Elastic and Inelastic Collisions

Elastic and Inelastic Collisions

Introduction

We come across the term “collision” when we study science. This is because it has a significant role in physics. When one moving object collides powerfully with another entity, this phenomenon occurs.

Is there a chance that the collision will lead to  different questions? Like, is it elastic or inelastic? A completely elastic collision is just one with no kinetic energy loss. On the other hand, the kinetic energy of an inelastic collision is converted into a different sort of energy as the collision occurs. 

What is an Elastic Collision?

The term “elastic collision” refers to a collision that results in no net kinetic energy loss for the system. In elastic collisions, both momentum, and kinetic energy, are preserved. For example, assume that two similar trolleys are approaching each other at the same speed. They collide and bounce against one another at full speed. Because no energy has been lost, this collision is entirely elastic.

We don’t see examples of completely elastic collisions regularly. Perfectly elastic collisions include some atom-to-atom collisions in gases. However, there are some collision examples in mechanics in which the energy lost is minimal. Even if they are not fully elastic, these collisions can be termed elastic. Two examples are balls in Newton’s cradle or rigid billiard ball collisions.

Elastic Collisions Examples

• A collision occurs when two atoms collide. 
• When two billiard balls collide. 
• The ball bounced back when it was thrown to the ground.

Elastic Collision Formula

An elastic collision happens when both kinetic energy (KE) and momentum (p) are conserved.

Consider two particles that have mass m1 and m2 and their initial velocity is u1 and u2 respectively. These particles collide with each other and after collision their velocity is v1 and v2  respectively. 

As we know that Linear momentum p = mv

From momentum conservation, we can also write as;

m1u1+m2u2 = m1v1+m2v2

Kinetic energy formula is given as:

KE = 12mv2

From the conservation of kinetic energy

12m1(u1)2+ 12m2(u2)2 =12m1(v1)2+ 1 2 m2(v2)2

As a result, we can see that the ending KE of both bodies is the same as the beginning KE of these two bodies.

What is an Inelastic Collision?

An inelastic collision occurs when kinetic energy is lost during a collision. The system’s momentum is preserved in an inelastic collision, but the kinetic energy is not. Instead, it is due to transferring some kinetic energy to anything else. Thermal energy, sound energy, and material deformation are most likely to be responsible.

Assume two comparable trolleys are approaching each other. They collide, but because the trolleys are fitted with magnetic interconnects, they join together and become one connected mass due to the collision. Because a maximum amount of kinetic energy has been lost, this form of collision is perfectly inelastic. It does not always imply that the final kinetic energy is zero; momentum must be maintained.

Most collisions in the real world are fully elastic and completely inelastic. For example, depending on how stiff the ball is, a ball dropped from a height of h over a surface would generally bounce back to a height less than h. Collisions of this type are referred to as inelastic collisions.

Elastic Collisions Examples

• The accident between the vehicles

• If you throw a soft mud ball against the wall, it will stick to it.

• After falling from a certain height, a ball cannot return to its original bounce.

Inelastic Collision Formula

When two objects meet in an inelastic collision, the final velocity of the object can be calculated as follows:

V = (M1V1+M2V2)(M1+M2)

Where,

V= Final velocity of the object

M1= Mass of the first object (kg)

M2= Mass of the second object (kg)

V1 = Initial velocity of the first object (m/s)

V2 = Initial velocity of the second object (m/s)

Conclusion

If the kinetic energy is the same, the collision is elastic. If the kinetic energy varies, whether the components stick together or not, the collision is inelastic. Momentum is conserved in both cases for collisions with no external forces.