Elastic Collision

Introduction

In a nutshell, when many objects of varying masses and speeds clash, their contact point is referred to as a collision. Moreover, Elastic Collision is just the collision in which both momentum and kinetic energy are retained. Unlike inelastic collision, no kinetic or heat is dissipated during such an event. Following the Elastic Collision, the items frequently become glued to each other. You don’t need to learn squeezed information; here’s an Elastic collision study material provided below.

What is Elastic Collision?

The term ‘Elastic Collisions’ refers to the instance where two bodies of any mass coming at any velocities collide, and a big chunk of kinetic energy is retained. An elastic collision is one among two primary classes of collisions. The other one is inelastic collision which is the converse of the elastic collision. Inelastic collision, the energy is drained or say released during a collision. Moreover, these collisions conserve momentum and take place in a closed system. Also, there are collisions called perfectly elastic & inelastic collisions where the entire energy is retained or drained instead of any particular amount.

Definition of Perfectly elastic collisions- Collisions where the entire energy is retained and no energy conversion is observed are called ‘Perfectly Elastic Collisions“. Moreover, the average momentum of both objects remains the same post-collision.

Elastic Collision Formula

The elastic collisions formula is primarily used to calculate the average final momentum of an object. If the average momentum is equal on both times, we can say that the momentum is conserved, which takes place in an elastic collision only. The formula for determining Elastic collision is given below:

Pi1 + Pi2 = Pf1 + Pf2

∴ Mi1 * Vi1 + Mi2 * Vi2 = Mf1 * Vf1 + Mf2* Vf2

With the above formulas, P stands for momentum, M stands for the mass of objects and V without subscripts stands for initial velocity or velocity before the collision of an object. Moreover, ‘i’ in subscripts represent the initial velocities and masses and F denotes final masses and velocities. 

Elastic Collisions Examples

• The collision between two atoms (they bounce after the collision and total energy is conserved)
• Collision of two shopping trolleys. (They bounce back and don’t stick)
• While playing pool, when two balls hit each other. (bounce can be observed and momentum gets preserved)
• A badminton racquet hitting the ball. (Bounce can be observed) 

Illustration

In a pool game, a cue ball with an initial velocity of 6 m/s collides with an 8-ball that is initially at rest. Its cue ball is 0.30 kilograms, whereas the 8-ball is 0.4 kilograms. Then what will be the final velocity of the cue ball if a final velocity of 8 balls is 4.4 m/s?

• Given, Vi1 = 6 m/s

• Vi2 = 0 m/s
• M1 = 0.30 Kg
• M2 = 0.40 Kg
• Vf2  = 4.4 m/s

To find, final velocity of cue ball or say Vf1. So, in order to determine the final velocity of Cue ball, let is implement the Elastic collision formula

=M1 . Vi1 + M2 . Vi2 = M1 . Vf1 + M2 . Vf2

= 0.30 . 6 + 0.40 . 0 = 0.30 . Vf1 + 0.40 . 4.4 m/s 

= 1.8 + 0 = 0.30 . Vf1 + 1.76 

∴ Vf1 = 1.8 – 1.76 / 0.30 

= 0.04 / 0.30

= 0.13 (Approx.)

How are Elastic and elastic collisions identified?

Three points recognise these collisions. The points are as follows-

• Effect on kinetic energy – When two objects are in motion, they carry specific kinetic energy within them. Though, when they collide, they have that energy preserved In them. When the elastic collision occurs, this energy is retained post-collision. Similarly, Inelastic collisions release this energy by converting it to thermal, potential or some other form of energy during a collision.
• Momentum- In physics, momentum is the product of an object’s mass and velocity. When the momentum is the same post-collision, the collision can be referred to as the elastic collision and vice versa.
• Effect of collision– The colliding objects often stuck with each other in Inelastic collisions. At the same time, they bounce back with the same momentum inelastic collision.

Conclusion

From all the above, we learned the crucial concept of Elastic collision. After discussing till now, we can say that collisions where the energy and momentum are conserved and where the objects do not stick are called elastic collisions. Moreover, in the case of inelastic collisions, the conservation of any kinetic energy doesn’t occur and so sound, heat or any other form of energy isn’t observed.