• This force is irreversible.

Difference between the Conservative Force and Non-conservative Force

The detailed difference between conservative and non-conservative force is tabulated below:

Property	Conservative Force	Non-conservative Force
Dependency on Path	Independent on path travelled.	Dependent on path travelled.
Law of Conservation of Energy	It follows the law.	It does not follow the law.
Work Done	In closed path, work done is zero in case of Conservative force.	Work done is not zero in case of Non-conservative force.
Recoverable of Word done	It is recoverable.	It is not recoverable.
Mechanical Energy	Mechanical energy is conserved in case of Conservative force.	It may or may not be conserved in case of Non-conservative force.
Examples	magnetic force and gravitational force	Friction.

Conclusion

Through this article, we learnt and got adequate knowledge on Conservation force and Non-conservative force, the major differences between them. Like these forces, there are many forces available in our surroundings. Force is a very important term in physics.

Conservative Forces FAQs

What is meant by a Conservative force?

A force that can move an object from one place to another place, is known as Conservative force. Conservative force is dependent upon the initial and final point of the path covered. When an object is moving in a closed loop, the total work done by the conservative force is zero.

What are the 4 examples of Conservation forces?

The four examples of Conservation forces are: Magnetic force, Electrostatic force, Spring force and Gravitational force

What is meant by a Non-conservative force?

The non-conservative force are the force that depends on the path covered by a body as well as initial and final position of the object. Non-conservative force is also depends on the final and initial position of the body.

Is gravitational force a conservative force?

Yes, gravitational force is a conservative force

Is friction a conservative force?

No, friction is not a conservative force but it is a non-conservative force