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Conservative force is a type of force acting on a body when it moves from one point to another. Conservative force acts on the body but it is also independent to the direction of the movement of the body. Herein, the two types of forces are conservative and nonconservative forces.
For every conservative force, potential energy (PE) can be expressed. The potential energy which is contributed is the effort given against a conservative force to reach a final configuration, that can be evaluated by the configuration rather than the path taken.
If a force comes with the following properties, then it is a conservative force.
- When the force is dependent only on the initial and final position, regardless of the taken path.
- In a closed path, the work done by a conservative force is considered to be zero.
- The work done by a conservative force is known to be reversible.
Also Read: Gravitational force
| Table of Content |
Key Terms: Conservative Force, Non-Conservative Force, Law of Energy Conservation, Constant Forces, Potential Energy
What is Conservative force?
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Conservative force functions in a line with the law of energy conservation. All the forces which come in the category of conservative force tend to conserve energy from one mode to another. Conservative force acts on the body when it moves from one place to another and it completely depends upon the initial and the final position of the object in motion.
A conservative force can be defined as:
| “A force that is required to move a particle from one point to another, in order for that force to be independent of the path taken by the particle.” |
- The conservative force is dependent only on the initial and final position of the particle.
- Gravitational force and elastic spring forces are the two conservative forces examples.
- Similarly, the total work done (which is the sum of the force that acts along the path multiplied by displacement) in case a particle moves in a closed loop by a conservative force is zero.
Gravitational Force Acting on a Particle
In the given diagram,
- The magnitude of the gravitational force which is acting over the object is ‘mg’.
- ‘mg’ here means mass of the object for “m” and acceleration due to gravity is represented through g.
- The distance covered by the object is AB, that is, the initial and the final points for the object are A and B.
- The vertical displacement between the initial and final objects is Δh.
- And the force of gravity which is the conservative force depends only on this vertical displacement, rather than depending on the illusionary path as shown in the diagram which is a result of other forces acting on the body.
Therefore, the total work done by gravity on the body is shown as,
| Wg = – mg (Δh) |
Here,
- Δh is the vertical displacement which is the difference between the final position (at point B) and the initial position of the object moving (at point A).
- g represents the acceleration due to gravity acting on the body.
- m is the mass of the body.
Conservative Force Formula
Conservative force can be defined as the force where the work done is independent of the path taken, and depends only on the initial and final position. Conservative force can be applied to the law of conservation of energy.
It can be represented as:
| \(\begin{array}{l}\Delta KE=\int F.dr\end{array}\) |
Read More: Mechanical Advantage Formula
Properties of Conservative Force
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Conservative force is a commonly used force which we experience in our everyday life. Conservative force can be identified by the following properties:
- Conservative force completely depends only on the initial position and the final position of the object which is moving, rather than depending on the path taken by the object.
- Therefore, in any closed path, the work done by the conservative force shall always be zero only.
- Another property of the conservative force is that the work done by it is reversible in nature.
Proof of Conservative Force being Path-IndependentConsider, F = mg
Thus, it gives two different paths wherein the same ball has reached the height (H). Let’s determine the work done in either case: Case 1: The work done, \(W_1 = \int_0^L (- mg)dx = -mgH\) Case 2: The work done, \(W_2 = \int_0^L (- mg)dx - \int_L^H (-mg)dx = -mgH\) Thus, it is observed that W1 = W2. As per the Conservative Force definition, it can be said that the Work is a 'conservative force' because it is path-independent. |
Read More:
| Concept-Related Topics | ||
|---|---|---|
| Conservation of Mechanical Energy | Work and Energy | Energy |
| Potential Energy Formula | Work Formula | Power Formula |
Non-Conservative Force
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Non-conservative force is completely opposite of the conservative force. It does not work as per the law of energy conservation, rather in this case, the energy lost is not recovered completely.
- The non-conservative force depends upon the path taken by the object while moving.
- It adds or removes the mechanical energy, which is the potential and the kinetic energy.
- Some examples of non-conservative forces include air drag, friction, and tension exerted on the cord.
Non-conservative forces examples in a baseball game:
- Normal force: The collision that occurs between a baseball and a bat (macroscopic motion), thus making a sound (microscopic motion).
- Air drag: Following a baseball player hitting the baseball, the ball will pass via the air (which is a macroscopic motion). The ball starts to transmit kinetic energy to air molecules, making them vibrate faster and create (microscopic motion). It is the mechanical equivalent of heat, helping to convert the motion of fluid to heat. The more the air drag, the faster the ball is going to dissipate kinetic energy into thermal energy.
- Friction: After the player slides to the base (macroscopic motion), the friction which occurs will start to transmit energy into the ground and the player's pants, causing the atoms of the ground to vibrate more (microscopic motion). It can lead to plastic deformation that can further cause the loss of kinetic energy.
Read More: Relation Between eV And Joule
Properties of Non-Conservative Force
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Non-Conservative force is also a commonly used force which we experience in our everyday life, such as the frictional force. Thus, in order to identify Non-conservative force easily, we should be familiar with its properties. Such as,
- The non-conservative force depends on the path of the object which is moving rather than depending on the initial position and the final position of the object which is moving.
- Therefore, in any closed path, the work done by the Non-conservative force shall never be zero.
- Another property of the Non-conservative force is that the work done by a Non-conservative force is irreversible in nature.
Read More: Elastic Collision Formula
Difference Between Conservative Force and Non-Conservative Force
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Some of the differences between Conservative and Non-Conservative Forces include:
| Conservative Force | Non-Conservative Force |
|---|---|
| It completely depends only on the initial position and the final position of the object which is moving. | It completely depends only on the path of the object which is moving. |
| In any closed path, the work done by the conservative force shall always be zero only. | In any closed path, the work done by the Non-conservative force shall never be zero. |
| The work done by it is reversible in nature. | The work done by a Non-conservative force is irreversible in nature. |
Things to Remember
- In any enclosed path, the work done by the conservative force shall always be zero only.
- While in any enclosed path, the work done by the Non-conservative force shall never be zero.
- It is found that all the constant forces are conservative in nature, that is, they can store and conserve the energy and the energy wouldn’t be lost.
- Gravitational force is the most common conservative force present in the nature which is also the weakest one.
- The work done by a conservative force is reversible in nature. While the work done by a Non-conservative force is irreversible in nature.
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Previous Year Questions
- Two springs A and B having spring constant...[NEET 2001]
- A particle is projected making an angle of…..[NEET 2001]
- A block of mass M is attached to the lower end of a vertical spring….[NEET 2009]
- A body initially at rest and sliding along a frictionless track from a …..[NEET 2018]
- A body moves a distance of 10 m along a straight …...[NEET 1997]
- A body of mass (4m) is lying in x−y …..[NEET 2014]
- A body of mass 1 kg begins to move under the action of a time dependent….[NEET 2016]
- Consider a drop of rain water having mass ….[NEET 2017]
- A car of mass m starts from rest and accelerates….[NEET 2012]
- A shell of mass 200 gm is ejected from a gun of mass….[NEET 2008]
Sample Questions
Ques. What is non-conservative force? (1 mark)
Ans. Non-conservative force is completely opposite of the conservative force. It does not work as per the law of energy conservation, rather in this case, the energy lost is not recovered completely. The non-conservative force depends upon the path taken by the object while moving. It adds or removes the mechanical energy, that is the potential and the kinetic energy.
Ques. What is a factor upon which the conservative force depends upon? (1 mark)
Ans. One essential factor on which the conservative force depends upon is that it completely relies only on the initial position and the final position of the object which is moving, rather than depending on the path taken by the object.
Ques. What is a factor upon which the non-conservative force depends upon? (1 mark)
Ans. The non – conservative force completely depends only on the path of the object which is moving rather than depending upon the initial position and the final position of the object which is moving.
Ques. What is Hooke’s Law? (2 marks)
Ans: Hooke’s Law claims that the “strain of a material is always proportional to applied stress, within the elastic limit of it. In relation to Conservative and Non-conservative forces, it suggests that when a conservative force is seen to interact with an object's motion, the motion of the given object reverses and the object regains its initial motion. "Conservative" forces conserve energy for the purpose of re-use. However, the forces which do not store energy for reuse are called "nonconservative" forces.
Ques. What is non-conservative force? Mention one non-conservative force. (2 marks)
Ans. Non-conservative force is completely opposite of the conservative force. It does not work as per the law of energy conservation, rather in this case, the energy lost is not recovered completely. The non-conservative force depends upon the path taken by the object while moving. It adds or removes the mechanical energy, that is the potential and the kinetic energy. Such as Frictional Force.
Ques. How is conservative force different from that non-conservative force? (3 marks)
Ans. The difference between the conservative and the non – conservative force is tabulated below.
| Conservative Force | Non-Conservative Force |
|---|---|
| It completely depends only on the initial position and the final position of the object which is moving. | It completely depends only on the path of the object which is moving. |
| In any closed path, the work done by the conservative force shall always be zero only. | In any closed path, the work done by the Non-conservative force shall never be zero. |
| The work done by this force is reversible in nature. | The work done by a Non-conservative force is irreversible in nature. |
Ques. Assume that a ball is dropped from a ladder. As a conservative force, gravity is going to be evaluated when the ball is at the maximum height and again when it reaches the ground. Thus, prove Wg = – mgh. (3 marks)
Ans. As per the question, Gravitational force = m x g
Here,
m = mass of the ball
g = gravitational acceleration,
Hence, it can be said that the work done on the body is:
Wg = -mgh
Herein, h is the difference between the final position of a body and its initial position.
Ques. Mention three essential properties of a conservative force. (3 marks)
Ans. Conservative force is a widely applied force in almost every sphere of life. Thus, in order to identify the conservative force more easily, we should be familiar with its properties. Such as,
- Conservative force depends only on the initial position and the final position of the object which is moving, rather than depending upon the path taken by the object.
- Therefore, in any closed path, the work done by the conservative force shall always be zero only.
- Another property of the conservative force is that the work done by this force is reversible in nature.
Ques. What are the properties of non-conservative force? (3 marks)
Ans. Non-conservative force is also a commonly used force which we experience in our everyday life, such as the frictional force. Thus, in order to identify the Non-conservative force more easily, we should be familiar with its properties. Such as,
- The most important property of the non-conservative force is that it completely depends only on the path of the object which is moving rather than depending on the initial position and the final position of the object which is moving.
- Therefore, in any closed path, the work done by the non-conservative force shall never be zero.
- Another property of the Non-conservative force is that the work done by a non-conservative force is irreversible in nature.
Ques. What is conservative force? Explain with the help of an example. (5 marks)
Ans. Conservative force is a type of force acting on a body when it moves from one point to another. Conservative force acts on the body but it is also independent of the direction of the movement of the body. Gravitational force is considered a type of conservative force. For example,
- The magnitude of the gravitational force which is acting over an object is ‘mg’.
- ‘mg’ here means the mass of the object for m and acceleration due to gravity is represented through g.
- The distance covered by the object is AB, that is, the initial and the final points for the object are A and B.
- The vertical displacement between the initial and final objects is Δh.
And the force of gravity which is the conservative force depends only on this vertical displacement, instead of depending on the illusionary path which is a result of other forces acting on the body.
Hence, the total work done by gravity on the body is shown as, Wg = – mg (Δh).
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