Elastic Collision

Elastic Collision Definition:

An elastic collision is a collision in which there is no net loss in kinetic energy in the system due to the collision. Both momentum and kinetic energy are conserved in an elastic collision.

Basically in the case of elastic collision, the kinetic energy before and after the collision remains the same and is not converted to any other form of energy.

It can be either one-dimensional or two-dimensional. In the real world, perfectly elastic collision is impossible because there is bound to be some energy conversion, however small.

However, though there is no change in the linear momentum of the whole system, there is a change in the individual momenta of the involved components, which are equal and opposite in magnitude and cancel each other out and the initial energy is conserved.

Elastic Collision Examples

• When a ball at a billiard table hits another ball, it is an example of elastic collision.
• When you throw a ball on the ground and it bounces back to your hand, there is no net change in the kinetic energy, and hence, it is an elastic collision.

Read More: Kinetic Energy

Watch the video and learn more about collision

Elastic Collision Formula

The Elastic Collision formula of momentum is given by:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where,

• m₁ = Mass of 1st body
• m₂ = Mass of 2nd body
• u₁ =Initial velocity of 1st body
• u₂ = Initial velocity of the second body
• v₁ = Final velocity of the first body
• v₂ = Final velocity of the second body

The Elastic Collision formula of kinetic energy is given by:

(1/2) m₁u₁² + (1/2) m₂u₂² = (1/2) m₁v₁² + (1/2) m₂v₂²

Elastic Collision Example Problem

Two billiard balls collide. Ball 1 moves with a velocity of 6 m/s, and ball 2 is at rest. After the collision, ball 1 comes to a complete stop. What is the velocity of ball 2 after the collision? Is this collision elastic or inelastic? The mass of each ball is 0.20 kg.

Solution:
To find the velocity of ball 2, use a momentum table.

Objects	Momentum Before	Momentum After
Ball 1	0.20 kg × 6 m/s = 1.2	0
Ball 2	0	0.20 kg × v2
Total	1.2 kg × m/s	0.20 kg × v2

1.2 kg × m/s = 0.20 kg × v₂

v₂ =1.2 / 0.20 = 6 m/s

To determine whether the collision is elastic or inelastic, calculate the total kinetic energy of the system both before and after the collision.

Objects	KE Before (J)	KE After (J)
Ball 1	0.50 × 0.20 × 62 = 3.6	0
Ball 2	0	0.50 × 0.20 × 62 = 3.6
Total	3.6	3.6

Since the kinetic energy before the collision equals the kinetic energy after the collision (kinetic energy is conserved), this is an elastic collision.

Watch the video and learn about important problems in elastic collisions

Difference between Elastic and Inelastic Collision

Some key differences between inelastic and elastic collisions are given below in tabular format.

Elastic Collision	Inelastic Collision
The total kinetic energy is conserved.	The total kinetic energy of the bodies at the beginning and the end of the collision is different.
Momentum is conserved.	Momentum is conserved.
No conversion of energy takes place.	Kinetic energy is changed into other energy such as sound or heat energy.
Highly unlikely in the real world as there is almost always a change in energy.	This is the normal form of collision in the real world.
An example of this can be swinging balls or a spacecraft flying near a planet but not getting affected by its gravity in the end.	An example of an inelastic collision can be the collision of two cars.

Applications of Elastic Collision

• The collision time affects the amount of force an object experiences during a collision. The greater the collision time, the smaller the force acting upon the object. Thus, to maximize the force experienced by an object during a collision, the collision time must be decreased.
• Likewise, the collision time must be increased to minimise the force. There are several real-world applications of these phenomena. The airbags in automobiles increase the collapse time and minimize the effect of force on objects during a collision. Airbag accomplishes this by extending the time required to stop the momentum of the passenger and the driver.

Watch the video to learn about Coefficient-of-Restitution

Frequently Asked Questions – FAQs

Q1

What is Elastic Collision?

An elastic collision is a collision in which there is no net loss in kinetic energy in the system due to the collision.

Q2

Does Elastic Collision conserve momentum?

Momentum is conserved in an elastic collision.

Q3

What is an example of an elastic collision?

When you throw a ball on the ground, and it bounces back to your hand, there is no net change in the kinetic energy, and hence, it is an elastic collision.

Q4

What is the difference between elastic and inelastic collision?

Unlike the elastic collision, where the kinetic energy is conserved, the kinetic energy in an inelastic collision is not conserved. In an inelastic collision, the kinetic energy between the colliding bodies is different at the beginning and the end of the collision.

Q5

What are the applications of the elastic collision?

The airbags in automobiles increase the collapse time and minimize the effect of force on objects during a collision.

Q6

What is inelastic collision?

An inelastic collision is a type of collision where this is a loss of kinetic energy. The lost kinetic energy is transformed into thermal energy, sound energy, and material deformation.

Q7

State the law of conservation of linear momentum.

According to the law of conservation of linear momentum, if the net external force acting on a system of bodies is zero, then the system’s momentum remains constant.

Q8

Write some applications of conservation of linear momentum.

One of the applications of conservation of momentum is the launching of rockets. The rocket fuel burns are pushed the exhaust gases downwards, and the rocket gets pushed upwards. Motorboats also work on the same principle. They push the water backwards and get pushed forwards in reaction to conserving momentum.

Q9

What is elastic potential energy?

Elastic potential energy is energy stored as a result of applying a force to deform an elastic object. The energy is stored until the force is removed and the object springs back to its original shape, doing work in the process.

Q10

What is contact force?

A contact force is any force that requires contact to occur. If two surfaces are not in contact, they can’t exert a normal force on each other.

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