# Introduction

The difference between elastic and inelastic collision mainly depends upon the kinetic energy. In simple words, in an elastic collision, no loss of kinetic energy occurs whereas, in an inelastic collision, the loss of kinetic energy occurs.

• When two objects come near each other, a force affects them for a short period, causing a change in their velocities, momentum, and energies based on conservation laws. This is called a collision between two objects.
• In a collision between two objects, both objects experience forces equal in magnitude and opposite in direction. When objects collide, energy transfers from one object to another.
• In physics, unlike in everyday life, collision, the two bodies need not necessarily have physical contact. Deviation (scattering) of Alpha-particles by the atomic nucleus is a collision process with no physical contact.
• Physicists use collisions to determine the properties of atomic and subatomic particles.  Collision, as a process, is of paramount importance in atomic and nuclear physics, Where the colliding bodies are microparticles which may be atoms, nuclei, and various elementary particles, including photons.

## Definition of collision

An event in which two or more objects come in direct contact with each other with some force for a short interval of time and keep the total momentum conserved is called a collision.

Example: a collision of two cars, the collision of two billiard balls, throwing a ball on the ground.

## Types of collision

Generally, there are two types of collision.

1. Elastic collision

2. Inelastic collision.

### 1. Elastic collision

#### A collision where the kinetic energy of the particles before the collision and after the collision is the same, then this type of collision is known as an elastic collision.

In an elastic collision, the particles before and after the collision are the same.

Example:

(1) Atomic particles like (electrons, protons, and Alpha-particle) collide with each other. There is no loss of energy after the collision, this is an example of a perfectly elastic collision.

(2) Swinging balls.

(3) When a ball at a billiard table hits another ball, the collision of billiard balls is nearly elastic because the kinetic energy is conserved before and after the collision.

(4) When you throw a ball on the ground and it bounces back to your hand, it is also an elastic collision.

### 2. Inelastic collision

A collision in which the kinetic energy of the particles before the collision and after the collision are different means there may be a loss or gain in kinetic energy due to the collision, then this type of collision is known as an inelastic collision.

The lost kinetic energy is transformed into thermal energy, sound energy, and material deformation.

In inelastic collisions, the particles before collision are the same as those after the collision.

Example:

(1) Collision between two cars.

(2) A bat striking a baseball.

(3) A bullet embeds itself in a wooden door.

(4)A hammer and a nail head.

## Difference between elastic collision and inelastic collision

### Inelastic collision

The total kinetic energy of the particle before the collision and after the collision is the same.  That is the kinetic energy is conserved in this type of collision. The total kinetic energy of the particle before the collision and after the collision is different.
All of the forces involved in this are non-conservative in nature. All of the forces involved in the inelastic collision are conservative in nature.
No conversion of energy occurred. Kinetic energy is changed into other energy like sound energy and thermal energy.
Examples of this collision are rarely seen in our daily life. This collision is commonly seen in our daily life.

### Example 1

When a ball is dropped to the ground, and it rebounds at the same speed at which it hit the ground, then this is an example of elastic collision. So here no energy is lost during collision. The kinetic energy in this process remains conserved.  For this reason, we can consider it an elastic collision.

Now when we dropped this ball again to the ground at the same speed as earlier but it bounced back with a reduced speed, then we can consider it an inelastic collision.  The kinetic energy in this process changed because in this process the ball reduces its energy during a collision.

(Kinetic energy is the energy that an object possesses due to its motion. It is a scalar quantity.)

• Since, in elastic and inelastic collisions, the interacting particles are isolated, no external force or torque is acting on the collision system. So, in all the processes, the conservation of linear and angular momentum holds
• However, in an inelastic collision, the kinetic energy is changed after the collision; but the total energy (kinetic, potential, and others) of the collision system remains to conserve

## The equation for elastic and inelastic collision

Let two particles of masses m1 and m2 move with infinite velocities u1 and u2 respectively before collision in an inertial frame. The velocities of the particles after the collision become infinite v1 and v2 respectively. If there is no external force acting, the total linear momentum of the particle is conserved.

Therefore,          m1u12+ m2u22 = m1v12 + m2v2

for both elastic and inelastic collisions.

In an elastic collision, the kinetic energies also remain unchanged; they are conserved in the collision process.

So, 1/2 m1u1+ 1/2m2 u2 = 1/2m1v1 + 1/2m2v22

In an inelastic collision, however, there may be an increase or a decrease in kinetic energy. In simple words, if the kinetic energy is increasing in the inelastic collision process, we call it endoergic collision.

So, 1/2 m1u1+ 1/2m2 u2 = 1/2m1v1 + 1/2m2v22 + Q

Here, Q is the excitation energy.

If the kinetic energy is decreasing in the inelastic collision process, we call it exoergic collision.

So,    1/2 m1u1+ 1/2m2 u2 + Q = 1/2m1v1 + 1/2m2v22

## What is excitation energy?

The energy is needed to take the atom from its ground state to an excited state. The atoms may absorb a part of kinetic energy or discharge a part of kinetic energy during the collision process.

## Types of inelastic collision

### Endoergic Collision

In an inelastic collision, microscopic particles (atoms, molecules) absorb some part of kinetic energy for the transition state to excited states. As a result, there is a reduction in kinetic energy. Such collisions in which the final kinetic energy is less than the initial kinetic energy are called endoergic collisions.

### Exoergic collision

In an inelastic collision, if however, the atoms are already in the excited state and after the collision, they come down to the normal ground state, then the excitation energy is added to the final kinetic energy.

As a result, there is an addition in the kinetic energy. Such a collision in which the final kinetic energy is more than the initial kinetic energy is called an exoergic collision.

## Difference between perfectly elastic collision and elastic collision

A perfectly elastic collision is only a rare part of elastic collision. In an elastic collision two particles collide with each other with some negligible change in the kinetic energy which we do not consider as a change of total kinetic energy, whereas in a perfectly elastic collision when two particles collide with each other, there is absolutely no change in kinetic energy during a collision. That is nearly impossible in the real physical world. A perfectly elastic collision is only possible in particle physics.

Perfectly inelastic collision-A collision is called perfectly inelastic if the colliding particles or bodies permanently stick together and the loss of kinetic energy is a maximum, consistent with the law of conservation of momentum.

In such a collision, kinetic energy is lost by bonding the two bodies together.

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

## Q&A

### 1. Why is perfectly elastic collision not possible in the physical world?

A perfectly elastic collision cannot be possible in the real world because at least a small amount of energy is lost whenever two bodies collide with each other

### 2. How is collision impact measured?

A collision impact is measured by dividing kinetic energy by distance.

### 3. What is the difference between Inelastic collision and perfectly inelastic collision?

1. In a perfectly inelastic collision, the particles stick together after the collision but in an inelastic collision, the particles do not stick together and move separately.
2. In a perfectly inelastic collision, the maximum kinetic energy is lost but in an inelastic collision, neither the kinetic energy is conserved nor the loss of kinetic energy is maximum.

Written By: Sumita Banerjee