Introduction to an elastic and inelastic collision
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;
Complete Inelastic Collision – It includes objects which will stick together afterward. Kinetic energy conservation has failed. It is quite easy to calculate the result using the conservation of momentum.
Partially Inelastic Collision – It involves objects which cut apart after their collision, but deformations appear in some ways by the point of interaction.
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.
FAQs on Elastic and Inelastic Collisions
1. A Ball Of Mass 0.4kg Traveling At A Velocity 5m/S Collides With Another Ball Having Mass 0.3kg, Which is At Rest. Find Out The Final Velocity Of The First Ball Using The Equation For The Conservation Of Kinetic Energy in An Elastic Collision?
Data are given in the question
Mass of the first ball, m1 = 0.4 kg
Mass of the second ball, m2 = 0.3 kg
The initial velocity of the first ball, v1x = 5 m/s
Though the second ball is at rest, so its initial velocity v2x= 0m/s
So, the final velocity of the first ball v1y =0
We know the formula;
\[\frac{1}{2}\] M₁ (V₁x)² + \[\frac{1}{2}\] m₂ (V2x)² = \[\frac{1}{2}\] m₁(V₁y)² + \[\frac{1}{2}\] m₂(V2y)²
\[\frac{1}{2}\] (0.4kg)(5 \[\frac{m}{s}\] )2 + \[\frac{1}{2}\] (0.3kg)(0) = \[\frac{1}{2}\] (0.4)(0)+ \[\frac{1}{2}\] (0.3)(v2y)2
(0.2 * 25) = ( \[\frac{0.3}{2}\] )(v2y)2
v2y2 = 5 * ( \[\frac{2}{0.3}\] ) =14.68
v2y = 14.68 = 3.83 m/s
2. Why is There A Loss Of Kinetic Energy in Inelastic Collisions?
In an inelastic collision, there is a huge chance of loss of kinetic energy. The conservation of the momentum of the system is possible in an inelastic collision. Kinetic energy conservation failed in this collision. This happens because the kinetic energy is transferred into some other form of energy. Mainly, this kinetic energy is lost due to factors like friction, sound and heat. For example - when two blocks are strikes against each other, it produce
noise - here, kinetic energy is transferred in the form of sound.
Friction - this strike produces some energy or force known as friction. The production of this friction uses kinetic energy equivalent to the amount of friction produced.
3. The Crash Of Two Cars Is Elastic or Not. Explain?
We know that the conservation of kinetic energy is not maintained. The kinetic energy is transformed into sound energy, heat energy, and deformation of the objects. An elastic collision happens when two objects collide and bounce back to its initial place. So, the collision of two cars is not elastic rather, inelastic. Also, this crash between two cars will be two-dimensional collisions (Non head-on collisions). This is because the car (after crash) will break down after collision but the total system momentum will be conserved.
4. Is There Any Possibility to Conduct Perfectly Elastic Collisions?
For a collision to be termed as 'Perfectly Elastic Collisions', it must have no loss of kinetic energy, which is not possible in practical life. It is only possible in subatomic particles. In this type of collision, the objects stick together after impact. Therefore, we cannot experience Perfectly Elastic Collisions with the items we can see.
An example of perfectly elastic collision is the collision between atoms in gases . These atoms collide and the overall energy remains conserved.
5. Give examples of the following :
(i) Perfectly elastic collision
(ii) Perfectly inelastic collision
Perfectly elastic collision :
Perfectly elastic collision is not seen in everyday life but seen commonly on a microscopic level. During bouncing of electrically charged particles, no heat is generated when they collide.
The billiard ball game is also an example of perfectly elastic collision. Here, the collision of two billiard balls is perfectly elastic in nature.
When two lumps of clay collide, the collision is seen to be Perfectly elastic.
All the atomic collisions are termed as perfectly elastic collisions.
When we slam our fist in the wall, the collision taking place is a perfectly elastic collision.
Perfectly inelastic collision :
Suppose a ball is dropped from some height. It does not rise again to the original height it was dropped. This is the example of a perfectly inelastic collision. Due to the loss in kinetic energy, the bouncing of the ball didn't take place with the same energy.
When we throw a soft mudball to the wall, it sticks there but does not bounce back. This is also an example of inelastic collision with loss in kinetic energy. Along with that, friction is also produced during this process.
If a car hits a tree, it exerts pressure on car as well as the wall. This force is frictional in nature and is produced by loss of kinetic energy.
6. Describe the followings related to collision of bodies :
Kinetic energy
friction
Kinetic energy
Kinetic energy is the type of energy possessed due to the body's motion.
Kinetic energy is numerically defined as the amount of work needed for accelerating a body (from rest to a certain speed).
In the case of a rollercoaster, it reaches its maximum kinetic energy at the bottom of it's path. Whereas, its kinetic energy is minimum at the top of the moving path.
The kinetic energy of an object having mass equals to m and speed equals to v is ½ mv².
It plays an important role in determining the elastic collision of 2 or more objects.
Friction
It is a type of force between two sliding surfaces (which are acting upon each other).
The material of the sliding surfaces decides the amount of friction produced between them.
It is most commonly known to provide grip between two surfaces. The more grip between 2 surfaces, the more is the value of friction force.
With the help of frictional force, we are able to slide our shoes on the ground without slipping.
Rigid surfaces tend to exert more friction than smooth surfaces.
Friction is also helpful in the elastic collision concept.
With the help of vedantu's free PDF and course , students can understand the topic 'friction' in depth along with some FAQ.