[Physics Class Notes] on Elastic and Inelastic Collisions Pdf for Exam

You might have come across the word “collision” in our day-to-day life. It has a significant role in physics as well. It is a phenomenon that appears when one moving object is contacting violently with the other object. Does the collision develop two different questions? Whether it is elastic or inelastic? A perfectly elastic collision can be elaborated as one in which the loss of kinetic energy is null. An inelastic collision can be pressed as one in which the kinetic energy is transformed into some other energy form while the collision takes place. If two or more hard spheres collide, it may be nearly elastic. That’s why; it is used to measure the limiting case of an elastic collision. The assumption about conservation of the kinetic energy as well as conservation of momentum appears possible in the valuation of the final velocities of two-body collisions. Before moving to the topic ‘Elastic collision’, students should learn about ‘Elasticity’

Elasticity :

Elasticity is the property of deformable bodies to oppose the distorting effect and come back to the original shape and size when the force is removed from that body.

Materials like steel, aluminium, rubber, wood, crystals are elastic etc. The value of elasticity is directly proportional to the amount of force a body can handle without breaking or permanent change in shape.

Elasticity depends on the following factors :

• Temperature – Heating or an increase in temperature decreases the elasticity of the material.

• Impurities in the material – The impurity decides the increase or decrease in elasticity of the material.

• Annealing leads to a decrease in the material’s elasticity.

• The elasticity of a material can also be increased by treating the material by processes like hammering and rolling.

Elastic Collisions

In this type of collision, both conservations of kinetic energy, and conservation of momentum are noticed. This signifies that there is no dissipative force acting during the collision, which results in the kinetic energy of the objects prior to the collision, and is not altered after the collision. Macroscopic objects, when it comes into a collision, there is some energy dissipation. They are never truly elastic. The collision between two hard steel balls is hardly elastic as in swinging balls apparatus. It is also proved that collision within ideal gases is very close to elastic collision, and the fact is implemented in the development of the theories for gas pressure confined inside a container.

Elastic And Inelastic Collisions Equations

Elastic Collision Formula

An elastic collision occurs when both the Kinetic energy (KE) and momentum (p) are conserved. If we explain in other words, it will be;

KE = [frac{1}{2}] mv²

We can write;

[frac{1}{2}] m₂(₁)²+ [frac{1}{2}] m₂(v₂)² = [frac{1}{2}] m₁(v₁₁)²+ [frac{1}{2}]  m₂(V₂)²

Thus, we can observe that the final KE of both bodies are equivalent to the initial KE of these two bodies. As we know that momentum p = Linear momentum = mv, we can also write as;

m₁v₁,i + m₂V₂,i = M₁ V₁f +M₂V₂,f

Where,

KE = Kinetic energy

P = Momentum

m1 = Mass of the first object

m2 = Mass of the second object

v = Velocity (m/s)

vi = Initial velocity

vf = Final velocity

v1 = Velocity of first object

v2 = Velocity of the second object

Inelastic Collision Formula

When two objects collide with each other under inelastic conditions, the final velocity of the object can be obtained as;

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)

Partially Elastic Collision

Many elements will come under this category. These elements have both dissipated elastic and inelastic collisions. Some examples in real life will rectify the doubts. Practically, all collisions are partially elastic and partially inelastic as well. For instance, collisions of billiard balls are almost perfectly elastic, but there is still some short of energy loss. On the other hand, a bullet being shot into a target covering itself would be more inelastic, since the final velocity of a bullet, and the target must be at the same.

Three Types Of Collisions

The total momentum of all the objects in an isolated system remained the same when the momentum of individual objects changed during collisions. Collisions may be categorized into several categories; some of them are easier to calculate than others;

• Elastic Collisions – It consists of objects which depart after the collision. The elasticity of objects are not altered after the interaction. Some examples are; billiard balls, ping pong balls, and other hard objects.

Elastic and Inelastic Collisions Examples

Elastic Collisions Examples

• The collision between atoms.

• The collision between two billiard balls.

• The bounced back ball when thrown to floor.

Inelastic Collisions Examples

• The accident between two cars or any other vehicles.

• When a soft mud ball is thrown against the wall, it will stick to the wall.

• A ball falling from a certain altitude and unable to return to its original bounce.

• A vehicle hitting a pole.

What Happens in a Head-on Collision?

When two cars, driving in opposite directions collide with each other, it is called a head-on collision. It is some sort of mistake, such as one driver is driving the car in the wrong direction of the road. It is also known as one dimensional collision. This may also happen due to drunk and drive, distracted driving, or brake failure.

What Happens in a Non head-on Collision?

In this collision, the collision angle between 2 bodies of equal mass is seen to be 90°. This type of collision has a good use in billiards. The spot placed on the pool table sends the ball to one corner pocket whereas the cue ball to another corner pocket.

In a non head-on collision, total momentum of the system is always conserved.