*When each of the systems remains the same after the collision as it was before, it is known as an elastic collision.*

**The definition of the elastic collision itself exclaims that the kinetic energy** **and the momentum of a body are conserved after the collision. This means that the kinetic energy and momentum will be identical before and after the collision.**

This article will try to answer the question ‘Is Kinetic Energy Conserved in an Elastic Collision?’ by understanding why and when it is conserved.

To recognize the difference between kinetic energy and potential energy, let us look at their definitions.

**Kinetic Energy** – it is the energy that a body has when it is in motion.

**Potential Energy** – it is the energy that a body has when it is at rest. It is also known as stored energy.

**Why is Kinetic Energy Conserved in an Elastic Collision?**

In an elastic collision, there is no disfigurement in the colliding objects.

**If two objects collide and are distorted invariably, it is known as an Inelastic Collision.** **But, if the objects return to their original shape and size, the deformation is known as Elastic Collision.**

In an elastic collision, the deformation occurs just for a fraction of seconds while the objects are colliding as soon as the collision is over, the objects reform into their natural shape and size.

No collision is 100% elastic. There is a little energy lost in any way. But, this loss is exceptionally minor that it can be neglected. Ideal elastic collisions only exist in theories.

For example, suppose two balls of mass M_{1} and M_{2} travel towards each other with velocities U_{1} and U_{2}, respectively. They strike and rebound in a different direction with velocities V_{1} and V_{2}, respectively. No loss of energy has been observed in this reaction.

If one reactant losses its momentum or kinetic energy, the other object would gain the same amount of momentum or kinetic energy. Thus, the total amount of kinetic energy and momentum of the system will remain as it is, and therefore, it is said that the kinetic energy and momentum is conserved.

Not only is kinetic energy conserved in an elastic collision, but momentum is also conserved in this reaction.

Therefore, the equation for the conservation of momentum is given as:

**M _{1}U_{1} + M_{2}U_{2} = M_{1}V_{1} + M_{2}V**

_{2}

There are various reasons why the ball bounces back. One main reason can be the material of the ball. A rubber ball will rebound more than a metal ball. So the effect of collision depends on the material of the colliding substance.

When the collision occurs, the kinetic energy is converted into potential energy, but that is for a very brief moment and instantly turns back into kinetic energy. Therefore, if asked ‘Is kinetic energy conserved in an elastic collision?’, its answer would be yes, with the above explanation.

**Read more on** **15+ uses of kinetic energy**.

**Is Kinetic Energy Conserved in a Perfectly Elastic Collision?**

Perfectly elastic collision only exists in theories, and it is generally not observed in our day- to- day life.

**When we talk about “perfect” elastic collision, one should remember that it does not exist because a minimal amount of energy is lost to the surrounding. But, this energy is so small and thus has no significant effect on the collision and therefore, it is disregarded.**

A change in movement is experienced by the body when a collision eventuates. If the objects are of the same size and shape, say two objects are colliding, and both are of the same weight and both move with the same velocity. Then, there are chances of this collision to be a perfectly elastic collision if there is no external force applied to it.

When the objects collide, the kinetic energy starts to decrease slowly, and simultaneously, the potential energy increases gradually. In a perfectly elastic collision, this potential energy will completely be recovered into kinetic energy when the collision ends.

When a collision occurs, the objects are compressed and sometimes deformed. But, in perfectly elastic collisions, the objects regain their original shape and size as soon as the collision ends, producing no sound or heat. One can also say that the reformation is 100% in perfectly elastic collisions.

To conclude the answer to the question ‘Is kinetic energy conserved in an elastic collision?’, we can say that the kinetic energy is conserved in the perfectly elastic collision in the same manner as it is conserved in the simple elastic collision.

**Is Kinetic Energy always Conserved in an Elastic Collision?**

The momentum and kinetic energy are preserved at all times in the occurrence of an elastic collision.

**If momentum and kinetic energy are not conserved in an elastic collision, it would simply become an inelastic collision.**

Therefore, the answer to the question ‘Is kinetic energy conserved in an elastic collision?’ is that the conservation of kinetic energy and elastic collision go hand- in- hand. If kinetic energy is conserved, then indeed it is an elastic collision, and if an elastic collision occurs, kinetic energy is definitely conserved.

**Read more on Is Net Force a Vector.**

**Is Kinetic Energy only Conserved in an Elastic Collision?**

In addition to kinetic energy, momentum is also preserved in an elastic collision.

**Momentum is always conserved in a collision till an exterior force is applied. As an outcome, kinetic energy, as well as momentum, is conserved consistently in the occurrence of an elastic collision**.

The following example can explain the proof for the conservation of momentum.

Consider a 4 kg ball thrown at 50 km/ hr velocity towards a 50 kg girl standing still (at rest).

The momentum of the ball before the collision is = mv = 4 x 50 = 200 kg. km/ hr.

The momentum of the girl before collision is = mv = 50 x 0 = 0 kg. km/ hr.

Therefore, the total momentum of the system before the collision = **200 + 0 = 200 kg. km/ hr**.

Now, the velocity of the ball and the girl after the collision is unknown.

Thus, the momentum of the ball after the collision = mv = 4 kg x v = 4v

And the momentum of the girl after the collision = mv = 50 kg x v = 50 v

So, the total momentum of the system after the collision = **50 x 4 = 200 kg km/ hr**

So, there might be internal changes in the magnitudes, but the system’s total momentum before and after the collision is the same.

Therefore, it culminates that the momentum of the system is conserved.

Along with the elastic collisions, the system’s momentum is conserved for inelastic collisions as well. There is a change in the conservation of kinetic energy only. If the kinetic energy is conserved, then it is an elastic collision, and if there is a change in kinetic energy, then it is an inelastic collision.

**How to Find Kinetic Energy after Elastic Collision?**

One can find is kinetic energy conserved in an elastic collision by the formula described below.

We know that the equation for the conservation of momentum is given as:

M_{1}U_{1} + M_{2}U_{2} = M_{1}V_{1} + M_{2}V_{2} – eq. A

And the equation for kinetic energy is: =(1/2)mv^{2}

Thus, the equation for the conservation of kinetic energy can be given as:

(1/2) M_{1}U_{1}^{2 }+ (1/2) M_{2}U_{2}^{2 }= (1/2) M_{1}V_{1}^{2} + (1/2) M_{2}V_{2}^{2} – eq. B

This gives an equation that consists of two unknown quantities. Now, for finding these quantities, we need to simplify the equation.

Once we rearrange the quantities in eq. B, we can cancel out 1/2 and subsequently, we get

M_{1}U_{1}^{2 }+ M_{2}U_{2}^{2 }= M_{1}V_{1}^{2} + M_{2}V_{2}^{2}

M_{1}U_{1}^{2 }– M_{1}V_{1}^{2} = M_{2}V_{2}^{2 }– M_{2}U_{2}^{2}

M_{1 }(U_{1}^{2 }– V_{1}^{2}) = M_{2 }(V_{2}^{2 }– U_{2}^{2}) – eq. C

With the help of factoring binomials theorem eq. C can be written as:

M_{1 }(U_{1}– V_{1}) (U_{1}+ V_{1}) = M_{2 }(V_{2}– U_{2}) (V_{2}+ U_{2}) – eq. D

Again, (U_{1}+ V_{1}) and (V_{2}+ U_{2}) cancel out each other as they are the same quantities but on different sides of the equation. Thus, eq. D is now written as:

M_{1 }(U_{1}– V_{1}) = M_{2 }(V_{2}– U_{2}) – eq. E

With the help of eq. E, it is now easy to find the unknown quantities by simply rearranging the equation.

For Finding U_{1}

For finding V_{1 }

For finding U_{2 }

For finding V_{2}

In such a way, the initial and final velocities of the body can be found out, with the help of which, one can further find the kinetic energy of the system.

Once all the quantities are recognised, one can equate these quantities to identify is kinetic energy conserved in an elastic collision or not. Suppose the quantities on the left- hand side are equal to the quantities on the right- hand side, then it can be confirmed that the kinetic energy is conserved, and it is an elastic collision.

If the sum of quantities on the left- hand side are not equal the sum of quantities on the right- hand side, then the kinetic energy is not conserved, and the collision is inelastic.

Another equation that can be used to find the velocities is:

Thus, by all these processes we are able to answer the question ‘Is Kinetic Energy Conserved in an Elastic Collision?’