Elastic and inelastic collision

Introduction

Collision may be defined as the short duration interaction between two or more than two bodies simultaneously leading to change in motion of bodies due to internal forces acting on them. They can be elastic or inelastic, depending on momentum and kinetic energy conservation. A collision is an elastic collision if it conserves both momentum and kinetic energy. The collision is said to be inelastic if it conserves momentum only. Some basic terms essential to understanding the concept of collision are:

• Kinetic energy Momentum – It is defined as the energy possessed by an object due to its motions
• Momentum – It can be defined as the dot product of the mass and velocity of an object
• Force – It is a physical quantity that defines the ability to pull, push, accelerate or twist a body, whose SI unit is Newton (N)
• Dimension – It is defined as the spatial arrangement of an object in context to a particular direction such as height, width, depth, or breadth, it is also often referred to as the degree of freedom

Elastic Collision

When there is no net loss of kinetic energy after the collision of two bodies, such a collision is called an elastic collision. In such a case, both the momentum and the Kinetic energy remain conserved. Generally, in the case of collision of two bodies, the Kinetic energy before and after the collision remains the same, i.e., not converted to another form of energy. But in the case of elastic collision, the kinetic energy before and after the collision remains the same, but perfect elastic collision is not possible, so there is always some conversion of energy, which may be very small. It can be either one-dimensional or two-dimensional.

Examples of elastic collision:

1. Consider an example of billiard balls: When a billiard ball strikes another ball, it shows a perfect example of elastic collision.
2. While we throw a ball on the ground, it comes back to us after bouncing. This is also an example of elastic collision. However, there is no net change in the kinetic energy.

Elastic Collision Formula:

The elastic collision formula in mathematics can be written as m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ Where, m₁ = Mass of the first body m₂ = Mass of the second body u₁ = Initial velocity of the first body u₂ = The Initial velocity of the second body v₁ = The final velocity of the first body v₂ = The final velocity of a second body The formula of elastic collision for the kinetic energy is given as; ½ m₁u₁² + ½ m₂u₂² = ½ m₁v₁² + ½ m₂v₂² This formula can calculate the mass or velocity of elastic bodies.

Properties of elastic collision:

1. The time of collision affects the amount of force that objects experience in a collision. The greater the time, the smaller the force on the object. So to maximize the force, the collision time must be reduced.
2. Similarly, to minimise the force, the time must be increased. A real-world example is the airbags in the car, the airbags increase the collision time and reduce the effect of force on the object.

Inelastic Collision

It is a type of collision which involves the loss of Kinetic energy during the collision. This lost kinetic energy is converted into sound, thermal or material deformation. In a perfectly inelastic collision, the colliding particles stick together.

The formula of Inelastic collision:

When two bodies collide in an inelastic collision, the final velocity of the object is given by; V = (M₁V₁) + (M₂V₂) / (M₁+ M₂), where V is the final velocity, M₁ is the mass of object 1 (in kg) M₂ is the mass of object 2 (in kg) V₁ is the velocity of object 1 (in m/s) and V₂ is the velocity of object 2 (in m/s)

Example of inelastic collision:

Some daily life examples in which inelastic collision is observed are listed below –

• A car that hits the tree
• When subjected to drop from a certain height, a ball does not rise back to its original height
• When a mud ball is thrown on a wall, it gets stuck

Difference between elastic and inelastic collision:

• In an elastic collision, the total kinetic energy remains conserved, whereas, in an inelastic collision, the total kinetic energy at the starting and ending of the collision is different
• In the case of an elastic collision, no energy conversion occurs, whereas, in an inelastic collision, the energy is converted into heat or sound
• Pure elastic collisions never exist in the real world, whereas inelastic collisions are normal
• An example of elastic collision: Spacecraft flying near a planet is never affected by gravitational forces
• An example of an inelastic collision: A collision of two cars

Conclusion:

A collision results from friction between two objects that are touching each other. The collision is always elastic or inelastic. There is no loss in kinetic energy in the elastic collision, whereas the inelastic collision involves the loss of kinetic energy of the system. The perfectly elastic collision does not exist in the real world as there is always some energy exchange, however, up to a small extent. The collision can exist in one dimension, or it can be two-dimensional.