Elastic and Inelastic Collisions

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You might have come across the word “collision” in our day-to-day life. It has a significant role in physics as well. It is a phenomenon that appears when one moving object is contacting violently with the other object.

Does the collision develop two different questions? Whether it is elastic or inelastic?

A perfectly elastic collision can be elaborated as one in which the loss of kinetic energy is null.

An inelastic collision can be pressed as one in which the kinetic energy is transformed into some other energy form while the collision takes place.

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If two or more hard spheres collide, it may be nearly elastic. That’s why; it is used to measure the limiting case of an elastic collision. The assumption about conservation of the kinetic energy as well as conservation of momentum appears possible in the valuation of the final velocities of two-body collisions.

Elastic Collisions

In this type of collision, both conservations of kinetic energy, and conservation of momentum are noticed. This signifies that there is no dissipative force acting during the collision, which results in the kinetic energy of the objects prior to the collision, and is not altered after the collision.

Macroscopic objects, when it comes into a collision, there is some energy dissipation. They are never truly elastic. The collision between two hard steel balls is hardly elastic as in swinging balls apparatus.

It is also proved that collision within ideal gases is very close to elastic collision, and the fact is implemented in the development of the theories for gas pressure confined inside a container.

Elastic And Inelastic Collisions Equations

  1. Elastic Collision Formula

An elastic collision occurs when both the Kinetic energy (KE) and momentum (p) are conserved.

If we explain in other words, it will be;

KE = ½ mv2

We can write;

1/2 m1(v1i)2+ 1/2 m2(v2i)2 =1/2m1(v1f)2+ 1/2 m2(v2f)2

Thus, we can observe that the final KE of both bodies are equivalent to the initial KE of these two bodies.

As we know that momentum p = Linear momentum = mv, we can also write as;

m1v1i+m2v2i = m1v1f+m2v2f


KE = Kinetic energy

P = Momentum

m1 = Mass of the first object

m2 = Mass of the second object

v = Velocity (m/s)

vi = Initial velocity

vf = Final velocity

v1 = Velocity of first object

v2 = Velocity of the second object

  1. Inelastic Collision Formula

When two objects collide with each other under inelastic condition, the final velocity of the object can be obtained as;

V = (M1V1+M2V2)(M1+M2)


V= Final velocity of the object

M1= Mass of the first object (kg)

M2= Mass of the second object (kg)

V1 = Initial velocity of the first object (m/s)

V2 = Initial velocity of the second object (m/s)

Partially Elastic Collision

Many elements will come under this category. These elements have both dissipated elastic and inelastic collisions. Some examples in real life will rectify the doubts.

Practically, all collisions are partially elastic and partially inelastic as well.

For instance, collisions of billiard balls are almost perfectly elastic, but there is still some short of energy loss.

On the other hand, a bullet being shot into a target covering itself would be more inelastic, since the final velocity of a bullet, and the target must be at the same.

Three Types Of Collisions

The total momentum of all the objects in an isolated system remained the same when the momentum of individual objects changed during collisions.

Collisions may be categorized into several categories; some of them are easier to calculate than others;

  • Complete Inelastic Collision – It includes objects which will stick together afterward. Kinetic energy conservation has failed. It is quite easy to calculate the result using the conservation of momentum.

  • Partially Inelastic Collision – It involves objects which cut apart after their collision, but deformations appear in some ways by the point of interaction.

  • Elastic Collisions – It consists of objects which depart after the collision. The elasticity of objects are not altered after the interaction. Some examples are; billiard balls, ping pong balls, and other hard objects.

Elastic and Inelastic Collisions Examples

  1. Elastic Collisions Examples

  • The collision between atoms

  • The collision between two billiard balls

  • The bounced back ball when thrown to floor

  1. Inelastic Collisions Examples

  • The accident between two cars or any other vehicles

  • When a soft mud ball is thrown against the wall, it will stick to the wall.

  • A ball falling from a certain altitude and unable to return to its original bounce

  • A vehicle hitting a pole

What Happens in a Head on Collision?

When two cars, driving in opposite directions collide with each other, is called a head on collision. It is some sort of mistake, such as one driver is driving the car in the wrong direction of the road.

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This may also happen due to drunk and drive, distracted driving, or brake failure.

FAQ (Frequently Asked Questions)

1. A Ball Of Mass 0.4kg Traveling At A Velocity 5m/S Collides With Another Ball Having Mass 0.3kg, Which is At Rest. Find Out The Final Velocity Of The First Ball Using The Equation For The Conservation Of Kinetic Energy in An Elastic Collision?

Data given in the question

Mass of the first ball, m1 = 0.4 kg

Mass of the second ball, m2 = 0.3 kg

The initial velocity of the first ball, v1x = 5 m/s

Though the second ball is at rest, so its initial velocity v2x= 0m/s

So, the final velocity of the first ball v1y =0

We know the formula;

½ m1 (v1x)2 + ½ m2 (v2x)2 = ½ m1(v1y)2 + ½ m2(v2y)2

½(0.4kg)(5m/s)2 + ½ (0.3kg)(0) = 1/2(0.4)(0)+1/2(0.3)(v2y)2

(0.2 * 25) = (0.3/2)(v2y)2

v2y2 = 5 * (2/0.3) =14.68

v2y = 14.68 = 3.83 m/s

2. Why is There A Loss Of Kinetic Energy in Inelastic Collisions?

In an inelastic collision, there is a huge chance of loss of kinetic energy. The conservation of the momentum of the system is possible in an inelastic collision. Kinetic energy conservation failed in this collision. This happens because the kinetic energy is transferred into some other form of energy.

3. The Crash Of Two Cars Is Elastic or Not. Explain?

We know that the conservation of kinetic energy is not maintained. The kinetic energy is transformed into sound energy, heat energy, and deformation of the objects. An elastic collision happens when two objects collide and bounce back to its initial place. So, the collision of two cars is not elastic rather, inelastic.

4. Is There Any Possibility to Conduct Perfectly Elastic Collisions?

No, it is impossible. It is only possible in subatomic particles. In this type of collision, the objects stick together after impact.