Collision of Point Masses

The meeting of two or more point masses in split-second contact is a collision of point masses. The meeting could be due to excitation or the natural motion of the point masses. Collision may be defined as the short duration interaction between two or more than two point masses simultaneously leading to change in motion of point masses due to internal forces acting on them. They can be elastic or inelastic, depending on momentum and kinetic energy conservation. A collision of point masses is an elastic collision if it conserves kinetic energy as well as moment. The collision is said to be inelastic if it conserves momentum only. 

Types of collision of point masses

When two point masses collide and bounce off of each other with the same amount of kinetic energy before the collision, the collision is said to be elastic. An inelastic collision between two point masses is one in which the total kinetic energy of all point masses after the collision is significantly less than before.

Elastic Collision

When there is no net loss of kinetic energy after the collision of point masses, 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 point masses, the Kinetic energy before the collision 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 the collision 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.

collision of point masses examples:

• Consider an example of billiard balls: When a billiard ball strikes another ball, it shows a perfect example of elastic collision of point masses.
• 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 point mass

m2 = Mass of the second point mass

u1 = Initial velocity of the first point mass

u2 = The Initial velocity of the second point mass

v1 = The final velocity of the first point mass

v2 = The final velocity of a second point mass

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 point masses.

Properties of elastic collision:

• 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.
• 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.

The formula of Inelastic collision:

When two point masses 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 elastic and inelastic collisions. 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.