What is Elastic Collision | Civil Engineering Optional Notes for UPSC PDF Download

What is an Elastic Collision?

Elastic Collision Definition:

• An elastic collision is a collision where there is no net loss in kinetic energy in the system because of the collision. Both momentum and kinetic energy are conserved in an elastic collision.
• In an elastic collision, the kinetic energy before and after the collision remains unchanged and is not transformed into any other form of energy.
• Elastic collisions can be either one-dimensional or two-dimensional. In reality, achieving a perfectly elastic collision is unattainable due to some energy conversion, however minimal.
• While the linear momentum of the entire system remains constant, there is a shift in the individual momenta of the components involved, which are equal and opposite in magnitude, canceling each other out while conserving the initial energy.

The collision of billiard balls is nearly elastic because the kinetic energy is conserved before and after the collision

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.

Elastic Collision Formula

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

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.

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

Difference between Elastic and Inelastic Collision

• Applications of Elastic Collision

  • Effect of Collision Time on Force

    The duration of a collision plays a crucial role in determining the force exerted on an object. When the collision time is extended, the force acting on the object diminishes. On the contrary, reducing the collision time amplifies the force experienced by the object.

  • Real-World Application: Airbags in Automobiles

    One practical application of collision time manipulation is evident in the design of airbags in vehicles. Airbags are engineered to increase the duration of the collision, thereby reducing the impact force on the individuals involved in a crash. By elongating the time required to decelerate the passengers and drivers, airbags effectively mitigate the force exerted during a collision.