Conservative Force - Properties, Examples, FAQs

Edited By Team Careers360 | Updated on Jul 02, 2025 04:25 PM IST

What is Conservative Force?

A conservative force is one that is applied to move a particle from one point to another while remaining independent of the particle's route. It is solely determined by the particle's starting and final positions. Conservation forces include gravitational and elastic spring forces, for example. Gravity is a classic example of a conservative force. Magnetic, electrostatic, and elastic forces are more examples.

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What is Conservative Force?
Properties of Conservative Force
Examples-
What is Non-Conservative Force?
Difference Between Conservative and Non-Conservative Force

Conservative Force - Properties, Examples, FAQs

Properties of Conservative Force

A force is said to be conservative if it possesses the properties listed below.

When the force is solely determined by the initial and final positions, regardless of the path followed.
The work done by a conservative force on any closed path is zero.
The work done by a conservative force can be reversed.

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Examples-

Gravitational Force

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Assume you're at the top of a ladder and you drop a ball. The gravity will be estimated while the ball is at its maximum height and again when it reaches the ground as a conservative force.

Gravitational force = m × g,

Where m is the mass of the ball and g is the acceleration due to gravity.

Therefore work done by the gravitational force

W = -mgh

Where h is the difference between the initial and final position of the body.

$h=h_{\text {final }}-h_{\text {initial }}$

We can simply find out the work done by gravity on the particle using the above expression just by knowing the vertical displacement, regardless of how intricate the particle's journey is. We can deduce from this that the gravitational force is independent of the path traveled, but only of the initial and final positions. As a result, gravitation is a conservative force.

Magnetic Force

The force of magnetism is a conservative force. Any two electrically charged particles moving together produce a magnetic force, which is a relative phenomenon. The magnetic force is a conservative force since it is a velocity-dependent vector.

Electrostatic Force

The force of electrostatic attraction is a conservative force. The work done by an electrostatic force in the presence of an electric field is determined by the charge's initial and ending positions, not its path. The electrostatic force is a conservative force since it is route-independent.

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What is Non-Conservative Force?

A non-conservative force is one whose output is dependent on the path chosen. Friction is an example of a force that is not conservative. If a force causes a change in mechanical energy, which is equal to the total of potential and kinetic energy, it is said to be non-conservative. A non-conservative force's work adds or subtracts mechanical energy. Thermal energy is dissipated when work is done by friction, for example. It is impossible to restore all of the energy that has been lost.

Properties of Non-Conservative Force

Its properties are the opposite of conservative forces. The following are the properties:

Because it is path-dependent, it is also affected by the initial and final velocity.
The total work done by a non-conservative force in any closed path is not zero.
The work done by a non-conservative force is irreversible

NCERT Physics Notes :

Difference Between Conservative and Non-Conservative Force

Conservative Force	Non-Conservative Force
Inside a closed loop, work done by conservative forces is always zero.	Inside an enclosed path, the work done by a non-conservative force is never zero.
Conservative force is any force in which the work done by or against a body is determined by its initial and final positions.	Any force in which the path traveled by an object determines the work done by or against that body is referred to as non-conservative force.
Electrostatic force, gravitational force, magnetic force, and other conservative forces are examples.	Frictional force, cyclotron induction force, and viscous force are all common examples.

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Frequently Asked Questions (FAQs)

1. What do you mean by central force?

The force acting on an object that is directed along the line between the object and the origin is known as the central force.

2. Is the electric field a conservative field?

Yes, the electric field is a conservative field.

3. What is a conservative field?

A field where conservative force can be experienced is called a conservative field.

4. What is the SI unit of work done?

The SI unit of work done is joule (J).

5. Which of the following is not a non conservative force? A. Force of friction B. Gravitational force C. Magnetic Force D. Electrostatic Force

Friction is a force that is non conservative. Work is required to overcome the effect of frictional force when a body is moved against friction. The work done by the frictional force is determined not only by the body's initial and ultimate positions, but also by the length of the path travelled.

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

The key difference is that for conservative forces, the work done is path-independent and only depends on the start and end points. Non-conservative forces, like friction, depend on the specific path taken and typically convert mechanical energy into other forms like heat.

7. Why is friction typically not considered a conservative force?

Friction is not conservative because the work done by friction depends on the path taken. It always opposes motion and dissipates energy as heat, which means the total mechanical energy of the system is not conserved.

8. Can a force be conservative in one situation and non-conservative in another?

No, a force is either always conservative or always non-conservative. The nature of the force itself determines this property, not the specific situation or system in which it acts.

9. How do conservative forces relate to the concept of work-energy theorem?

The work-energy theorem states that the work done on an object equals its change in kinetic energy. For conservative forces, this work can also be expressed as the negative change in potential energy, simplifying energy calculations in many physical systems.

10. How does the presence of conservative forces affect the analysis of collisions?

In collisions where only conservative forces are involved (like ideal elastic collisions), the total mechanical energy of the system is conserved. This principle greatly simplifies the analysis of such collisions, allowing for the use of energy conservation equations alongside momentum conservation.

11. Why is gravitational force considered a conservative force?

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

12. How does the concept of conservative forces apply to planetary motion?

In planetary motion, gravitational force acts as a conservative force. This allows for the application of energy conservation principles, leading to important results like Kepler's laws of planetary motion and the concept of orbital energy.

13. What is the significance of conservative forces in analyzing simple harmonic motion?

In simple harmonic motion, such as a mass on a spring, the restoring force is conservative. This allows for easy analysis of energy transfer between kinetic and potential forms and helps explain why the motion is periodic.

14. What role do conservative forces play in the concept of escape velocity?

Escape velocity is calculated using the principle of energy conservation involving gravitational potential energy, which is associated with the conservative gravitational force. An object needs enough initial kinetic energy to overcome the total gravitational potential energy to escape a body's gravitational field.

15. How do conservative forces contribute to the stability of orbits?

The conservative nature of gravitational force allows for stable, repeating orbits. The total energy (kinetic + potential) of an orbiting body remains constant, leading to closed orbital paths in the absence of other perturbations.

16. Can you explain the concept of potential energy in relation to conservative forces?

Potential energy is associated with conservative forces. It represents the stored energy due to an object's position or configuration in a force field. For conservative forces, the change in potential energy between two points is equal to the negative of the work done by the force, regardless of the path taken.

17. How does the concept of energy conservation relate to conservative forces?

Conservative forces allow for the conservation of mechanical energy (kinetic + potential) in a closed system. As an object moves in a conservative force field, energy can be transferred between kinetic and potential forms, but the total mechanical energy remains constant if no other forces are present.

18. What is the significance of path independence in conservative forces?

Path independence means that the work done by a conservative force depends only on the initial and final positions, not the path taken between them. This property allows for the definition of potential energy and simplifies many calculations in physics.

19. How can you mathematically determine if a force is conservative?

A force is conservative if its curl is zero in all space, or if the work done in a closed path is always zero. Mathematically, for a force F(x,y,z), if curl F = 0 everywhere, then F is conservative.

20. What is the relationship between conservative forces and vector fields?

Conservative forces can be represented as the gradient of a scalar potential field. This means that for any conservative force F, there exists a scalar function V (potential energy) such that F = -∇V, where ∇ is the gradient operator.

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. It depends only on the initial and final positions of the object. Examples include gravitational force and elastic spring force.

22. How does the concept of conservative forces apply to quantum mechanics?

In quantum mechanics, conservative forces are associated with time-independent potential energy functions in the Schrödinger equation. This leads to stationary states and energy quantization, fundamental concepts in quantum theory.

23. Can you explain how conservative forces relate to the principle of least action?

The principle of least action states that the path taken by a system between two points is the one that minimizes the action integral. For systems with only conservative forces, this principle leads to the same equations of motion as derived from Newton's laws.

24. How do conservative forces affect the motion of a pendulum?

In an ideal pendulum, gravity acts as a conservative force. This allows for the periodic conversion between potential and kinetic energy, resulting in the characteristic oscillatory motion. The total mechanical energy remains constant in the absence of non-conservative forces like air resistance.

25. What is the significance of conservative forces in defining potential energy functions?

Conservative forces allow for the definition of potential energy functions that depend only on position. This is crucial because it means the change in potential energy between two points is path-independent, simplifying energy calculations and analysis in many physical systems.

26. What is the importance of conservative forces in understanding the behavior of particles in magnetic fields?

While magnetic forces themselves are not conservative, they can lead to conservative effective potentials in certain situations, like charged particles in uniform magnetic fields. This allows for the analysis of cyclotron motion and magnetic confinement, important in plasma physics and particle accelerators.

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

Distinguishing between these forces is crucial because it determines which energy principles can be applied. Conservative forces allow for the use of potential energy and total energy conservation, simplifying many problems, while non-conservative forces require more complex analysis involving energy dissipation.

28. What is the significance of conservative forces in the formulation of Lagrangian mechanics?

In Lagrangian mechanics, conservative forces are easily incorporated through potential energy terms in the Lagrangian function. This formulation simplifies the analysis of complex systems and provides a powerful method for deriving equations of motion, especially for systems with constraints.

29. What is the importance of conservative forces in the study of fluid dynamics?

In ideal fluid dynamics, conservative forces like gravity and pressure gradients play a crucial role. They allow for the application of Bernoulli's principle, which relates pressure, velocity, and height in a flowing fluid, and is fundamental to understanding phenomena like lift in aerodynamics.

30. How does the presence of conservative forces affect the analysis of oscillatory systems?

In oscillatory systems governed by conservative forces, like ideal springs or pendulums, energy is continually converted between kinetic and potential forms. This leads to periodic motion and allows for the application of simple harmonic motion principles in analysis.

31. Can you explain the concept of equipotential surfaces in relation to conservative forces?

Equipotential surfaces are regions where the potential energy due to a conservative force is constant. Work done by the conservative force in moving an object along an equipotential surface is zero, as there's no change in potential energy.

32. How do conservative forces relate to the concept of force fields?

Conservative forces can be represented as force fields where the work done moving an object between any two points is independent of the path. These force fields can be visualized using field lines, and the force at any point is tangent to these lines.

33. Can you explain the role of conservative forces in the analysis of roller coaster physics?

In an ideal roller coaster (ignoring friction and air resistance), the gravitational force is conservative. This allows for the application of energy conservation principles, explaining how kinetic energy at the bottom of a hill relates to potential energy at the top, and why the coaster can complete loops without additional energy input.

34. How do conservative forces contribute to the concept of binding energy in atomic physics?

In atomic physics, the electrostatic force between protons and electrons is conservative. This allows for the definition of potential energy curves and wells, which are crucial in understanding binding energies, atomic stability, and electron energy levels.

35. What is the relationship between conservative forces and the concept of potential wells?

Conservative forces give rise to potential wells, which are regions in space where potential energy is lower than in surrounding areas. These wells can trap particles, explaining phenomena like atomic bonding, planetary orbits, and the stability of certain physical systems.

36. Can you explain how conservative forces relate to the concept of central forces?

Many conservative forces, like gravity and electrostatic forces, are also central forces (directed towards or away from a fixed point). This property, combined with their conservative nature, leads to the conservation of angular momentum in addition to energy, simplifying the analysis of orbital motion.

37. How do conservative forces affect the behavior of objects in potential energy diagrams?

In potential energy diagrams, conservative forces drive objects towards lower potential energy. Objects oscillate in potential wells, can become trapped in local minima, or escape if given enough energy. These diagrams provide a visual and intuitive way to understand system behavior under conservative forces.

38. How do conservative forces contribute to the stability of atomic nuclei?

In atomic nuclei, the strong nuclear force acts as a conservative force at short ranges. This allows for the definition of nuclear potential energy, which, balanced against the repulsive electrostatic force, determines nuclear stability and explains phenomena like radioactive decay and nuclear binding energies.

39. Can you explain the role of conservative forces in the analysis of celestial mechanics?

In celestial mechanics, the gravitational force between celestial bodies is conservative. This property allows for the application of energy and angular momentum conservation principles, leading to the derivation of Kepler's laws and the analysis of complex orbital dynamics in multi-body systems.

40. How does the concept of conservative forces apply to the analysis of potential energy surfaces in chemistry?

In chemistry, conservative forces (like electrostatic interactions) give rise to potential energy surfaces that describe molecular configurations. These surfaces are crucial for understanding chemical bonding, reaction pathways, and molecular stability, as molecules tend to adopt configurations that minimize potential energy.

41. How do conservative forces relate to the concept of equilibrium in physical systems?

Conservative forces drive systems towards states of minimum potential energy, which often correspond to equilibrium positions. This principle is fundamental in understanding stability in various systems, from simple mechanical arrangements to complex molecular structures.

42. Can you explain how conservative forces contribute to the phenomenon of resonance?

In systems with conservative forces, like ideal springs or pendulums, the natural frequency of oscillation is determined by the properties of the force (e.g., spring constant, gravitational acceleration). When an external periodic force matches this natural frequency, resonance occurs, leading to large amplitude oscillations.

43. What is the significance of conservative forces in the analysis of molecular dynamics?

In molecular dynamics simulations, conservative forces (like van der Waals and electrostatic interactions) are used to model interatomic and intermolecular potentials. This allows for the calculation of molecular motion and properties, crucial for understanding complex biological and chemical systems.

44. How do conservative forces affect the behavior of quantum particles in potential wells?

In quantum mechanics, conservative forces create potential wells that lead to quantized energy levels for particles. This explains phenomena like electron energy levels in atoms, molecular bonding, and the behavior of quantum dots, where particles are confined by potential barriers.

45. Can you explain the role of conservative forces in the analysis of small oscillations about equilibrium?

For small oscillations around equilibrium positions, conservative forces can often be approximated as linear restoring forces. This leads to simple harmonic motion, allowing for straightforward analysis of vibrations in various systems, from mechanical oscillators to molecular vibrations.

46. How does the concept of conservative forces apply to the study of solid-state physics?

In solid-state physics, the interactions between atoms in a crystal lattice are often modeled using conservative forces. This allows for the analysis of lattice vibrations (phonons), thermal properties, and the behavior of electrons in periodic potentials, leading to the understanding of band structures and electrical properties of materials.

47. How do conservative forces contribute to the concept of adiabatic invariants in physics?

In systems with slowly varying conservative forces, certain quantities (adiabatic invariants) remain approximately constant. This principle is crucial in understanding phenomena like the motion of charged particles in slowly varying magnetic fields and the behavior of quantum systems under gradual changes.

48. Can you explain how conservative forces relate to the principle of virtual work in mechanics?

The principle of virtual work states that a system is in equilibrium if the virtual work of all forces (including conservative forces) for any virtual displacement is zero. For conservative forces, this principle simplifies to finding configurations where the potential energy is stationary, providing a powerful method for analyzing equilibrium in complex systems.

49. What role do conservative forces play in the analysis of coupled oscillators?

In systems of coupled oscillators, like coupled pendulums or springs, conservative forces (gravitational or elastic) govern the interactions. This allows for the analysis of normal modes of vibration, energy transfer between oscillators, and phenomena like beat frequencies, important in various fields from mechanics to quantum optics.

50. How does the presence of conservative forces affect the analysis of chaotic systems?

Even in chaotic systems, the presence of conservative forces ensures energy conservation, constraining the possible trajectories in phase space. This leads to interesting phenomena like strange attractors in conservative chaotic systems, different from the behavior seen in dissipative chaotic systems.

51. Can you explain the significance of conservative forces in the study of statistical mechanics?

In statistical mechanics, conservative forces determine the potential energy landscape of a system. This is crucial for calculating partition functions, which in turn allow for the derivation of thermodynamic properties. The conservative nature of these forces ensures that energy is a well-defined quantity for statistical ensembles.

52. How do conservative forces contribute to the understanding of symmetry and conservation laws in physics?

Conservative forces are often associated with spatial symmetries in physical systems. For example, the conservative nature of gravitational force is related to the homogeneity of space. This connection between conservative forces and symmetries is fundamental to understanding conservation laws through Noether's theorem.

53. What is the role of conservative forces in the analysis of quantum tunneling phenomena?

In quantum tunneling, particles can penetrate potential barriers created by conservative forces, a phenomenon impossible in classical mechanics. The shape of these potential barriers, determined by conservative forces, is crucial in calculating tunneling probabilities, important in various quantum phenomena from nuclear decay to scanning tunneling microscopy.

54. How does the concept of conservative forces apply to the study of superconductivity?

In superconductivity, the interaction between electrons and the crystal lattice can be modeled using conservative forces. This leads to the formation of Cooper pairs and the BCS theory of superconductivity, explaining phenomena like zero electrical resistance and the Meissner effect.

55. Can you explain how conservative forces relate to the concept of gauge theories in modern physics?

In gauge theories, fundamental forces are described by conservative vector fields that are invariant under certain transformations. This concept, rooted in the properties of conservative forces, is crucial in the formulation of modern theories like quantum electrodynamics and the Standard Model of particle physics.