Collisions and Its types

• There are many examples of collisions occurring in our daily life.
• Some of the examples are:

1. A person walking with his head down may collide with another person walking against him.
2. A car or a vehicle may collide with another car or a vehicle in an accident.
3. The billiard balls collides each other in a billiard game.
4. The gas molecules contained in a box (or vessel) collides with each other and with the walls of the vessels.
5. Similarly, when two charge particles move towards each other, their paths are deviated.

• All of these events are called collisions.
• In fact, we may knowingly or unknowingly undergo collisions many times during our everyday activities.
• The collision takes place for very short period of time. During the collision, the colliding particles or bodies exchange their momentum and energy.
• Thus, the collision is the interaction between particles or bodies in which they exchange their momentum and energy in a short interval of time.
• A collision is said to occur if the particles or bodies come in physical contact with each other or if the path of particle is affected by other.

Types of collision

• On the basis of whether the kinetic energy is conserved or not, the collisions are divided into two types: elastic and inelastic collision.

a) Elastic collision

• The collisions in which both momentum and kinetic energy of the system remain constant are called elastic collisions.
• For example: the collisions between atomic and sub-atomic particles are elastic.

• In an elastic collision,

1. The momentum is conserved.
2.  The total energy of the system is conserved.
3. The kinetic energy of the system is conserved.
4. The forces involved in the collision are conservative.
5. No mechanical energy is converted into other form such as sound, light, heat, etc.

b) Inelastic collision

• The collisions in which the momentum of the system is conserved and kinetic energy is not conserved are called inelastic collisions.
• For example: the collisions between vehicles such as buses, cars, trucks, etc. are inelastic collisions.
• In inelastic collision,

1. The momentum is conserved.
2. Kinetic energy of the system is not conserved.
3. The total energy of the system is conserved.
4. Some part of the mechanical energy is converted into other forms such as heat, sound, light, etc.
5. The forces involved in the collision are non-conservative.

Perfectly Inelastic Collision

• It is a kind of inelastic collision in which two colliding particles or bodies stick together after the collision.
• After the collision, the two bodies move as a single unit and hence they have a common velocity.

Let two bodies, one body of mass m₁ and another of mass m₂ are moving in the same direction as in the figure.

The first body is moving with velocity u₁ and the second is moving with velocity u₂ where u₁is greater than u₂. After the collision, they stick together and move with velocity v.

The momentum of the system (two bodies) before collision is given by

Pi = m₁u₁ + m₂u₂

Similarly, the momentum of the system after collision is given by

Pf = (m₁ + m₂) v

Since the momentum is conserved, we have,

Pi = Pf

Or, m₁u₁ + m₂u₂ = (m₁ + m₂) v

∴ V = (m₁u₁ + m₂u₂) / (m₁ + m₂)

References: 

i) https://byjus.com/physics/elastic-collision/

ii) https://isaacphysics.org/concepts/cp_collisions?stage=all

Collisions and Its types