## Collision

### Definition

A collision is an isolated event in which two or more colliding bodies exert relatively strong forces on each other for a relatively short time.

### Introduction

Generally, we say that collision occurs when two cars moving on road may strike each other accidently. Collision occurs between billiard balls in the game of billiards strike and collision occurs between gas atoms and molecules at room temperature. For the collision to take place, physical contact of bodies is not always necessary.

In case of Rutherford’s α-scattering experiment, the α-particles are scattered due to electrostatic interaction between the α-particles and the nucleus from a distance. There is no physical contact between the α-particle and the nucleus.

Two key rules regarding collision are

• Law of conservation of linear momentum
• Law of conservation of energy

Thus collision between two bodies may also be defined as natural interaction of the bodies for a short interval of time as a result of which the energy and momentum of the interacting bodies changes.

### Types of collisions

Collision between bodies is broadly categorized into two types:

• Elastic collisions
• Inelastic collisions

#### Elastic Collision

A collision in which linear momentum and kinetic energy, both are conserved is called elastic collision. For example, collision between two ivory balls.

Characteristic of an Elastic collision are:-

1. Linear momentum is conserved
2. Kinetic Energy is conserved.
3. Total Energy is conserved.
4. No part of mechanical energy is converted into any other form of energy like heat energy, should energy etc.
5. Forces involved during elastic collisions are conservative.

#### Inelastic collision

A collision in which only linear momentum  is conserved but kinetic energy is not conserved is called an inelastic collision. Most of the collisions in everyday life are inelastic in nature as there is always some definite loss of kinetic energy during collision. If two bodies stick to each other after colliding, the collision is said to be perfectly inelastic. For example, Mud ball thrown on the wall sticks to the wall.

Characteristics of an Inelastic collision are:-

1. Linear momentum is conserved.
2. Kinetic energy is not conserved.
3. Total energy is conserved
4. A part of mechanical energy is converted into other forms of energy like light, heat or sound energy.
5. Some or all forces involved in an inelastic collision may be non-conservative in nature.

Consider an example when a rubber ball from a height is dropped on floor and if a collision between ball and floor is elastic then there is no loss of kinetic energy and the ball will attain its original height after rebound. But we find that rebound height is shorter than actual height so we can say collision is inelastic. However, if we neglect the small loss of kinetic energy, we may approximate the collision as elastic.

### Coefficient of Restitution or Co-efficient of Resilience

All types of collision in practical, are neither perfectly elastic nor inelastic they are somewhat called semi–elastic collision. The degree of elasticity of a collision is determined by the term called coefficient of restitution or coefficient of resilience of the collision. The coefficient of restitution is defined as the ratio of the velocity of separation to the velocity of approach of the colliding bodies. It is denoted by ‘e’,

Where U1 and U2 are the initial velocities of two bodies before collision and V1 and V2 are their respective velocities after collision.
Case 1
For an elastic collision, e = 1

Setting e = 1 in equation (1) we get,

i.e. for an elastic collision the velocity of separation is equal to velocity of approach.

Case 2
For an inelastic collision, 0 < e < 1

Setting o < e < 1 in eq. (1), we have

In an inelastic collision, the two bodies possess a non–zero velocity of separation, which is always less than the velocity of approach.

Case 3
For perfectly inelastic collision, e = 0

Setting e = 0 in eq. (1) we have,

That is, in perfectly inelastic collision, the two bodies move with a common velocity or in other words, the two bodies stick together.