The type of collision in which sum of the kinetic energy by both the bodies after a collision is equal to that of their collective kinetic energy prior to the encounter is an elastic collision. Elastic collision happens only when there would be no net conversion of the kinetic energy into others kinds. A perfectly elastic collision is one wherein there would be no loss of kinetic energy during the collision process. The elastic collision has properties such that its momentum conservation and kinetic energy are preserved.

If two elastic bodies having masses m1, m2 have their initial velocities as u1 and u2 approaching to collide with one another.

Formula

The Elastic Collision formula of momentum is given below

 

elastic collision formula for momentum

Where,

m1 is mass of 1st body

m2 is the mass of 2nd body

v1 is initial velocity of 1st body

v2 is the initial velocity of 2nd body

v1 is the final velocity of the 1st body

v2 is the final velocity of the 2nd body

Momentum Before Collision = Momentum After the Collision

The Kinetic Energy of Elastic Collision is given by

Elastic collision formula is used to find mass or velocity of elastic bodies

Solved Examples

Example 1: If the mass of the ball is 5 Kg and moving with a velocity of 12 m/s collides with a stationary ball of mass 7 kg and comes to rest. Calculate the velocity of the ball of mass 7 kg after collision.

Solution:

 Given,

Mass of 1st ball, m1 is 5 kg 

The initial velocity of the 1st ball, u1   is 12 m/s

The mass of the 2nd ball, m2 is 7 kg

The initial velocity of the second ball, u2 is 0

The final velocity of the 1st ball, v1 is 0

Final Velocity of the 2nd ball, v2 =?

Elastic Collision Formula is,

Example 2: A 10 Kg block moving with initial velocity of 12 m/s with 8 Kg wooden block moving toward the first block with a velocity of 4 m/s. The second body comes to rest after collision. Calculate the final velocity of the first body

Solution:

Given,

Mass of 1st ball, m1 is 10 kg

Initial Velocity of the first ball, u1 is 12 m/s

Mass of the 2nd ball, m2 is 8 kg

First ball initial velocity, u1 = 12 m/s

The initial velocity of the second ball, u2 is 4 m/s

 Final Velocity of 2nd ball, v2 is 0

The final Velocity of the first ball, v1 =?

The formula of the elastic collision is presented as,

(10 × 12) + (8 × 4 )= (10 × v1) + (8 × 0)

120 + 32 = 10 v1 + 0

152 = 10 v1

∴   v1 = 15.2 m/s