Inelastic Collision - Definition, Formula, Examples, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 04:49 PM IST

An inelastic collision refers to an event whereby two rigid bodies collide, and as a result, both of them lose a part of their kinetic energy – usually in the form of heat, sound or even changes to the deformation of the two colliding bodies. While these collisions cannot be referred to as elastic because kinetic energy before the collision and after the collision is not the same, momentum is still conserved. Inelastic collision examples can be observed in most daily activities: for instance, in a car crash, the vehicles deform inwards when they collide or when a ball of clay is thrown on the pavement and sticks. This is extremely important when discussing energy loss and how materials behave in practice.

Inelastic Collision - Definition, Formula, Examples, FAQs

What is Collision?

A collision is a unique event where two or more bodies interact by getting in contact with each other for a short period of time, whereby they apply force on each other causing a change in their motion (velocity) or shape. In physics, the latter is an important subject since colliding bodies allow students to study the transfer and conservation of momentum and energy.

Collisions are classified based on how energy and momentum are conserved. They are,

Elastic collision: Kinetic energy is conserved
Inelastic collision: Kinetic energy is not conserved
Completely inelastic collision: Kinetic energy is not conserved and the objects are attached after colliding.

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What is Inelastic Collision?

An inelastic collision is a collision in which there is a loss of kinetic energy. While the momentum of the system is conserved in an inelastic collision, kinetic energy is not. This is because some kinetic energy had been transferred to something else.

Inelastic collision examples:

Two vehicles crashed.
Clay ball when thrown against the wall.
A vehicle hit the compound.

What is a Perfectly Inelastic Collision?

A perfectly inelastic collision is a special case of inelastic collision. In this scenario, the two objects stick together after the collision and move as a single unit. For instance, consider a wet ball of mud thrown against a wall - the mud ball sticks to the wall, exemplifying a perfectly inelastic collision.

The Formula for Inelastic Collision

When two objects collide inelastically, they move with a final velocity that can be calculated using the following formula:

$
V=\frac{\left(M_1 v_1+M_2 v_2\right)}{\left(M_1+M_2\right)}
$
Where,
$\mathrm{V}=$ Final velocity
$\mathrm{M}_1=$ Mass of the first object in kgs
$\mathrm{M}_2=$ Mass of the second object in kgs
$\mathrm{V}_1=$ Initial velocity of the first object in $\mathrm{m} / \mathrm{s}$
$\mathrm{V}_2=$ Initial velocity of the second object in $\mathrm{m} / \mathrm{s}$

Inelastic Collision in Two Dimensions

In a two-dimensional inelastic collision, the conservation of momentum is applied separately along each axis. This is because momentum is a vector equation, and there is a separate conservation of momentum equation for each dimension. However, there is only one conservation of energy equation.

Kinetic Energy in Inelastic Collision

In inelastic collisions, kinetic energy isn't conserved. The lost energy is often due to internal friction, which can cause the atoms to vibrate (creating heat) and deform the bodies involved.

Loss of kinetic energy in an inelastic collision

Consider $m_1$and $m_2$ to be the masses of the two colliding objects. The object with mass $m_1$ moves with velocity $v_1$ and the object with mass $m_2$ is at rest position.

After the collision, the momentum of the objects is conserved. But, the two objects stick to each other. Hence, the kinetic energy is not conserved.

Kinetic energy, $\mathrm{E}=\mathrm{mv}^2 / 2$
The kinetic energy of the object $m_1$ before the collision, $\mathrm{E}_{\mathrm{i}}=\mathrm{m}_1 \mathrm{v}_1{ }^{2 / 2}$
Kinetic energy after the collision is, $E_{\mathrm{f}}=\left(m_1+m_2\right) v_{\mathrm{f}}^2 / 2$
Therefore, the loss of kinetic energy is given by,

$
(E i-E f) / E i=1-\frac{m_1+m_2}{m_1}\left(\frac{v_f^2}{v_i^2}\right)
$

Elastic Collision

Any collision in which the collided objects get separated after the collision is known as an elastic collision. In the case of elastic collision, kinetic energy gets conserved. One must use both conservation of momentum and conservation of energy to find the motions of the objects later.

Related Topics

Difference Between Elastic Collision and Inelastic Collision

Aspect	Elastic Collision	Inelastic Collision
Definition	A collision in which both momentum and kinetic energy are conserved.	A collision in which momentum is conserved, but kinetic energy is not conserved.
Energy Conservation	Total kinetic energy remains constant before and after the collision.	Some kinetic energy is converted into other forms of energy (e.g., heat, sound).
Deformation	No permanent deformation occurs; objects return to their original shape.	Objects may deform permanently during the collision.
After Collision	Objects separate after the collision and move independently.	Objects may stick together or move separately depending on the situation.
Example	Collision between two billiard balls.	A car crash or clay ball collision.
Mathematical Relation	Coefficient of restitution is equal to 1.	Coefficient of restitution is less than

Frequently Asked Questions (FAQs)

1. What is the meaning of inelastic?

Inelastic means the one which loses kinetic energy.

2. Is momentum conserved in an inelastic collision?

Yes, momentum is conserved in an inelastic collision.

3. Write elastic and inelastic collisions examples.

An example of elastic collision is the bouncing back of the thrown sponge ball.

An example of an inelastic collision is two vehicles hitting each other.

4. In inelastic collision what is conserved and what is not conserved?

In an inelastic collision, momentum is conserved and energy is not conserved.

5. What happens to the object during the collision?

During the collision, an object undergoes a force that changes the velocity of the object.

6. Define stick.

In a perfectly inelastic collision, if the two objects join together without bouncing it is called a stick in an inelastic collision.

7. What is the value of e in a perfectly inelastic collision?

For an inelastic collision the value of e is zero.

8. In an inelastic collision what is conserved?

Momentum

9. How does an inelastic collision differ from an elastic collision?

In an inelastic collision, kinetic energy is not conserved, and the objects may deform or stick together. In contrast, an elastic collision conserves both momentum and kinetic energy, and the objects bounce off each other without deformation.

10. Can you explain a perfectly inelastic collision?

A perfectly inelastic collision is an extreme case where the colliding objects stick together and move as a single unit after the collision. In this type of collision, the maximum amount of kinetic energy is converted to other forms of energy.

11. How is kinetic energy affected in an inelastic collision?

In an inelastic collision, kinetic energy is not conserved. Some of the initial kinetic energy is converted into other forms of energy, such as heat, sound, or deformation of the objects. The final kinetic energy of the system is less than the initial kinetic energy.

12. How do you calculate the velocity after a perfectly inelastic collision?

To calculate the velocity after a perfectly inelastic collision, use the formula: v' = (m1v1 + m2v2) / (m1 + m2), where m1 and m2 are the masses of the objects, v1 and v2 are their initial velocities, and v' is the final velocity of the combined objects.

13. What is the coefficient of restitution in inelastic collisions?

The coefficient of restitution (e) is a measure of the "bounciness" of a collision. In inelastic collisions, 0 ≤ e < 1. A perfectly inelastic collision has e = 0, while a perfectly elastic collision has e = 1. It's calculated as the ratio of the relative velocity of separation to the relative velocity of approach.

14. What is the principle of conservation of momentum in inelastic collisions?

The principle of conservation of momentum states that the total momentum of a closed system remains constant before and after a collision, even in inelastic collisions. This means that the sum of the momenta of all objects involved in the collision remains the same.

15. Can energy be created or destroyed in an inelastic collision?

No, energy cannot be created or destroyed in an inelastic collision, as per the law of conservation of energy. However, kinetic energy can be converted into other forms of energy, such as heat, sound, or potential energy stored in deformed objects.

16. How do you determine if a collision is elastic or inelastic?

To determine if a collision is elastic or inelastic, compare the total kinetic energy before and after the collision. If the total kinetic energy remains the same, it's elastic. If there's a decrease in kinetic energy, it's inelastic. You can also observe if the objects stick together or deform, which indicates an inelastic collision.

17. Can an inelastic collision ever result in an increase in kinetic energy?

No, an inelastic collision cannot result in an increase in kinetic energy of the system. By definition, inelastic collisions involve a loss of kinetic energy, which is converted into other forms of energy. The total kinetic energy after the collision is always less than or equal to the initial kinetic energy.

18. How do inelastic collisions affect the motion of galaxies in space?

Inelastic collisions between galaxies, often called galaxy mergers, result in the formation of larger galaxies. During these collisions, stars rarely collide due to the vast distances between them, but gas clouds interact inelastically, leading to increased star formation and changes in galaxy structure.

19. What is an inelastic collision?

An inelastic collision is a type of collision where kinetic energy is not conserved. In these collisions, some of the initial kinetic energy is converted into other forms of energy, such as heat or sound. The objects may deform or stick together after the collision.

20. What is the formula for momentum in an inelastic collision?

The formula for momentum in an inelastic collision is: m1v1 + m2v2 = (m1 + m2)v', where m1 and m2 are the masses of the objects, v1 and v2 are their initial velocities, and v' is the final velocity of the combined objects.

21. What are some real-life examples of inelastic collisions?

Real-life examples of inelastic collisions include: a car crash where the vehicles crumple, a baseball being caught by a glove, two lumps of clay colliding and sticking together, or a meteorite striking the Earth's surface.

22. How does mass affect the outcome of an inelastic collision?

In an inelastic collision, the mass of the objects affects their final velocity. Objects with larger masses will have a greater influence on the final velocity of the combined system. The total mass of the system also affects how much kinetic energy is lost during the collision.

23. What is the role of friction in inelastic collisions?

Friction plays a significant role in inelastic collisions by converting kinetic energy into heat energy. It contributes to the energy dissipation process, making the collision inelastic. Friction can occur between the colliding objects and between the objects and their environment.

24. What is the relationship between impulse and momentum in inelastic collisions?

The impulse-momentum theorem applies to inelastic collisions. It states that the impulse (the product of force and time) experienced by an object is equal to its change in momentum. This relationship helps in analyzing the forces involved during the collision.

25. How do inelastic collisions affect the behavior of granular materials?

Inelastic collisions are fundamental to the behavior of granular materials. When granular particles collide, they lose energy through deformation and friction, leading to phenomena like compaction, segregation, and jamming. Understanding these collisions is crucial for industries dealing with powders, grains, and other particulate materials.

26. What happens to the temperature of objects during an inelastic collision?

During an inelastic collision, the temperature of the objects typically increases. This is because some of the kinetic energy is converted into heat energy, which causes the objects to warm up. The amount of temperature increase depends on the objects' specific heat capacities and the energy converted.

27. How does the center of mass behave in an inelastic collision?

In an inelastic collision, the center of mass of the system continues to move at a constant velocity, assuming no external forces are acting on the system. This is a consequence of the conservation of momentum, which applies to both elastic and inelastic collisions.

28. What is the difference between partially inelastic and perfectly inelastic collisions?

In a partially inelastic collision, some kinetic energy is lost, but the objects do not stick together after the collision. In a perfectly inelastic collision, the maximum amount of kinetic energy is lost, and the objects move together as one unit after the collision.

29. How does the concept of work relate to inelastic collisions?

In inelastic collisions, work is done by the forces acting between the colliding objects. This work results in the conversion of kinetic energy into other forms of energy, such as heat or deformation. The total work done during the collision equals the change in kinetic energy of the system.

30. Can you have an inelastic collision in a vacuum?

Yes, you can have an inelastic collision in a vacuum. The inelastic nature of a collision depends on the properties of the colliding objects and their interaction, not on the presence of a medium. Even in a vacuum, objects can deform or stick together, resulting in an inelastic collision.

31. How do inelastic collisions affect the design of safety features in vehicles?

Inelastic collisions are crucial in vehicle safety design. Crumple zones are designed to undergo inelastic deformation during a collision, absorbing kinetic energy and reducing the force experienced by passengers. This conversion of kinetic energy into deformation energy helps protect occupants.

32. What role do inelastic collisions play in the formation of planets?

Inelastic collisions play a crucial role in planet formation. As small particles in a protoplanetary disk collide inelastically, they stick together and gradually grow larger. This process, known as accretion, continues until planetesimals and eventually planets are formed.

33. How does the velocity of approach affect an inelastic collision?

The velocity of approach directly affects the amount of kinetic energy available in an inelastic collision. Higher approach velocities result in more kinetic energy being converted to other forms during the collision. This can lead to greater deformation, heat generation, or a more significant change in the objects' final velocities.

34. What is the significance of inelastic collisions in atomic and nuclear physics?

In atomic and nuclear physics, inelastic collisions are important for studying particle interactions. When particles collide inelastically, they can excite internal energy states, leading to emission of radiation or changes in particle properties. This helps scientists understand the structure and behavior of atoms and nuclei.

35. How do you calculate the energy lost in an inelastic collision?

To calculate the energy lost in an inelastic collision, subtract the final kinetic energy from the initial kinetic energy of the system. The formula is: Energy lost = (1/2)m1v1² + (1/2)m2v2² - (1/2)(m1+m2)v'², where m1 and m2 are the masses, v1 and v2 are initial velocities, and v' is the final velocity.

36. Can an inelastic collision ever be reversible?

In practice, inelastic collisions are generally irreversible processes. The energy converted to heat, sound, or deformation is not easily converted back into kinetic energy. However, in some idealized scenarios or at the microscopic level, certain types of inelastic collisions might be considered reversible under specific conditions.

37. How do inelastic collisions affect the motion of objects in fluids?

In fluids, inelastic collisions between particles contribute to viscosity and energy dissipation. When objects move through fluids, they undergo numerous inelastic collisions with fluid molecules, converting kinetic energy into heat. This process results in drag forces and affects the object's motion through the fluid.

38. What is the importance of inelastic collisions in the field of materials science?

In materials science, studying inelastic collisions helps in understanding material properties such as ductility, malleability, and impact resistance. Inelastic collisions provide insights into how materials deform, absorb energy, and fail under stress, which is crucial for developing new materials and improving existing ones.

39. How do inelastic collisions relate to the concept of entropy?

Inelastic collisions generally increase the entropy of a system. As kinetic energy is converted into heat or deformation during the collision, the energy becomes more dispersed and less organized. This increase in disorder aligns with the second law of thermodynamics, which states that the entropy of an isolated system always increases.

40. What is the difference between elastic strain and inelastic strain in collisions?

Elastic strain occurs when an object deforms during a collision but returns to its original shape afterward, conserving energy. Inelastic strain involves permanent deformation of the object, where some energy is converted to heat or other forms. Inelastic collisions typically involve inelastic strain.

41. How do inelastic collisions affect the motion of subatomic particles in a particle accelerator?

In particle accelerators, inelastic collisions between high-energy particles can lead to the creation of new particles or excitation of internal energy states. These collisions are crucial for studying fundamental physics, as they allow scientists to observe rare particle interactions and verify theoretical predictions.

42. What is the role of inelastic collisions in the process of nuclear fusion?

Inelastic collisions play a crucial role in nuclear fusion. When atomic nuclei collide at high energies, they can undergo inelastic collisions that bring them close enough for the strong nuclear force to overcome electrostatic repulsion. This can lead to fusion reactions, releasing enormous amounts of energy.

43. How do inelastic collisions contribute to energy dissipation in mechanical systems?

Inelastic collisions contribute significantly to energy dissipation in mechanical systems. They convert kinetic energy into heat, sound, or deformation, which is often considered "lost" energy in terms of the system's useful work. This dissipation is important in understanding and designing damping mechanisms in various applications.

44. What is the significance of inelastic collisions in the study of astrophysics?

In astrophysics, inelastic collisions are important for understanding various phenomena. They play a role in star formation, planetary collisions, and the behavior of interstellar gas. Inelastic collisions also contribute to the energy transfer processes in stellar interiors and the dynamics of galaxy interactions.

45. What is the relationship between inelastic collisions and the coefficient of restitution?

The coefficient of restitution (e) quantifies the elasticity of a collision. For inelastic collisions, 0 ≤ e < 1. A perfectly inelastic collision has e = 0, meaning all relative motion between the colliding objects is lost. As e approaches 1, the collision becomes more elastic, with less energy dissipation.

46. How do inelastic collisions affect the design of sports equipment?

Inelastic collisions are considered in sports equipment design to control energy transfer and absorption. For example, in helmet design, the goal is to make the collision between the head and an obstacle as inelastic as possible to absorb impact energy. In contrast, in the design of golf club faces, a more elastic collision is desired to maximize energy transfer to the ball.

47. What is the importance of understanding inelastic collisions in forensic science?

In forensic science, understanding inelastic collisions is crucial for accident reconstruction and crime scene analysis. It helps in determining the forces involved in impacts, the sequence of events in collisions, and the behavior of materials under sudden stresses. This knowledge aids in interpreting evidence and reconstructing incidents accurately.

48. How do inelastic collisions relate to the concept of mechanical energy?

Inelastic collisions demonstrate that mechanical energy (the sum of kinetic and potential energy) is not always conserved in a system. While total energy is conserved, some mechanical energy is converted to non-mechanical forms like heat or sound. This conversion results in a decrease in the system's total mechanical energy.

49. What is the significance of inelastic collisions in the field of nanotechnology?

In nanotechnology, understanding inelastic collisions at the nanoscale is crucial for developing and manipulating nanomaterials. These collisions affect how nanoparticles interact, aggregate, and respond to external stimuli. This knowledge is essential for applications in drug delivery, nanoelectronics, and nanoscale energy transfer.

50. How do inelastic collisions affect the behavior of gases at the molecular level?

At the molecular level, inelastic collisions between gas molecules can lead to energy transfer between translational, rotational, and vibrational modes. This energy redistribution affects the gas's thermodynamic properties, such as specific heat capacity and thermal conductivity, and plays a role in phenomena like sound propagation in gases.

51. What is the role of inelastic collisions in the process of nuclear fission?

In nuclear fission, inelastic collisions play a crucial role. When a neutron collides inelastically with a fissile nucleus, it can excite the nucleus to a higher energy state. This excitation can lead to the nucleus splitting, releasing more neutrons and energy, and potentially triggering a chain reaction.

52. How do inelastic collisions contribute to the heating of celestial bodies?

Inelastic collisions contribute to the heating of celestial bodies in several ways. During planet formation, the kinetic energy of colliding bodies is partially converted to heat. In stars, inelastic collisions between particles in the core contribute to maintaining high temperatures. In planetary atmospheres, inelastic collisions between molecules can lead to heating through friction and energy dissipation.

53. What is the importance of inelastic collisions in the design of crash test dummies?

Inelastic collisions are crucial in the design of crash test dummies. These dummies are engineered to simulate how the human body responds to the inelastic collisions experienced during a vehicle crash. By accurately modeling these collisions, engineers can design and test safety features to minimize injury to vehicle occupants.

54. How do inelastic collisions affect the behavior of polymers and other complex materials?

Inelastic collisions in polymers and complex materials lead to energy dissipation through molecular rearrangements, bond breaking, and heat generation. This behavior influences properties like viscoelasticity, impact resistance, and fatigue strength. Understanding these collisions is crucial for developing materials with specific mechanical and thermal properties.

55. What is the relationship between inelastic collisions and the concept of plasticity in materials?

Plasticity in materials is closely related to inelastic collisions at the atomic and molecular level. When a material undergoes plastic deformation, it experiences numerous inelastic collisions between its constituent particles.