Elastic and Inelastic collisions – definition, facts, sample numerical problem

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Collisions are often classified according to whether the total kinetic energy changes during the collision and as per this classification collisions are of 2 types, Elastic collision, and Inelastic collision. Let’s find out their definitions, types, and examples.

Define elastic and inelastic collisions

An elastic collision is one in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision.

And Inelastic collision is one in which the total kinetic energy of the system is not the same before and after the collision; if the objects stick together after colliding, the collision is said to be completely inelastic.

State the basic difference between elastic and inelastic collisions

The basic difference between elastic and inelastic collisions is as follows:

  • An Elastic Collision is one in which both the kinetic energy and momentum of the system are conserved.
  • And an Inelastic Collision is a collision in which momentum is conserved but the total kinetic energy of the system is not the same before and after the collision. This lack of conservation of kinetic energy in inelastic collisions means that the forces between colliding objects may convert kinetic energy to other forms of energy, such as potential energy or thermal energy.

Give examples of Elastic collisions

Perfectly elastic collisions do not exist in everyday situations, but they do exist in the interactions between atoms and subatomic particles.

Almost-elastic collisions are seen in reality. (discussed under inelastic collisions in the next section)

Inelastic collisions – types and examples

Inelastic collisions can vary from almost elastic to perfectly inelastic.

Almost-elastic collision

Almost elastic collisions are those collisions where very little kinetic energy is transformed into other forms of energy. These collisions include those where little friction acts, for example between billiard balls. A collision between two billiard balls is almost elastic because very little of their kinetic energy is transformed into heat and sound energy.

Moderately-elastic collision

Collisions such as a bouncing basketball, a gymnast on a trampoline, and a tennis ball being hit are moderately elastic with about half the kinetic energy of the system being retained.

Perfectly Inelastic collision

Perfectly inelastic collisions are those in which the colliding bodies stick together after impact. Some car crashes, a collision between a meteorite and the Moon, and a collision involving two balls of plasticine would be perfectly inelastic. In these collisions, much, and sometimes all, of the initial kinetic energy of the system is lost.

Sample Numerical problem solving

Numerical Question] A car of mass 1000 kg traveling west at 20 m/s crashes into the rear of a stationary bus of mass 5000 kg. The vehicles lock together on impact.

a) What is their joint velocity immediately after the collision?

b) What is the total kinetic energy of the system before the collision?

c) What is the total kinetic energy of the system after the collision?

d) Is this an elastic or inelastic collision? Explain.

Solution:

a) Total initial momentum = 1000 x 20 Kgm/s = 20000 Kgm/s

Let the joint velocity after the collision is V. After the collision total mass = 1000 + 5000 = 6000 Kg
So, final momentum = 6000. V

Considering conservation of momentum, 20000 = 6000. V

=> V = 20/6 m/s = 3.33 m/s

b) total kinetic energy of the system before the collision = (1/2) 1000. 20^2 = 200000 Joule

c) total kinetic energy of the system after the collision = (1/2) 6000. (20/6)^2 = 33333.33 Joule

d) Here, conservation of Kinetic energy is not maintained. Hence, this collision is an inelastic collision.

Summary

In this post, we have discussed different types of collisions with their definitions, types, and examples. Also, we have added one sample numerical for the students and readers to solve.

Not only that, but you can also refer to our dedicated post on Numerical Problems based on collisions.

Also here is an interesting post that discusses the Relationship between Collisions and Newton’s Laws of motion.

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Elastic and Inelastic collisions – definition, facts, sample numerical problem
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