Collision: Definition, Formula, Calculator, Examples, Questions, Equation

Collision

Edited By Vishal kumar | Updated on Jul 02, 2025 07:28 PM IST

Collisions are all about objects bumping into each other, causing changes in motion and energy. These encounters are a lot like the conflicts and interactions we face in real life, where different forces and impacts shape our paths. A collision occurs when two objects come into direct contact and exert forces on each other over a short period. There are two main types of collisions: elastic, where both momentum and kinetic energy are conserved, like billiard balls colliding; and inelastic, where momentum is conserved but some kinetic energy is lost, such as in car crashes. Understanding collisions helps us predict and analyze physical interactions in everyday life and various scientific fields.

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Collision
Momentum And Energy Conservation In Collision
Solved Examples Based on Collision
Summary

Collision

In this article, we are going to study about Collision stage of collision and more. This collision concept belongs to the chapter work, energy, and power, which is an important chapter in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), no questions have been asked on this concept. And for NEET twp questions were asked from this concept. Let's read this entire article to understand collision in depth.

Collision

The interaction between two or more objects is called a collision. And during this interaction strong force acts between two or more bodies for a short time as a result of which the energy and momentum of the interacting particle change.

Stages of Collision

There are three distinct identifiable stages in collision

Before the collision

The interaction forces are zero

During the collision

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The interaction forces are very large and these forces act for a very short time. And because of these interaction forces the energy and momentum of the interacting particle change.

After the collision

The interaction forces are zero

Momentum And Energy Conservation In Collision

The magnitude of the interacting force is often unknown, therefore, Newton’s second law cannot be used. However, the law of conservation of momentum is useful in relating the initial and final velocities.

Momentum conservation

In a collision, the effect of external forces such as gravity or friction is not taken into account as due to the small duration of collision (t) average impulsive force responsible for the collision is much larger than the external force acting on the system and since this impulsive force is 'Internal' therefore the total momentum of the system always remains conserved.

Energy conservation

In a collision 'total energy' is also always conserved. Here total energy includes all forms of energy such as mechanical energy, internal energy, excitation energy, radiant energy, etc.

But in a collision Kinetic energy may or may not be conserved.

Coefficient of Restitution

The ratio of the relative velocity of separation to the relative velocity of approach.

$e = \frac{v_{2} - v_{1}}{u_{1} - u_{2}} = \frac{Relative velocity of separation}{Relative velocity of approach}$

Solved Examples Based on Collision

Example 1: A ball of mass 'm' moving with velocity 'v ', collides inelastically with another identical ball. After the collision, the 1st ball moves with velocity $v / \sqrt{2}$ in a direction perpendicular to the initial direction of motion. Find the speed of the second ball after the collision?

1) $\frac{\sqrt{3}}{2} v$
2) $\frac{1}{2} v$
3) $\sqrt{\frac{3}{2}} v$
4) $\sqrt{2} v$

Solution:

Momentum conservation along X-axis
$\begin{aligned} m v = m v_{1} \cos θ \\ v = v_{1} \cos θ \dots . (1) \end{aligned}$

along $y$ -axis

$\begin{aligned} 0 = m v / \sqrt{2} - m v_{1} \sin θ \\ \frac{v}{\sqrt{2}} = v_{1} \sin θ \dots (2) \\ v^{2} + \frac{v^{2}}{2} = v_{1}^{2} (\sin^{2} θ + \cos^{2} θ) \\ v_{1}^{2} = \frac{3 v^{2}}{2} \Rightarrow v_{1} = \sqrt{\frac{3}{2}} v \end{aligned}$

Hence, the answer is the option (1).

Example 2: A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length L (L>>r) and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed$v$, the average force experienced by each support after a long time is (assume all collisions are elastic) :

1) $\frac{m v^{2}}{L - n r}$
2) $\frac{m v^{2}}{L - 2 n r}$
3) $\frac{m v^{2}}{2 (L - n r)}$
4) Zero

Solution:

Perfectly Elastic Collision

The law of conservation of momentum and that of Kinetic Energy hold good.

wherein
$\begin{aligned} \frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2} \\ m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2} \\ m_{1}, m_{2} : masses \end{aligned}$

$u_{1}, v_{1}$ : initial and final velocity of the mass $m_{1}$
$u_{2}, v_{2}$ : initial and final velocity of the mass $m_{2}$
Average time for one collision

$= \frac{2 L - 4 n r}{v}$
Since the diameter of each base $= 2 r$
Change in momentum per collision $= 2 mv$

$\begin{aligned} ∴ F_{a v} = \frac{Δ p_{a v}}{Δ t_{a v}} = \frac{2 m v}{(2 L - 4 n r) / v} = \frac{m v^{2}}{L - 2 n r} \\ F_{a v} = \frac{m v^{2}}{L - 2 n r} \end{aligned}$

Hence, the answer is the option(2).

Example 3: A block of mass 0.50 kg is moving with a speed of 2.00 ms^-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss (in Joule) during the collision is :

1) 0.34 Joule

2) 0.16 Joule

3) 1 Joule

4) 0.67 Joule

Solution:
$Initial kinetic energy = \frac{1}{2} \times (0.50) \times 4 = 1 J$
After collision momentum $= 1.5 v$

From momentum conservation,

$1.5 v = 1 \Rightarrow v = \frac{2}{3} m / s$
Final kinetic energy

$= \frac{1}{2} \times (1.5) \times {(\frac{2}{3})}^{2} = \frac{3}{4} \times \frac{4}{9} = \frac{1}{3} J$
Loss in kinetic energy

$= K \cdot E_{f} - K \cdot E_{i} = - \frac{2}{3} J$
So, the loss will be 0.67 Joule

Hence, the answer is the option(4).

Summary

Collisions involve interactions where objects exert forces on each other, leading to changes in momentum and energy. There are two main types: elastic (both momentum and kinetic energy conserved) and inelastic (only momentum conserved). Understanding collisions is crucial for solving physics problems related to momentum and energy conservation, particularly in competitive exams like JEE and NEET.

Frequently Asked Questions (FAQs)

1. What is a collision in physics?

A collision in physics is an event where two or more objects come into contact and exert forces on each other for a short time. During a collision, momentum and energy are transferred between the objects involved.

2. How does the angle of impact affect a collision?

The angle of impact affects how momentum is transferred between objects. In a head-on collision, momentum transfer is maximized along the line of impact. In angled collisions, momentum is transferred in components, affecting both the magnitude and direction of post-collision velocities.

3. What is the coefficient of restitution?

The coefficient of restitution is a measure of the "bounciness" of a collision. It's the ratio of the relative velocity of separation after collision to the relative velocity of approach before collision. It ranges from 0 (perfectly inelastic) to 1 (perfectly elastic).

4. Can a lighter object impart more momentum to a heavier object in a collision?

Yes, it's possible. Momentum is the product of mass and velocity. A lighter object moving at a very high velocity can have more momentum than a heavier object moving slowly. In a collision, this lighter object could impart more momentum to the heavier object.

5. What is impulse in the context of collisions?

Impulse is the product of the average force during a collision and the time interval over which the force acts. It represents the change in momentum of an object during the collision. The impulse-momentum theorem states that impulse equals the change in momentum.

6. How does the law of conservation of momentum apply to collisions?

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

7. What's the difference between elastic and inelastic collisions?

In an elastic collision, both momentum and kinetic energy are conserved. The objects bounce off each other without deformation. In an inelastic collision, momentum is conserved, but some kinetic energy is converted to other forms (like heat or sound). The objects may stick together or deform.

8. Can kinetic energy increase during a collision?

Generally, kinetic energy cannot increase during a collision in an isolated system. It can remain the same (in perfectly elastic collisions) or decrease (in inelastic collisions). An apparent increase in kinetic energy would require an external source of energy.

9. How does mass affect the outcome of a collision?

Mass plays a crucial role in collisions. Objects with larger mass have more momentum and are less likely to change their velocity significantly during a collision. Conversely, objects with smaller mass are more easily affected by collisions.

10. What is a perfectly inelastic collision?

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

11. What is the role of deformation in collision analysis?

Deformation during collisions affects energy transfer and the collision's elasticity. It can absorb energy, reducing the bounce effect. Understanding deformation is crucial in designing safety features, sports equipment, and in analyzing material properties under impact.

12. What is the role of virtual collisions in quantum field theory?

In quantum field theory, virtual collisions or interactions between particles explain forces and energy exchanges. These 'collisions' involve the exchange of virtual particles and are fundamental to understanding the behavior of subatomic particles and the nature of fundamental forces.

13. How do collisions at different temperatures affect material properties?

Collisions at different temperatures can significantly affect material properties. At high temperatures, increased molecular collisions can lead to phase changes, chemical reactions, or material breakdown. Understanding these effects is crucial in materials science, metallurgy, and high-temperature physics.

14. How do you calculate momentum in a collision?

Momentum is calculated by multiplying an object's mass by its velocity. In a collision, you calculate the momentum of each object before and after the collision. The total momentum before should equal the total momentum after in a closed system.

15. What happens to energy in an inelastic collision?

In an inelastic collision, some kinetic energy is converted to other forms of energy such as heat, sound, or deformation of the objects. The total energy is conserved, but the kinetic energy after the collision is less than before.

16. What is the role of friction in collisions?

Friction can play a significant role in collisions, especially those involving surfaces. It can affect the post-collision motion of objects, convert kinetic energy into heat, and influence the overall energy transfer during the collision process.

17. How do collisions relate to Newton's laws of motion?

Collisions directly demonstrate Newton's laws. The first law is seen in objects maintaining their motion before and after collision. The second law relates the force of impact to the change in momentum. The third law is evident in the equal and opposite forces exerted by colliding objects on each other.

18. What is the concept of center of mass in collisions?

The center of mass is the average position of mass in a system. In collisions, the motion of the center of mass of the system remains unchanged if no external forces are acting. This concept is crucial for understanding the behavior of complex colliding systems.

19. How do collisions in two dimensions differ from one-dimensional collisions?

Two-dimensional collisions involve motion and momentum transfer in multiple directions, unlike one-dimensional collisions. They require vector analysis to resolve forces and velocities into components, making the calculations more complex but allowing for a wider range of possible outcomes.

20. What is the significance of the line of impact in a collision?

The line of impact is the line along which the forces act during a collision. It's crucial for determining how momentum and energy are transferred. In central collisions, the line of impact passes through both objects' centers of mass, simplifying the analysis.

21. How do deformable objects behave differently in collisions compared to rigid objects?

Deformable objects can absorb more energy during a collision by changing shape. This often results in more inelastic collisions, where kinetic energy is converted to deformation energy. Rigid objects, in contrast, tend to have more elastic collisions with less energy loss.

22. What is the role of potential energy in collisions?

While collisions primarily involve kinetic energy, potential energy can play a role, especially in systems with springs or in gravitational fields. Potential energy can be converted to kinetic energy during a collision or vice versa, affecting the overall energy balance.

23. How do collisions at the atomic or subatomic level differ from macroscopic collisions?

Atomic and subatomic collisions involve quantum mechanical effects. They can result in the creation or annihilation of particles, and the outcomes are often probabilistic. These collisions can also involve the conversion of mass to energy, unlike macroscopic collisions.

24. What is the relationship between force and impulse in a collision?

Impulse is the integral of force over time during a collision. It represents the area under the force-time curve. A large force applied for a short time can produce the same impulse (and change in momentum) as a smaller force applied for a longer time.

25. How does the concept of work relate to collisions?

Work is done during a collision when a force causes displacement. In perfectly elastic collisions, the net work done is zero as all kinetic energy is conserved. In inelastic collisions, negative work is done on the system, reducing its kinetic energy.

26. What is the significance of the coefficient of restitution in real-world applications?

The coefficient of restitution is crucial in designing sports equipment (like golf clubs or tennis rackets), automotive safety features, and industrial processes involving impacts. It helps predict how objects will behave upon impact and how much energy will be dissipated.

27. How do collisions affect rotational motion?

Collisions can impart both linear and angular momentum. Off-center collisions can cause objects to start rotating or change their existing rotation. This is important in understanding phenomena like billiard ball collisions or spacecraft maneuvering.

28. What is the concept of perfectly elastic collision, and does it exist in reality?

A perfectly elastic collision is one where both kinetic energy and momentum are conserved. While it's a useful theoretical concept, truly perfect elastic collisions don't exist in reality due to factors like deformation, heat generation, and sound production. Some collisions, like those between subatomic particles, can come very close to being perfectly elastic.

29. How do collisions relate to the concept of energy transfer?

Collisions are prime examples of energy transfer. In elastic collisions, kinetic energy is transferred between objects without loss. In inelastic collisions, kinetic energy is partially converted to other forms like heat, sound, or deformation energy, demonstrating energy transformation.

30. What is the role of time in collisions?

The duration of a collision, though often very brief, is crucial. It affects the magnitude of the force (shorter time means higher force for the same impulse) and the energy transfer process. Understanding collision time is important in designing safety equipment and analyzing impact phenomena.

31. How do multiple collisions in a system behave differently from a single collision?

Multiple collisions in a system, like in a gas or a Newton's cradle, involve complex energy and momentum transfers. Each collision affects subsequent ones, leading to energy distribution throughout the system. This concept is fundamental in understanding thermodynamics and statistical mechanics.

32. What is the significance of momentum conservation in the absence of external forces?

Momentum conservation in the absence of external forces is a fundamental principle in physics. It allows us to predict the motion of objects after a collision knowing only their initial states, which is crucial in fields ranging from particle physics to astrophysics.

33. How do collisions in fluids differ from those between solid objects?

Collisions in fluids involve continuous interactions rather than discrete impacts. They are characterized by fluid dynamics principles, including pressure changes, viscosity effects, and wave propagation. Understanding these collisions is crucial in fields like oceanography and aerodynamics.

34. What is the concept of coefficient of restitution in oblique collisions?

In oblique collisions, the coefficient of restitution applies to the velocity component normal to the surface of contact. The tangential component is affected by friction. This concept is important in understanding complex collisions like those in sports or industrial processes.

35. How does the principle of conservation of energy apply differently to elastic and inelastic collisions?

In elastic collisions, both kinetic energy and momentum are conserved. In inelastic collisions, while total energy is conserved, kinetic energy is not – some is converted to other forms. This difference is key to understanding energy transformations in various physical processes.

36. How do relativistic effects come into play in high-speed collisions?

At very high speeds (close to the speed of light), relativistic effects become significant. Mass increases with velocity, affecting momentum calculations. Time dilation and length contraction also play roles, complicating the analysis of such collisions, which is important in particle physics.

37. What is the significance of collision cross-section in particle physics?

Collision cross-section is a measure of the probability of particle interactions. It's crucial in understanding subatomic collisions, determining reaction rates in nuclear physics, and designing particle accelerator experiments. It relates the concept of collisions to quantum mechanical probabilities.

38. How do collisions contribute to heat transfer and temperature change?

At the microscopic level, heat transfer is essentially a result of collisions between particles. In gases and liquids, these collisions lead to energy transfer, contributing to temperature changes. This concept is fundamental to understanding thermodynamics and kinetic theory.

39. What is the role of collisions in understanding the behavior of gases?

Collisions between gas molecules are key to understanding gas behavior. The kinetic theory of gases uses collision concepts to explain pressure, temperature, and volume relationships. This understanding is crucial in fields ranging from meteorology to chemical engineering.

40. How do collisions affect the stability of orbits in celestial mechanics?

In celestial mechanics, collisions and near-misses can significantly alter orbits. They play a role in the formation and evolution of planetary systems, asteroid belt dynamics, and the long-term stability of solar systems. Understanding these collisions is crucial in astrophysics and space exploration.

41. What is the concept of super-elastic collisions?

Super-elastic collisions are theoretical collisions where the kinetic energy after the collision is greater than before. While they don't occur spontaneously in closed systems (violating energy conservation), they can be simulated in systems with external energy input, like in some chemical reactions or biological processes.

42. How do collisions at the nanoscale differ from macroscopic collisions?

Nanoscale collisions involve quantum mechanical effects and surface forces that are negligible at larger scales. Van der Waals forces, electrostatic interactions, and quantum tunneling can significantly influence collision outcomes. Understanding these is crucial in nanotechnology and molecular biology.

43. What is the role of collisions in understanding chemical reactions?

In chemistry, collisions between molecules are essential for reactions to occur. The collision theory explains how reaction rates depend on the frequency and energy of molecular collisions. This concept bridges physics and chemistry, crucial for understanding reaction kinetics and catalysis.

44. How do collisions contribute to the concept of pressure in fluids?

Pressure in fluids results from the collective effect of numerous molecular collisions with container walls. The force exerted by these collisions, averaged over time and area, defines pressure. This microscopic view of pressure is fundamental to understanding fluid dynamics and thermodynamics.

45. What is the significance of inelastic collisions in energy dissipation systems?

Inelastic collisions are crucial in energy dissipation systems like shock absorbers, car crumple zones, and earthquake-resistant structures. They convert kinetic energy into other forms, reducing the impact force and protecting structures or passengers. Understanding these collisions is key to safety engineering.

46. How do collisions affect the behavior of plasma in fusion reactions?

In fusion reactions, collisions between high-energy plasma particles are essential. These collisions must overcome electrostatic repulsion to bring nuclei close enough for fusion. Understanding these collision dynamics is crucial for developing fusion energy and studying astrophysical phenomena.

47. How do collisions contribute to the phenomenon of Brownian motion?

Brownian motion, the random movement of particles in a fluid, results from countless collisions with fluid molecules. These collisions demonstrate the kinetic theory of matter and provide evidence for the existence of atoms and molecules. This concept is crucial in fields from physics to biology.

48. What is the importance of understanding collisions in the design of particle accelerators?

In particle accelerators, controlled high-energy collisions are used to study subatomic particles. Understanding collision dynamics is crucial for designing these machines, predicting particle behavior, and interpreting experimental results. This knowledge is fundamental to advancing particle physics.

49. What is the role of collisions in understanding the behavior of superconductors?

In superconductors, the behavior of electrons can be understood in terms of special types of collisions or interactions. Cooper pairs, formed by electron interactions, move through the material without resistance. Understanding these 'collisions' is key to advancing superconductor technology.

50. How do collisions contribute to our understanding of the early universe?

Collisions play a crucial role in cosmology, particularly in understanding the early universe. High-energy particle collisions in the moments after the Big Bang shaped the formation of matter and the universe's structure. Studying these primordial collisions helps physicists understand the universe's origins and evolution.