Elastic Collision

Concept of Elastic Collision

This is an encounter of the two bodies where the kinetic energy between the bodies remains unchanged. What we can observe is that there is no net conversion of the kinetic energy into any other forms.

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy.

During the collision of small objects it is observed that  kinetic energy is first converted to potential energy associated with a repulsive or attractive force between the particles then this potential energy is converted back to kinetic energy (when the particles move with this force, i.e. the angle between the force and the relative velocity is acute). Collisions of atoms are elastic, for example, Rutherford backscattering. A useful special case of elastic collision is when the two bodies have equal mass, in which case they will simply exchange their momenta.

The molecules from atoms of a gas or liquid rarely experience perfectly elastic collisions because kinetic energy is exchanged between the molecules’ translational motion and their internal degrees of freedom with each collision. At some instant , half the collisions are, to a varying extent, inelastic collisions.

The  molecular collisions can be regarded as essentially elastic as long as Planck's law forbids energy from being carried away by black-body photons. In the case of macroscopic bodies, perfectly elastic collisions are an ideal never fully realized, but approximated by the interactions of objects such as billiard balls.

Collision, in simple terms, is when one moving object strikes a stationary body placed in its trajectory. Also, this term applies when two moving objects collide into one another, causing an instance of impact. 

However, if you are wondering what elastic collision is, you have to understand a bit more than simple collision and impact. Elastic collision is an event of a collision between one moving and a stationary body or two objects in motion where the total kinetic energy and momentum remain unaltered. 

What is Elastic Collision?

Definition 

An elastic collision is that collision where there is no  net loss in kinetic energy in the system as a result of the collision. Both momentum and kinetic energy are conserved quantities inelastic collisions.

For example if two similar trolleys are traveling toward each other with equal speed then it is observed that they  collide, bouncing off each other with no loss in speed. This collision is perfectly elastic because no energy has been lost.

A stationary object possesses potential energy, whereas a moving one converts potential energy into kinetic energy when in motion. Besides, momentum refers to motion in a moving body, which you get from the product of mass and velocity. 

Moreover, the elastic collision definition states that the overall kinetic energy and the momentum are preserved in case of this category of collision. The concept itself assumes that the colliding objects preserve energy, which hardly happens in real-life events. 

Therefore, elastic collision in physics refers to a standardized and hypothetical situation where the colliding bodies conserve their kinetic energies even after the event of a collision. 

What are the Examples of Elastic Collision? 

Now that you know what elastic collision is, you must move on to a few examples of this phenomenon. It will help you understand the real-life implications of elastic collision and enable you to relate to the events that happen around us.

Therefore, Elastic Collision Examples are as Follows – 

• If you drop a ball on the floor, it bounces back towards you instantly. In this event, the ball in motion preserves its overall momentum and kinetic energy, which is why it bounces back. 

• When two atomic particles collide into each other, they undergo an elastic collision. In case there is no loss of energy after contact, you can call it a perfectly elastic collision. 

These instances will certainly help you comprehend and define elastic collision even better. 

What is Inelastic Collision? 

As you have already understood the instances and types of elastic collisions, you must also understand what its counterpart or inelastic collision stands for. 

An inelastic collision is a category of collision among two moving objects, and these objects lose kinetic energy and momentum after contact. For instance, say that you drop a mound of clay on the ground or you witness a car crash. The mound of clay will not bounce back to you, or the car will not continue in its previous trajectory. 

It happens because neither of these objects will be able to preserve its initial kinetic energy and momentum after striking another surface. 

About the  Elastic and Inelastic Collision

An  elastic collision is defined as one in which there is no loss of kinetic energy in the collision. An inelastic collision is one in which the part of the kinetic energy is changed to some other form of energy in the collision. 

As a result any macroscopic collision between objects will convert some of the kinetic energy into internal energy and other forms of energy, so no large-scale impacts are perfectly elastic.

Momentum is conserved in inelastic collision and we cannot track the  kinetic energy as  some of it is converted to other forms of energy. Collisions in ideal gasses approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic.

Characteristics of an Elastic Collision

Characteristics of elastic collision are as follows:

•  In an elastic collision, the linear momentum of an object is conserved.

•   The total energy is of the object conserved.

• The system’s kinetic energy is also conserved.

•  Conservative forces are involved during an elastic collision.

•   The mechanical energy in an elastic collision is not converted into heat 

What is the Formula for Elastic Collision?

The elastic collision formula comprises two parts, namely elastic collision formula for kinetic energy and elastic collision for momentum. 

However, Follow the Table Below to Understand What each Component in the Equation Signifies –

Therefore, the formula for elastic collision kinetic energy is – 

\[ \frac{1}{2}m_{1}u_{1}^{2} + \frac{1}{2}m_{2}u_{2}^{2} = \frac{1}{2}m_{1}v_{1}^{2} + \frac{1}{2}m_{2}v_{2}^{2} \]

On the other hand, the elastic collision derivation for momentum is – 

m₁ u₁ + m₂ u₂ = m₁v₁ + m₂v₂

A fundamental way to make sure whether a collision is elastic or inelastic is by equating their total kinetic energy. In case it remains the same as before and after the said collision, you can label it as an elastic collision. Contrarily, a shift in the total kinetic energy suggests that the category of collision is inelastic. 

However, the energy loss for inelastic collision usually dissipates into sound and heat energy. It helps in maintaining the balance of energy before and after.

Now that you know what elastic collision is, you should go through related topics to understand more about this concept. Besides, you can also download the Vedantu app for an interactive and personalized learning experience.