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A Comparative Study Between Non-Conservative and Conservative Force

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Last updated date: 16th Jul 2024
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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

Conservative Force

Nonconservative Force

WI = WII

WI ≠ WII

Independent of the path

Path dependent

Closed path: W = 0

Closed path: W ≠ 0

Examples:

  • Gravitational Force

  • Electrostatic Force

  • Spring Force

Examples:

  • Friction

  • Tension in cord

  • Air resistance

FAQs on A Comparative Study Between Non-Conservative and Conservative Force

1. What are the common forms of stored energy or potential energy?

The most common form of stored energy or potential energy is the 'Gravitational energy.' It is observed on any object located near a body having the effect of gravitational pull on it. Other common forms of potential energy are 'elastic force or spring force'. It depends on the change in the length of a spring or an elastic object. Another form is the 'Electrostatic force'. Any charged body exerts an attraction force on the nearby object with an opposite charge and depends on the distance between the two objects.

2. What is Friction?

When two objects move in opposite directions relative to each other with having a surface of contact between them then a force of inhibition acts over each other. This force is known as the Friction force. This is a non-conservative force and depends on the distance traveled by one object in relation to the other one. The energy used is not stored but gets dissipated or transformed into other unusable forms of energy such as heat or sound. It depends on the physical condition, texture, and material of the surfaces in contact.

3. What is a closed path?

When any object moves around a distance and returns to its initial position the path traveled by the object is termed a closed path. The net displacement in this is zero. If the movement happens due to any conservative force then the work done at the end is zero. But if the movement happens by the application of a non-conservative force then the work done is never zero and depends on the total distance traveled by the object. When we throw up a ball against gravity and return to the ground after attaining a certain height then it is an example of a closed path.

4. In which class do students learn about the conservative forces and non-conservative forces?

Conservative and non-conservative forces are the topics of physics. In the CBSE board, these topics are covered in class 11. The NCERT textbook for Physics mentions them in detail. Students can learn about these topics and the derivation of various formulas associated with them from this book. There are also many problem questions provided in the exercises of the chapter to practice more and understand the application of the topic. Students can also refer to physics books published by other publications.

5. Will it help me to understand the topic better if I join the Vedantu online classes?

Vedantu provides all types of resources for the easy understanding of each and every concept in a systematic approach. Students can also access the various study materials provided for the self-study of the subject. There are also sample question sets for practicing more problems to prepare well for the exams. Any student can get access to these resources by registering themselves on the website which is totally free of cost. The other study materials can also be downloaded without paying any price for it.

6. The work done during the zero displacements can never be zero. Justify this statement.

Consider a block displaced by ‘d’ meters from point A to B. A friction force acting on it is f, then work done by the frictional force will be:


                               W = - f. d….(1)


If the same block displaced from B to A, then again W = - f. d ….(2)


So, the network done = - f. d + (- f. d) = - 2f. D.


Hence,  WNET ≠ 0 during zero displacements.

7. Can the work done by a Conservative Force be negative?

Work done by a conservative force can either be positive or negative. 

  1. If the work done by the force is the direction of the displacement of the object, then the work done is positive. 

  2. If the work done by the force is in the opposite direction to that of the displacement of the object, then the work done by the force is negative.

8. Is tension a Nonconservative Force?

Yes, tension is a nonconservative force.

9. Why is the potential energy defined for the Conservative Force?

The potential energy of a system is due to the shape, position, and configuration stored in the system. It relies on the initial and the final point only; that's why it is defined for the conservative force.