[Physics Class Notes] on A Comparative Study Between Non-Conservative and Conservative Force Pdf for Exam

Conservative force is the work done by the force that depends on the initial and the final position of the object and is independent of the path a body has covered.

So, the work done at point A, i.e. WA = Work done at B, i.e. WB

A nonconservative force is a work done by the force that considers the path traced with the initial & final position of the object.

In this article, we will study what are conservative and nonconservative forces through illustrative examples.

What are a Conservative Force and a Non-Conservative Force?

Students learn about the concepts of displacement, force, energy, and work done in the initial chapters of physics in class 11. The chapter on the force is separated into two types namely ‘conservative’ forces and non-conservative forces. In this section, we are going to discuss these two types of forces. We already know that work is performed when an object moves from one position to another by the application of force. This movement can be in a straight line or by a path other than straight. So if any object doesn’t follow a straight path then the work done depends on the total path covered by the object. For such work the force applied is known as non-conservative force. Various examples of non-conservative forces are Friction, Air resistance, Viscosity, Non-elastic material stress, water drag on a moving boat, and as such. But in some other situations, the work done does not depend on the path covered by the object. It only depends on the initial position and final position of the object. In this situation, the force applied is known as the conservative force. Examples of conservative forces are Gravitational force, Elastic spring restoring force, Buoyancy force, Electrostatic force, among others. In the work done by the use of non-conservative forces the mechanical energy used gets dissipated into other forms of energy such as heat or sound or any other form. For this reason, Non-conservative forces are also known as dissipative forces. The resulting energy is in a less available form of doing work.

On the other hand, energy gets stored when any work is done by the use of conservative force. This stored energy is otherwise known as the potential energy of the object.

Examples of Conservative Forces

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A body displaces from A to B by ‘l’, and the force acting at point A is mg. So, the work done will be

WAB = mg . l. Cos (90 +θ) = – mglSinθ …..(1)

Similarly, from A to C, the work done will be:

WAC = mglCos90° = 0….(2), and

From C to B, the length component along CB is ‘lSinθ’ and the work done is:

WBC = – mg(lSinθ) Cos180° = – mglSinθ …(3)

Here, θ = 180° because the motion of the body is against gravity.

We can see that WAB = WBC (Independent of the path). The work done by the force is conservative.

Let’s Take Another Example:

Consider a block of mass 10 kg falling from 10 m height. The work done by the conservative force will be:

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W = F . d Cosθ

F = mg 

⇒ 10 x 9.8 = 98 N

Here, the angle between the gravity and the displacement is 0° because both of these are acting downwards. So, the work done will be:

W = 98  x 10  x Cos0° = 980 J

Now, let’s say this block moves up and then down.

Case1: The work done, W1 = 980 N

Case 2: When moves up

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Work done against the gravity, W2 = 98  x 10  x Cos180°= – 980 J 

Case 3: Ball drops

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Here, the work done, W3  = 980 N

∴ The total work done  = 980 – 980 + 980 = 980 N

Here, we can see that the gravitational force is the conservative force. 

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The work done by the spring force depends on the initial and the final position and not on the path traced by the spring. That’s why spring forces are called the conservative forces. 

Similarly, the work done by a conservative force in a closed path is zero.

Example of Nonconservative Force

Nonconservative force is a type of force whose work done relies on the path, not on the initial and the final position.

For example,

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If we go along a 5 m path, the frictional force will be less as compared to a 7m long path. This means that work is done at initial & final points, i.e., WI ≠ WII. 

Similarly, work done by a conservative force in the closed path is not zero.

Difference Between Conservative and NonConservative Force