9.4 Types of Collisions - University Physics Volume 1 | OpenStax (2024)

Learning Objectives

By the end of this section, you will be able to:

  • Identify the type of collision
  • Correctly label a collision as elastic or inelastic
  • Use kinetic energy along with momentum and impulse to analyze a collision

Although momentum is conserved in all interactions, not all interactions (collisions or explosions) are the same. The possibilities include:

  • A single object can explode into multiple objects (explosions).
  • Multiple objects can collide and bounce off each other, called an elastic collision, resulting in the same kinetic energy of the system before and after the collision.
  • Multiple objects can collide and the system loses kinetic energy, called an inelastic collision. One such case is where the two objects stick together, forming a single object.

It’s useful, therefore, to categorize different types of interactions, according to how the interacting objects move before and after the interaction.


The first possibility is that a single object may break apart into two or more pieces. An example of this is a firecracker, or a bow and arrow, or a rocket rising through the air toward space. These can be difficult to analyze if the number of fragments after the collision is more than about three or four; but nevertheless, the total momentum of the system before and after the explosion is identical.

Note that if the object is initially motionless, then the system (which is just the object) has no momentum and no kinetic energy. After the explosion, the net momentum of all the pieces of the object must sum to zero (since the momentum of this closed system cannot change). However, the system will have a great deal of kinetic energy after the explosion, although it had none before. Thus, we see that, although the momentum of the system is conserved in an explosion, the kinetic energy of the system most definitely is not; it increases. This interaction—one object becoming many, with an increase of kinetic energy of the system—is called an explosion.

Where does the energy come from? Does conservation of energy still hold? Yes; some form of potential energy is converted to kinetic energy. In the case of gunpowder burning and pushing out a bullet, chemical potential energy is converted to kinetic energy of the bullet, and of the recoiling gun. For a bow and arrow, it is elastic potential energy in the bowstring.


The second possibility is the reverse: that two or more objects collide with each other and stick together, thus (after the collision) forming one single composite object. The total mass of this composite object is the sum of the masses of the original objects, and the new single object moves with a velocity dictated by the conservation of momentum. However, it turns out again that, although the total momentum of the system of objects remains constant, the kinetic energy doesn’t; but this time, the kinetic energy decreases. This type of collision is called inelastic.

Any collision where the objects stick together will result in the maximum loss of kinetic energy (i.e., KfKf will be a minimum).

Such a collision is called perfectly inelastic. In the extreme case, multiple objects collide, stick together, and remain motionless after the collision. Since the objects are all motionless after the collision, the final kinetic energy is also zero; therefore, the loss of kinetic energy is a maximum.

  • If 0<Kf<Ki0<Kf<Ki, the collision is inelastic.
  • If KfKf is the lowest energy, or the energy lost by both objects is the most, the collision is perfectly inelastic (objects stick together).
  • If Kf=KiKf=Ki, the collision is elastic.


The extreme case on the other end is if two or more objects approach each other, collide, and bounce off each other, moving away from each other at the same relative speed at which they approached each other. In this case, the total kinetic energy of the system is conserved. Such an interaction is called elastic.

Problem-Solving Strategy


A closed system always conserves momentum; it might also conserve kinetic energy, but very often it doesn’t. Energy-momentum problems confined to a plane (as ours are) usually have two unknowns. Generally, this approach works well:

  1. Define a closed system.
  2. Write down the expression for conservation of momentum.
  3. If kinetic energy is conserved, write down the expression for conservation of kinetic energy; if not, write down the expression for the change of kinetic energy.
  4. You now have two equations in two unknowns, which you solve by standard methods.

Example 9.10

Formation of a Deuteron

A proton (mass 1.67×10−27kg1.67×10−27kg) collides with a neutron (with essentially the same mass as the proton) to form a particle called a deuteron. What is the velocity of the deuteron if it is formed from a proton moving with velocity 7.0×106m/s7.0×106m/s to the left and a neutron moving with velocity 4.0×106m/s4.0×106m/s to the right?9.4 Types of Collisions - University Physics Volume 1 | OpenStax (1)


Define the system to be the two particles. This is a collision, so we should first identify what kind. Since we are told the two particles form a single particle after the collision, this means that the collision is perfectly inelastic. Thus, kinetic energy is not conserved, but momentum is. Thus, we use conservation of momentum to determine the final velocity of the system.


Treat the two particles as having identical masses M. Use the subscripts p, n, and d for proton, neutron, and deuteron, respectively. This is a one-dimensional problem, so we have


The masses divide out:


The velocity is thus vd=(1.5×106m/s)i^vd=(1.5×106m/s)i^.


This is essentially how particle colliders like the Large Hadron Collider work: They accelerate particles up to very high speeds (large momenta), but in opposite directions. This maximizes the creation of so-called “daughter particles.”

Example 9.11

Ice Hockey 2

(This is a variation of an earlier example.)

Two ice hockey pucks of different masses are on a flat, horizontal hockey rink. The red puck has a mass of 15 grams, and is motionless; the blue puck has a mass of 12 grams, and is moving at 2.5 m/s to the left. It collides with the motionless red puck (Figure 9.20). If the collision is perfectly elastic, what are the final velocities of the two pucks?

9.4 Types of Collisions - University Physics Volume 1 | OpenStax (2)

Figure 9.20 Two different hockey pucks colliding. The top diagram shows the pucks the instant before the collision, and the bottom diagram show the pucks the instant after the collision. The net external force is zero.


We’re told that we have two colliding objects, and we’re told their masses and initial velocities; we’re asked for both final velocities. Conservation of momentum seems like a good strategy; define the system to be the two pucks. There is no friction, so we have a closed system. We have two unknowns (the two final velocities), but only one equation. The comment about the collision being perfectly elastic is the clue; it suggests that kinetic energy is also conserved in this collision. That gives us our second equation.

The initial momentum and initial kinetic energy of the system resides entirely and only in the second puck (the blue one); the collision transfers some of this momentum and energy to the first puck.


Conservation of momentum, in this case, reads


Conservation of kinetic energy reads


There are our two equations in two unknowns. The algebra is tedious but not terribly difficult; you definitely should work it through. The solution is


Substituting with the given numbers where a positive direction is to the left, we obtain



Notice that after the collision, the blue puck is moving to the right; its direction of motion was reversed. The red puck is now moving to the left.

Check Your Understanding 9.7

There is a possible mathematical second to the system of equations solved in this example (because the energy equation is quadratic): v1,f=0,v2,f=−2.5m/sv1,f=0,v2,f=−2.5m/s. This solution is unacceptable on physical grounds; what’s wrong with it?

Example 9.12

Thor vs. Iron Man

The 2012 movie “The Avengers” has a scene where Iron Man and Thor fight. At the beginning of the fight, Thor throws his hammer at Iron Man, hitting him and throwing him slightly up into the air and against a small tree, which breaks. From the video, Iron Man is standing still when the hammer hits him. The distance between Thor and Iron Man is approximately 10 m, and the hammer takes about 1 s to reach Iron Man after Thor releases it. The tree is about 2 m behind Iron Man, which he hits in about 0.75 s. Also from the video, Iron Man’s trajectory to the tree is very close to horizontal. Assuming Iron Man’s total mass is 200 kg:

  1. Estimate the mass of Thor’s hammer
  2. Estimate how much kinetic energy was lost in this collision


After the collision, Thor’s hammer is in contact with Iron Man for the entire time, so this is a perfectly inelastic collision. Thus, with the correct choice of a closed system, we expect momentum is conserved, but not kinetic energy. We use the given numbers to estimate the initial momentum, the initial kinetic energy, and the final kinetic energy. Because this is a one-dimensional problem, we can go directly to the scalar form of the equations.


  1. First, we posit conservation of momentum. For that, we need a closed system. The choice here is the system (hammer + Iron Man), from the time of collision to the moment just before Iron Man and the hammer hit the tree. Let:
    • MH=MH= mass of the hammer
    • MI=MI= mass of Iron Man
    • vH=vH= velocity of the hammer before hitting Iron Man
    • v == combined velocity of Iron Man + hammer after the collision

    Again, Iron Man’s initial velocity was zero. Conservation of momentum here reads:


    We are asked to find the mass of the hammer, so we have


    Considering the uncertainties in our estimates, this should be expressed with just one significant figure; thus, MH=7×101kgMH=7×101kg.
  2. The initial kinetic energy of the system, like the initial momentum, is all in the hammer:


    After the collision,


    Thus, there was a loss of 3500J960J=2540J3500J960J=2540J.


From other scenes in the movie, Thor apparently can control the hammer’s velocity with his mind. It is possible, therefore, that he mentally causes the hammer to maintain its initial velocity of 10 m/s while Iron Man is being driven backward toward the tree. If so, this would represent an external force on our system, so it would not be closed. Thor’s mental control of his hammer is beyond the scope of this book, however.

Example 9.13

Analyzing a Car Crash

At a stoplight, a large truck (3000 kg) collides with a motionless small car (1200 kg). The truck comes to an instantaneous stop; the car slides straight ahead, coming to a stop after sliding 10 meters. The measured coefficient of friction between the car’s tires and the road was 0.62. How fast was the truck moving at the moment of impact?


At first it may seem we don’t have enough information to solve this problem. Although we know the initial speed of the car, we don’t know the speed of the truck (indeed, that’s what we’re asked to find), so we don’t know the initial momentum of the system. Similarly, we know the final speed of the truck, but not the speed of the car immediately after impact. The fact that the car eventually slid to a speed of zero doesn’t help with the final momentum, since an external friction force caused that. Nor can we calculate an impulse, since we don’t know the collision time, or the amount of time the car slid before stopping. A useful strategy is to impose a restriction on the analysis.

Suppose we define a system consisting of just the truck and the car. The momentum of this system isn’t conserved, because of the friction between the car and the road. But if we could find the speed of the car the instant after impact—before friction had any measurable effect on the car—then we could consider the momentum of the system to be conserved, with that restriction.

Can we find the final speed of the car? Yes; we invoke the work-energy theorem.


First, define some variables. Let:

  • McandMTMcandMT be the masses of the car and truck, respectively
  • vT,iandvT,fvT,iandvT,f be the velocities of the truck before and after the collision, respectively
  • vc,iandvc,fvc,iandvc,f Z be the velocities of the car before and after the collision, respectively
  • KiandKfKiandKf be the kinetic energies of the car immediately after the collision, and after the car has stopped sliding (so Kf=0Kf=0).
  • d be the distance the car slides after the collision before eventually coming to a stop.

Since we actually want the initial speed of the truck, and since the truck is not part of the work-energy calculation, let’s start with conservation of momentum. For the car + truck system, conservation of momentum reads


Since the car’s initial velocity was zero, as was the truck’s final velocity, this simplifies to


So now we need the car’s speed immediately after impact. Recall that






The work is done over the distance the car slides, which we’ve called d. Equating:


Friction is the force on the car that does the work to stop the sliding. With a level road, the friction force is


Since the angle between the directions of the friction force vector and the displacement d is 180°180°, and cos(180°)=–1,cos(180°)=–1, we have


(Notice that the car’s mass divides out; evidently the mass of the car doesn’t matter.)

Solving for the car’s speed immediately after the collision gives


Substituting the given numbers:


Now we can calculate the initial speed of the truck:



This is an example of the type of analysis done by investigators of major car accidents. A great deal of legal and financial consequences depend on an accurate analysis and calculation of momentum and energy.

Check Your Understanding 9.8

Suppose there had been no friction (the collision happened on ice); that would make μkμk zero, and thus vc,f=2μkgd=0vc,f=2μkgd=0, which is obviously wrong. What is the mistake in this conclusion?

Subatomic Collisions and Momentum

Conservation of momentum is crucial to our understanding of atomic and subatomic particles because much of what we know about these particles comes from collision experiments.

At the beginning of the twentieth century, there was considerable interest in, and debate about, the structure of the atom. It was known that atoms contain two types of electrically charged particles: negatively charged electrons and positively charged protons. (The existence of an electrically neutral particle was suspected, but would not be confirmed until 1932.) The question was, how were these particles arranged in the atom? Were they distributed uniformly throughout the volume of the atom (as J.J. Thomson proposed), or arranged at the corners of regular polygons (which was Gilbert Lewis’ model), or rings of negative charge that surround the positively charged nucleus—rather like the planetary rings surrounding Saturn (as suggested by Hantaro Nagaoka), or something else?

The New Zealand physicist Ernest Rutherford (along with the German physicist Hans Geiger and the British physicist Ernest Marsden) performed the crucial experiment in 1909. They bombarded a thin sheet of gold foil with a beam of high-energy (that is, high-speed) alpha-particles (the nucleus of a helium atom). The alpha-particles collided with the gold atoms, and their subsequent velocities were detected and analyzed, using conservation of momentum and conservation of energy.

If the charges of the gold atoms were distributed uniformly (per Thomson), then the alpha-particles should collide with them and nearly all would be deflected through many angles, all small; the Nagaoka model would produce a similar result. If the atoms were arranged as regular polygons (Lewis), the alpha-particles would deflect at a relatively small number of angles.

What actually happened is that nearly none of the alpha-particles were deflected. Those that were, were deflected at large angles, some close to 180°180°—those alpha-particles reversed direction completely (Figure 9.21). None of the existing atomic models could explain this. Eventually, Rutherford developed a model of the atom that was much closer to what we now have—again, using conservation of momentum and energy as his starting point.

9.4 Types of Collisions - University Physics Volume 1 | OpenStax (3)

Figure 9.21 The Thomson and Rutherford models of the atom. The Thomson model predicted that nearly all of the incident alpha-particles would be scattered and at small angles. Rutherford and Geiger found that nearly none of the alpha particles were scattered, but those few that were deflected did so through very large angles. The results of Rutherford’s experiments were inconsistent with the Thomson model. Rutherford used conservation of momentum and energy to develop a new, and better model of the atom—the nuclear model.

9.4 Types of Collisions - University Physics Volume 1 | OpenStax (2024)


What are the types of collisions in physics? ›

There are two types of collisions: Inelastic collisions: momentum is conserved, Elastic collisions: momentum is conserved and kinetic energy is conserved.

What are the 4 types of collisions? ›

Types of Collisions
  • Elastic collisions: both momentum as well as kinetic energy are conserved.
  • Inelastic collisions: only momentum is conserved.
  • Perfectly inelastic collisions: The kinetic energy is lost, resulting in the colliding objects to stick to one another after the collision.
  • Head-on collision and oblique collision.

What is collision in physics class 9? ›

A collision is an event in which two or more objects exert forces on each other for a short interval of time.

What are 5 examples of collision? ›

collision, also called impact, in physics, the sudden, forceful coming together in direct contact of two bodies, such as, for example, two billiard balls, a golf club and a ball, a hammer and a nail head, two railroad cars when being coupled together, or a falling object and a floor.

How many collisions are there? ›

The three collisions that happen in a car accident are vehicle collision, human collision, and internal collision. Knowing these three types of collisions and their related dangers helps to understand where and how injury occurs. Collisions follow a sequence, and each can lead to different and substantial injuries.

What are 3 stages of a collision? ›

What you might not have realized, however, is that within every collision, there are three stages that take place: the vehicle collision, human collision, and internal collision.

What is collision in physics? ›

Any interaction between particles, aggregates of particles, or rigid bodies in which they come near enough to exert a mutual influence, generally with exchange of energy.

What are the types of collision with examples? ›

Types of collision
ParameterPerfectly elastic collisionInelastic collision
ExampleThe collision between atomic particles.The collision between two vehicles on a road.
3 more rows
Jul 29, 2021

How do you find collisions in physics? ›

What is the formula of collision? From the conservation of momentum, the formula during a collision is given by: m1v1 + m2v2 = m1v'1 + m2v'2.

What is a collision quizlet? ›

Collision. A situation in which two objects in close contact exchange energy and momentum. Momentum. the force an object has because of its motion; equals mass x velocity.

What are elastic and Inelastic collisions? ›

A state where there is no net loss in kinetic energy in the system as the result of the collision is called an elastic collision. Inelastic collisions. A type of collision where this is a loss of kinetic energy is called an inelastic collision.

Which of Newton's laws is collision? ›

Newton's third law of motion is naturally applied to collisions between two objects. In a collision between two objects, both objects experience forces that are equal in magnitude and opposite in direction. Such forces often cause one object to speed up (gain momentum) and the other object to slow down (lose momentum).

What force is collision? ›

Consider the situation where two bodies collide with each other. During the collision, each body exerts a force on the other. This force is called an impulsive force, because it acts for a short period of time compared to the whole motion of the objects, and its value is usually large.

What is the most common collision physics? ›

Partially inelastic collisions are the most common form of collisions in the real world. In this type of collision, the objects involved in the collisions do not stick, but some kinetic energy is still lost. Friction, sound and heat are some ways the kinetic energy can be lost through partial inelastic collisions.

What are 3 examples of elastic collisions? ›

  • When we throw a ball on the floor, it bounces back. This is an example of elastic collision where both momentum and kinetic energy are conserved.
  • The collision between the atoms is also an example of elastic collision.
  • The collision between two biliard balls is an example of elastic collision.

Are there 3 collisions in every crash? ›

There Are Three Collisions

There are actually three collisions in every crash: the vehicle collision; the human collision; and the internal collision (inside your body).

What is simple collision? ›

A simple collision is a collision mesh that uses basic shapes, such as boxes, spheres, capsules, and convex shapes, to define the bounds of our object.

What is the biggest collision? ›

The wave was caused by a collision between two huge black holes in a deep corner of space. Today, astronomers have announced it is officially the biggest collision ever detected, forming a black hole 150 times more massive than the sun.

Where are most collisions? ›

Parking lots are arguably the place where most low-speed collisions occur. Common parking lot accidents include vehicles backing up into each other, vehicles backing up and getting clipped by passing vehicles, vehicles sideswiping other vehicles as they park, etc.

How common are collisions? ›

Car accidents are a fact of life. In 2020, a total of 35,766 fatal car accidents occurred on roadways across the United States. Another 1,593,390 crashes resulted in injuries and 3,621,681 caused property damage. That means a total of 5,250,837 collisions happened over the course of a single year.

What is collision grade 4? ›

COLLISION DEFINITION. A collision happens when one object runs into another. When objects collide, the energy transfers from one object to the other.

What are 3 the most common cause of a collision? ›

The Six Most Common Causes of Collisions
  1. Distracted Driving. Distracted driving is the most common cause of motor vehicle accidents in the United States. ...
  2. Speeding. ...
  3. Driving Under the Influence of Alcohol and Drugs. ...
  4. Aggressive Driving. ...
  5. Falling Asleep Behind the Wheel. ...
  6. Adverse Weather Conditions.

What are the 3 forces of impact in a collision? ›

The three types of impact that occur (in succession) are those involving the vehicle, the body of the vehicle occupant, and the organs within the body of the occupant.

What are the most common collisions? ›

Rear-End Collisions: the Most Common Type of Accident

As their name suggests, rear-end collisions occur when one vehicle strikes the back of another vehicle, says the NHTSA.

How to find momentum? ›

p = m v . p = m v . You can see from the equation that momentum is directly proportional to the object's mass (m) and velocity (v). Therefore, the greater an object's mass or the greater its velocity, the greater its momentum. A large, fast-moving object has greater momentum than a smaller, slower object.

Why are collisions important in physics? ›

Physicists use collisions to determine the properties of atomic and subatomic particles. Essentially, a particle accelerator is a device that provides a controlled collision process between subatomic particles so that, among other things, some of the properties of the target particle can be studied.

What determines a collision? ›

If objects stick together, then a collision is perfectly inelastic. When objects don't stick together, we can figure out the type of collision by finding the initial kinetic energy and comparing it with the final kinetic energy. If the kinetic energy is the same, then the collision is elastic.

What energy is in collisions physics? ›

The total kinetic energy before the collision is equal to the total kinetic energy after the collision. A collision in which total system kinetic energy is conserved is known as an elastic collision.

What do you call a collision? ›

Some common synonyms of collision are concussion, impact, and shock. While all these words mean "a forceful, even violent contact between two or more things," collision implies the coming together of two or more things with such force that both or all are damaged or their progress is severely impeded.

How to calculate kinetic energy? ›

Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared.

What is 1 example of elastic collision? ›

Elastic Collision Examples

When a ball at a billiard table hits another ball, it is an example of elastic collision. When you throw a ball on the ground and it bounces back to your hand, there is no net change in the kinetic energy, and hence, it is an elastic collision.

What happens to kinetic energy in a collision? ›

The total kinetic energy before the collision is not equal to the total kinetic energy after the collision. A large portion of the kinetic energy is converted to other forms of energy such as sound energy and thermal energy.

What type of energy is lost in a collision? ›

An inelastic collision is a collision in which there is a loss of kinetic energy. While 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.

How do you find net force? ›

Net force is the sum of all forces acting on an object. The net force can be calculated using Newton's second law, which states that F = ma, where: F is the net force. m is the mass of the object.

Do all objects bend in a collision? ›

We figure out: All solid objects bend or change shape in a collision and when other contact forces are applied to them.

What is the law of inertia? ›

Newton's First Law of Motion (Inertia) An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.

What is the law of impulse? ›

The impulse-momentum theorem states that the impulse applied to an object will be equal to the change in its momentum. Δ→tF=m(vf)−m(vi)

How do you find impulse after collision? ›

The impulse experienced by the object equals the change in momentum of the object. In equation form, F • t = m • Δ v. In a collision, objects experience an impulse; the impulse causes and is equal to the change in momentum.

What is a perfect collision physics? ›

A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision.

Which type of collision is very rare? ›

The sum of this is equal to the product of the final velocity of the two objects with the sum of their masses. The other type of collision is an elastic collision. During elastic collisions, no heat is generated. This is why elastic collisions are extremely rare.

Which collision is most damaging? ›

Head-On Collisions

One of the most dangerous types of car accidents is a head-on collision. Because these crashes involve the full force of both vehicles colliding head-on, they have the potential to cause significant damage and even death.

What are the 3 types of collisions? ›

There are three types of collisions as follows:
  • Perfectly elastic collision.
  • Inelastic collision.
  • Perfectly inelastic collision.

What are the 3 types of collisions that occur in a crash? ›

There are actually three collisions in every crash: the vehicle collision; the human collision; and the internal collision (inside your body).

What are the 2 types of collisions? ›

There are two types of collisions between two bodies - 1) Head-on collisions or one-dimensional collisions - where the velocity of each body just before impact is along the line of impact, and 2) Non-head-on collisions, oblique collisions or two-dimensional collisions - where the velocity of each body just before ...

What are the most common types of collisions? ›

The 5 Most Common Types of Car Crashes
  • Rear-End Collisions. When you follow too closely behind another car or the other driver suddenly stops, you may end up rear-ending the other car. ...
  • Single Vehicle Crashes. ...
  • T-Bone or Cross-Traffic Accidents. ...
  • Clipping Other Cars When Merging. ...
  • Low Speed Accidents.
Apr 19, 2023

What is third collision? ›

The Third Collision: Internal Collision

This collision happens when the internal organs of the occupants collide with each other or with the bony structures of the body. During this collision, the kinetic energy of the impact is transferred to the body's organs, causing them to move and collide with each other.

What are the 4 major causes of vehicle collisions? ›

Common Causes of Vehicle Collisions

Unsafe speed. Driver distractions. Driving on the wrong side of the road. Improper turns.

What is the #2 cause of collisions? ›

Factor 2: Speeding

Speeding is one of the leading causes of accidents and fatalities on roads worldwide. It's important always to drive at an appropriate speed for the road conditions and the drivers around you.

What is a 2 body collision? ›

In physics, an elastic collision is an encounter (collision) between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy.

How do you determine the type of collision? ›

If objects stick together, then a collision is perfectly inelastic. When objects don't stick together, we can figure out the type of collision by finding the initial kinetic energy and comparing it with the final kinetic energy. If the kinetic energy is the same, then the collision is elastic.

How do collisions work? ›

In a collision between two objects, both objects experience forces that are equal in magnitude and opposite in direction. Such forces often cause one object to speed up (gain momentum) and the other object to slow down (lose momentum).


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