Key Differences Between Elastic and Inelastic Collisions
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 Explained
1. What is the fundamental difference between an elastic and an inelastic collision?
The fundamental difference lies in the conservation of kinetic energy. In an elastic collision, both total momentum and total kinetic energy of the system are conserved. In an inelastic collision, the total momentum of the system is conserved, but the total kinetic energy is not; some of it is converted into other forms of energy like heat, sound, or potential energy due to deformation.
2. How can you determine if a collision is elastic or inelastic using the coefficient of restitution?
The coefficient of restitution (e) is a key value used to classify collisions. It is the ratio of the final to initial relative velocity between two objects after they collide. You can determine the type of collision as follows:
- For a perfectly elastic collision, e = 1.
- For an inelastic collision, 0 ≤ e < 1.
- For a perfectly inelastic collision, e = 0, which means the objects stick together after impact.
3. In an inelastic collision, where does the 'lost' kinetic energy go?
The kinetic energy that is 'lost' is not actually destroyed but is transformed into other forms of energy. During an inelastic collision, this energy conversion can manifest as:
- Heat: Generated due to friction between the surfaces.
- Sound: The noise produced during the impact is a form of energy.
- Permanent Deformation: Energy is used to bend, break, or change the shape of the colliding objects, like a car crumpling in a crash.
4. Is a car crash an example of an elastic or inelastic collision? Explain why.
A car crash is a classic example of an inelastic collision. This is because a significant amount of kinetic energy is converted into other forms. The loud sound of the crash, the heat generated from twisting metal, and the permanent deformation (denting and crumpling) of the car bodies all represent a loss of kinetic energy from the system. Momentum is still conserved, but the kinetic energy is not.
5. What is a perfectly elastic collision, and are there any true examples in the real world?
A perfectly elastic collision is an idealised scenario where there is absolutely no loss of kinetic energy. While no macroscopic, everyday collision is perfectly elastic, this concept is an extremely useful approximation. The closest examples are found at the atomic and subatomic levels, such as the collisions between air molecules or subatomic particles in an accelerator. The collision of two billiard balls is often used as a close approximation in physics problems.
6. What defines a perfectly inelastic collision, and what is its most distinct feature?
A perfectly inelastic collision is one in which the maximum possible amount of kinetic energy is lost. Its most distinct feature is that the colliding objects stick together after the impact and move with a single, common final velocity. An example is a ball of wet clay thrown against a wall; it sticks to the wall instead of bouncing off.
7. How do one-dimensional and two-dimensional collisions differ in their analysis?
The primary difference is in the application of the conservation of momentum.
- In a one-dimensional (head-on) collision, all motion occurs along a single straight line. Therefore, momentum is conserved along that single axis.
- In a two-dimensional (oblique) collision, the objects move in a plane. To analyse this, momentum must be resolved into components and conserved independently along two perpendicular axes (e.g., x-axis and y-axis). This makes the calculation more complex.
8. If kinetic energy is lost in most real-world collisions, why is the concept of a perfectly elastic collision important in physics?
The concept of a perfectly elastic collision is crucial for several reasons. Firstly, it serves as a foundational theoretical model that simplifies complex interactions, making them easier to analyse and understand. Secondly, it provides a benchmark or an upper limit for energy and momentum transfer in scenarios. Lastly, it is a very accurate model for interactions at the atomic and subatomic levels, which are fundamental to chemistry and modern physics.
