Conservative and Non Conservative Force

Edited By Team Careers360 | Updated on Jul 02, 2025 05:17 PM IST

In this article, we will learn about the scientific term force and its effects. Then, we will discuss two types of forces - non-conservative and conservative forces with their examples and their important properties.

Forces which don’t conserve energy are generally known as non-conservative or dissipative forces.
Forces whose work depends only on the initial and final positions of the object are said to be conservative forces. Conservative forces do not depend upon the nature of the path drawn between the object’s initial and final positions.

Scientific Concept of Force

Force always plays an important role in Physics. The word force is used to express the push or pull in a particular direction which means the force is the external form of push and pull. Force has both magnitudes as well as directional properties. Following are the few effects of force:

Force can cause an object to move.
Force can make a moving object speed up.
Force can affect the direction of an object.
The shape of an object can also be changed due to force.

This Story also Contains

Scientific Concept of Force
What is a Non-Conservative Force?
What is a Conservative Force?
Examples of Non-Conservative and Conservative Force
Properties of Non-Conservative and Conservative Force

These are some important effects of force which can be felt in our daily life.

What is a Non-Conservative Force?

A non-conservative force is one where the work done on an object by the force depends on the path taken by that object. Mechanical energy may not be conserved during the work done by a non-conservative force.

What is a Conservative Force?

As the name suggests, this force conserves energy and it follows the law of conservation of energy. Conservative force is responsible for energy conservation and the stability of matter. Conservative force is a force wherein the work done by the force on an object only depends on the initial and final position of the object. So, the work done by this force on an object does not depend on the path taken by that object. The work done by this force on an object moving through any closed path equals zero. This is a very important property of conservative force. Another important property is that mechanical energy is conserved during the work done by a conservative force.

Examples of Non-Conservative and Conservative Force

Examples of Non-Conservative Forces

Tension force, rocket propulsion force, motor propulsion force, viscous force, air resistance and the force of friction are a few examples of non-conservative force.

Examples of Conservative Force

Consider that a ball is thrown vertically at height h from the ground. In this case, the gravitational force would become,

F_{g}=mg

Where, F_{g} is the gravitational force and m is the mass of the ball.

g is the acceleration due to gravity.

So, we can say that the work done on this ball is W=-mgh

Now, if the same ball falls down from that same height h , then we can say that the work done on this ball would be W'=mgh

So, total work done on the ball would be W_{Total}=W+W'

Substituting the values of W and W'

W_{Total}=-mgh+mgh=0

From this calculation, we can say that the total work done for the ball travelling from the ground to a height and then falling back to the ground is equal to zero. So, the work done is conserved. Hence, we can say that the gravitational force is a conservative force.

Other good examples of conservative force are magnetic force, elastic force and electrostatic force.

Properties of Non-Conservative and Conservative Force

The following are the properties of non-conservative force:

Non-conservative force is path-dependent so we can say that it depends on the object’s path.
The total work done by this non-conservative force is not zero in any closed path.
The work done by this force is irreversible and there is no potential energy function of frictional force.
The work done is not recoverable and this force dissipates energy as heat energy.

The following are the properties of conservative force:

The work done by a conservative force will remain zero in any closed path.
It is independent of the area covered by an object and depends upon the final and initial position of the object.
Work done is completely recov

Frequently Asked Questions (FAQs)

1. Explain central forces in simple words.

Central forces are long-range forces. They can produce uniform circular motion and they are conservative forces. They act along the line joining the centre of two objects.

2. State law of conservation of energy.

Energy can not be created or destroyed but it can be changed from one form to another form. The total amount of energy in a system remains constant which means, whenever energy gets transformed, the total energy remains unchanged. This important property of energy is called the law of conservation of energy.

3. State the characteristics of non-central force.

Here are the few characteristics of non-central force:

Non-central force is a short-range force.
It is non-conservative in nature.
Non-central forces do not act along the line joining the centres of the objects.

4. Is nuclear force a non-central force?

yes, nuclear force is a non-central force and it is a very short-range force.

5. Is gravitational force a non-central force? Give a reason.

No, the gravitational force is not a non-central force.

Gravitational force always acts along the line joining the centre of two objects and non-central forces do not act along the line joining the centres of the objects.
Another reason is that gravitational force is a conservative force and that is why it is a central force. Non-conservative forces are non-conservative in nature.

6. Can you give examples of non-conservative forces in everyday life?

Common examples of non-conservative forces include friction, air resistance, and tension in a rope. These forces depend on factors like the surface properties, speed, or the specific path taken, making the work done path-dependent. For instance, the work done by friction depends on the distance traveled, not just the start and end points.

7. Can you explain why the gravitational force between two masses is conservative, but air resistance is not?

The gravitational force between two masses is conservative because it depends only on the distance between the masses, not on their velocities or the path taken. The work done against gravity to lift an object depends only on the height change. Air resistance, however, depends on the object's velocity and shape, making the work done path-dependent. The energy lost to air resistance can't be recovered by reversing the path.

8. What is the significance of the potential energy curve for a conservative force?

The potential energy curve for a conservative force provides valuable information about the system's behavior. The shape of the curve indicates stable and unstable equilibrium points, the direction of force (given by the negative slope of the curve), and the amount of work required to move between different positions. It's a powerful tool for understanding the system without needing to solve detailed equations of motion.

9. How does the concept of conservative forces apply in quantum mechanics?

In quantum mechanics, conservative forces are associated with time-independent potential energy functions in the Schrödinger equation. The concept of path independence translates to the phase of the wavefunction being independent of the path in configuration space. This allows for the definition of stationary states and the use of energy conservation principles in quantum systems.

10. Why is it important to distinguish between conservative and non-conservative forces in physics?

Distinguishing between conservative and non-conservative forces is crucial because it determines which energy principles and problem-solving approaches we can use. Conservative forces allow us to use energy conservation principles and potential energy concepts, while non-conservative forces require more detailed force and work calculations. This distinction affects how we analyze and solve various physical scenarios.

11. How does a non-conservative force differ from a conservative force?

A non-conservative force is one where the work done depends on the path taken by the object, not just its initial and final positions. Friction is a common example of a non-conservative force. Unlike conservative forces, the work done by non-conservative forces cannot be expressed as the difference in potential energy.

12. Can you explain the concept of path independence in conservative forces?

Path independence in conservative forces means that the work done by the force on an object moving between two points is the same regardless of the path taken. This is a key characteristic of conservative forces. It implies that the energy associated with the force depends only on the position of the object, not how it got there.

13. Why is gravitational force considered a conservative force?

Gravitational force is considered conservative because the work done against gravity to lift an object to a certain height is independent of the path taken. Whether you lift the object straight up or along a winding path, the change in gravitational potential energy depends only on the initial and final heights.

14. How does the concept of potential energy relate to conservative forces?

Potential energy is directly related to conservative forces. For any conservative force, we can define a potential energy function. The work done by a conservative force is equal to the negative of the change in potential energy. This relationship allows us to use energy conservation principles in problems involving conservative forces.

15. How does the work-energy theorem apply differently to conservative and non-conservative forces?

The work-energy theorem states that the total work done on an object equals its change in kinetic energy. For conservative forces, this work can be expressed as a change in potential energy. For non-conservative forces, we can't define a potential energy function, so the work must be calculated directly from the force and displacement.

16. How does the concept of conservative forces extend to fields in physics?

The concept of conservative forces extends naturally to fields in physics. A conservative field is one where the work done in moving a particle between two points is independent of the path taken. Mathematically, a vector field F(r) is conservative if it can be expressed as the gradient of a scalar potential function: F = -∇V. This concept is crucial in electromagnetism, where the electrostatic field is conservative, but the full electromagnetic field is not.

17. Can you explain the relationship between conservative forces and closed loop integrals?

For a conservative force, the work done in moving an object around any closed path (a path that starts and ends at the same point) is always zero. Mathematically, this is expressed as a closed loop integral: ∮F·dr = 0. This property is a key characteristic of conservative forces and is related to the fact that the work done is path-independent.

18. How do conservative forces relate to the concept of reversibility in physics?

Conservative forces are closely related to the concept of reversibility in physics. In a system with only conservative forces, processes are theoretically reversible. This means that if you reverse the motion, the system can return to its initial state without any net change in energy. Non-conservative forces, on the other hand, often lead to irreversible processes due to energy dissipation.

19. What is the relationship between conservative forces and Noether's theorem?

Noether's theorem states that every continuous symmetry of a physical system corresponds to a conservation law. For conservative forces, the symmetry in question is time-translation invariance. The fact that the potential energy of a conservative force depends only on position, not time, leads to the conservation of energy. This deep connection between symmetries and conservation laws is a fundamental principle in physics.

20. Can a combination of non-conservative forces ever behave like a conservative force?

While individual non-conservative forces don't behave like conservative forces, in some special cases, a combination of non-conservative forces can result in a net force that appears conservative over a limited domain. However, this is usually an approximation and doesn't hold true globally. It's important to carefully analyze the specific situation to determine if such an approximation is valid.

21. What is a conservative force?

A conservative force is a type of force where the work done by it on an object moving between two points is independent of the path taken. The work done depends only on the initial and final positions of the object. Examples include gravitational force and elastic spring force.

22. How can you determine if a force is conservative based on its mathematical description?

A force is conservative if it can be expressed as the gradient (or negative gradient) of a scalar potential function. Mathematically, if F = -∇V, where F is the force and V is a scalar potential function, then F is conservative. Additionally, the curl of a conservative force field is always zero.

23. How does the principle of conservation of energy apply to systems with only conservative forces?

In systems with only conservative forces, the total mechanical energy (sum of kinetic and potential energies) remains constant. Energy can be transferred between kinetic and potential forms, but the total is conserved. This principle allows us to solve problems by comparing initial and final energies without needing to know the details of the path.

24. What is the significance of a force being path-independent in physics problems?

Path independence of conservative forces simplifies many physics problems. It allows us to focus on initial and final states rather than the specific path taken. This property enables the use of energy conservation principles, making calculations easier and providing insights into the system's behavior without needing detailed information about intermediate steps.

25. How does the concept of work differ for conservative and non-conservative forces?

For conservative forces, the work done is independent of the path and can be calculated as the negative change in potential energy. For non-conservative forces, the work depends on the specific path taken and must be calculated by integrating the force over the displacement. This fundamental difference affects how we approach problems involving these forces.

26. Why can't we define a potential energy function for non-conservative forces?

We can't define a potential energy function for non-conservative forces because the work done by these forces depends on the path taken, not just the initial and final positions. Potential energy is a property of position, but non-conservative forces don't have this path-independent quality, making it impossible to associate a unique potential energy with each position.

27. What happens to the conservation of mechanical energy when non-conservative forces are present?

When non-conservative forces are present, mechanical energy is not conserved. These forces, like friction, typically convert mechanical energy into other forms, such as heat. In such cases, we need to account for the work done by non-conservative forces separately in our energy calculations.

28. How does the presence of non-conservative forces affect the total energy of a system?

Non-conservative forces typically cause changes in the total energy of a system. They often convert mechanical energy into other forms, like heat or sound. As a result, the total mechanical energy (kinetic + potential) of the system is not conserved when non-conservative forces are present. We need to account for these energy transformations in our calculations.

29. Can a force be conservative in one reference frame but non-conservative in another?

No, the conservative or non-conservative nature of a force is an intrinsic property and doesn't change with the reference frame. If a force is conservative in one frame, it will be conservative in all inertial reference frames. This is because the path independence property is preserved across inertial frames.

30. How do conservative and non-conservative forces affect the phase space of a dynamical system?

In systems with only conservative forces, the phase space volume is conserved (Liouville's theorem). This leads to closed orbits in phase space for many systems. Non-conservative forces, however, typically cause the phase space volume to contract over time. This contraction often leads to attractors in the phase space, fundamentally changing the long-term behavior of the system.

31. Why is friction typically modeled as a non-conservative force, and are there any situations where it could be considered conservative?

Friction is typically modeled as a non-conservative force because the work done by friction depends on the path taken and is generally not recoverable. It converts mechanical energy into heat. However, in idealized situations with perfectly elastic materials and no energy dissipation, one could theoretically model certain types of friction (like rolling friction without slipping) as conservative. These situations are rare and usually only approximations of real-world scenarios.

32. How do conservative and non-conservative forces affect the predictability of a system's future state?

Systems with only conservative forces are generally more predictable in terms of their future states. The conservation of energy provides a powerful constraint on the possible states of the system. Non-conservative forces, especially those leading to energy dissipation, can make long-term predictions more challenging. They can lead to phenomena like limit cycles or strange attractors in phase space, which are harder to predict precisely over long time scales.

33. Can you explain the role of conservative forces in the formulation of Lagrangian mechanics?

Conservative forces play a crucial role in Lagrangian mechanics. The Lagrangian formulation is particularly powerful for systems with conservative forces because these forces can be derived from a potential energy function. This allows the entire dynamics of the system to be described by a single scalar function (the Lagrangian), which is the difference between kinetic and potential energies. The equations of motion then follow from the principle of least action, providing a elegant and powerful approach to mechanics.

34. How does the presence of non-conservative forces affect the applicability of Hamilton's principle?

Hamilton's principle, which states that the path taken by a system between two points is the one for which the action integral is stationary, is most directly applicable to systems with conservative forces. When non-conservative forces are present, the principle needs to be modified. One approach is to include these forces through generalized forces in the Lagrangian formulation. Alternatively, Rayleigh's dissipation function can be used to account for non-conservative forces in the variational principle.

35. What is the significance of the curl of a force field in determining whether it's conservative?

The curl of a force field is a crucial test for determining if the force is conservative. A force field F(r) is conservative if and only if its curl is zero everywhere: ∇ × F = 0. This condition ensures that the work done is path-independent. Physically, a non-zero curl indicates that the force field can induce rotational motion, which is characteristic of non-conservative forces. The curl test is particularly useful in vector calculus and electromagnetic theory.

36. How do conservative and non-conservative forces affect the stability of equilibrium points in a system?

Conservative forces lead to equilibrium points that can be classified as stable or unstable based on the shape of the potential energy function. A local minimum in potential energy corresponds to a stable equilibrium, while a local maximum is an unstable equilibrium. Non-conservative forces can create more complex equilibrium behaviors, including limit cycles and strange attractors. They can also shift the position of equilibrium points or change their stability characteristics.

37. Can you explain the concept of a pseudo-conservative force and how it relates to true conservative forces?

A pseudo-conservative force is a non-conservative force that can be treated as conservative under certain conditions or approximations. For example, the Coriolis force in a rotating reference frame can be treated as conservative for small-scale motions. While not truly path-independent, pseudo-conservative forces can sometimes be associated with an effective potential energy, allowing the use of energy conservation principles in limited contexts. It's crucial to understand the limitations of this approximation when applying it.

38. How does the presence of conservative versus non-conservative forces affect the evolution of a system's entropy?

In systems with only conservative forces, the entropy remains constant in reversible processes. The system can theoretically return to its initial state without any net change. Non-conservative forces, however, typically lead to an increase in entropy. They often cause irreversible energy dissipation, converting ordered mechanical energy into disordered thermal energy. This aligns with the second law of thermodynamics, which states that the entropy of an isolated system never decreases over time.

39. What is the relationship between conservative forces and the virial theorem in physics?

The virial theorem relates the time-averaged kinetic energy of a stable system to its total potential energy. It's particularly useful for systems with conservative forces, where the potential energy is well-defined. For a system bound by conservative forces (like gravity), the virial theorem provides a relationship between kinetic and potential energies. This theorem is widely used in astrophysics to understand the behavior of gravitationally bound systems like stars and galaxies.

40. How do conservative and non-conservative forces affect the phase transitions in a physical system?

Conservative forces play a crucial role in many phase transitions, particularly those that can be described by changes in potential energy landscapes. For example, the phase transition in ferromagnetic materials can be understood in terms of the conservative exchange interaction between spins. Non-conservative forces, on the other hand, often affect the dynamics of phase transitions. They can introduce dissipation and irreversibility, potentially altering the critical behavior or the nature of the transition itself.

41. Can you explain how the concept of conservative forces applies in the context of quantum field theory?

In quantum field theory, conservative forces are associated with interactions that preserve the total energy of the system. They arise from symmetries in the Lagrangian density of the field theory. For instance, the conservation of energy in quantum electrodynamics is related to the time-translation symmetry of the electromagnetic field. The concept of virtual particles exchanging conservative forces is fundamental to understanding interactions in particle physics.

42. How does the presence of non-conservative forces affect the applicability of Noether's theorem in classical mechanics?

Noether's theorem, which connects symmetries to conservation laws, is most directly applicable to systems with conservative forces. When non-conservative forces are present, the symmetries of the system may be broken, leading to the violation of certain conservation laws. However, modified versions of Noether's theorem can sometimes be applied to systems with non-conservative forces by incorporating these forces into the Lagrangian through generalized forces or dissipation functions.

43. What is the significance of conservative forces in the formulation of Hamilton-Jacobi theory?

Conservative forces play a central role in Hamilton-Jacobi theory. This theory transforms the Hamilton's equations of motion into a single partial differential equation (the Hamilton-Jacobi equation) for a scalar function (Hamilton's principal function). The theory is particularly powerful for systems with conservative forces because the potential energy term in the Hamiltonian is time-independent, allowing for separation of variables and often leading to exact solutions for complex problems.

44. How do conservative and non-conservative forces affect the concept of ergodicity in statistical mechanics?

Systems with only conservative forces are more likely to exhibit ergodic behavior, where the time average of a quantity equals its ensemble average. This is because conservative forces allow the system to explore its phase space more uniformly over time. Non-conservative forces can lead to dissipation and irreversibility, potentially breaking ergodicity by causing the system to settle into a subset of its phase space or creating attractors that limit the system's long-term behavior.

45. Can you explain the role of conservative forces in the formulation of the principle of least action?

Conservative forces are fundamental to the principle of least action. This principle states that the path taken by a system between two points is the one for which the action (the time integral of the Lagrangian) is stationary. For systems with conservative forces, the Lagrangian can be written as the difference between kinetic and potential energies. This formulation leads to the Euler-Lagrange equations, providing a powerful method for deriving equations of motion in complex systems.