Conservative and NonConservative Forces
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
FAQs on A Comparative Study Between Non-Conservative and Conservative Force
1. What is the fundamental difference between a conservative and a non-conservative force?
The fundamental difference lies in how work is calculated. For a conservative force, the work done in moving an object between two points depends only on the initial and final positions, not the path taken. For a non-conservative force, the work done is dependent on the specific path the object follows.
2. What are some common examples of conservative and non-conservative forces?
Examples help clarify the difference between these two types of forces:
- Conservative Forces: Gravitational force, electrostatic force, and the elastic force in a spring.
- Non-Conservative Forces: Frictional force, air resistance (drag), and tension in a cord.
3. Why is potential energy only associated with conservative forces?
Potential energy represents stored energy that can be fully recovered as kinetic energy. This is only possible with conservative forces because the work they do is path-independent and reversible. When you lift a book against gravity (a conservative force), the work you do is stored as gravitational potential energy. When you let it go, that energy is converted back to kinetic energy. Non-conservative forces, like friction, dissipate energy as heat or sound, which cannot be stored or fully recovered, so the concept of potential energy does not apply to them.
4. How does the concept of conservative forces relate to the law of conservation of mechanical energy?
The law of conservation of mechanical energy states that the total mechanical energy (sum of kinetic and potential energy) of a system remains constant. This law holds true only when all forces acting on the system are conservative. If any non-conservative forces, like friction, are present, mechanical energy is not conserved because some of it is converted into other forms of energy, such as heat.
5. Why is the net work done by a conservative force over a closed path always zero?
A closed path is one where the starting and ending points are the same. Since the work done by a conservative force depends only on the initial and final positions, and in a closed path these are identical, the net change in position is zero. Consequently, the total work done by the conservative force throughout this entire journey is zero. For example, the work done by gravity on a ball thrown upwards and caught back at the same height is zero.
6. Why is the work done by a non-conservative force like friction non-zero in a closed path?
The work done by a non-conservative force like friction depends on the total distance travelled, not the displacement. Friction always opposes motion. If you slide a block across a table and then slide it back to the start, friction opposes the motion in both directions. The work done against friction on the way out and on the way back are both negative (or energy is lost) and they add up, resulting in a non-zero total work done, even though the final displacement is zero.
7. How can you mathematically determine if a force is conservative?
In vector calculus, a force F is conservative if its curl is zero (∇ × F = 0). For students in Class 11, a simpler way to understand this is that a force is conservative if the work done by it can be expressed as the negative change in a potential energy function, i.e., W = -ΔU. This mathematical property is directly linked to the path independence of the force.
8. Can the work done by a conservative force be negative?
Yes, the work done by a conservative force can be negative. Work is negative when the force acts in the opposite direction to the object's displacement. For example, when you lift a book upwards, its displacement is upwards, but the conservative force of gravity is acting downwards. Therefore, the work done by gravity during this lift is negative.
9. In which chapter of the CBSE Class 11 Physics syllabus is this topic covered?
The comparative study of conservative and non-conservative forces is a key concept in the CBSE Class 11 Physics syllabus for the session 2025-26. It is detailed in Chapter 6: Work, Energy and Power, as per the NCERT curriculum.
