Is Mechanical Energy Conserved In An Inelastic Collision: Why, When And Detailed Facts and FAQs

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This article answers the question “is mechanical energy conserved in an inelastic collision?” Collisions are a very common part of our daily lives.

Collision does not necessarily mean two cars hitting each other someone getting hit by a car. Even a ball hitting bat is an example of collision. Although, not all collisions are same, they are different depending on various parameters. We will read further about collisions in this article.

What is a collision?

Collision is an event of two or more objects striking each other. Collisions can be of different types according to the angle of collision, final velocities of these objects etc.

Different types of collision commonly known are inelastic and elastic collision. We will study further about these types and their sub types in later sections of this article.

What are the types of collision?

Collisions can differ according to the angle of collision and final velocities of objects after collision. The different types of collision are-

  • Inelastic collision- A collision between two bodies is said to be inelastic when the momentum is conserved during the entire collision process. However, the kinetic energy is not conserved in this type of collision. The formula for inelastic collision is given below

m1v1i + m2v2i = (m1 + m2) vf

where,

m1 is the mass of first object

v1i is the initial velocity of first object

m2 is the mass of second object

v2i is the initial velocity of second object

vf is the combined final velocity of first and second object

is mechanical energy conserved in an inelastic collision
Image: Bouncing of a ball is an example of series of inelastic collisions

Image credits: MichaelMaggs Edit by Richard Bartz, Bouncing ball strobe edit, CC BY-SA 3.0

  • Elastic collision- A collision between two bodies is said to be elastic when both the momentum and kinetic energy is conserved during the entire process. The formula for elastic collision is given below-

m1v1i + m2v2i = m1v1f+ m2v2f

where,

m1 is the mass of first object

m2 is the mass of second object

v1i is the initial velocity of the first object

v2i is the initial velocity of the second object

v1f is the final velocity of the first object

vf2 is the final velocity of the second object

What is co efficient of restitution?

Co efficient of restitution can be defined as the ratio of final relative velocity after collision of the bodies to the final relative velocity before the collision of the two objects. It is denoted by e.

Mathematically, co efficient of restitution can be given as-

e = v2-v1/u1-u2

where

v2 is the final velocity of second object

v1 is the final velocity of first object

u2 is the initial velocity of second object

u1 is the initial velocity of first object

What is the significance of co efficient of restitution?

The co efficient of restitution helps us understand the types of collision taking place. Below is the list of values of co efficient of restitution and its meaning.

  • e=0: When the co efficient value s zero, we can say that the collision is perfectly inelastic. Entire kinetic energy is converted into other forms of energy mainly heat and deformation energy. 
  • 0<e<1: This means that the collision elastic (actual case).
  • e=1: This is a case of perfectly elastic collision. The conversion or dissipation of heat energy does not take place here. The objects will rebound back with the exact same velocity with which they approached.

In most common cases, the value of co efficient of restitution lies between 0 and 1.

Why is mechanical energy not conserved in inelastic collision?

In simple words, we can say that mechanical energy in an inelastic collision does not get conserved. This is so because the kinetic energy of the object after collision is dissipated into heat energy.

The heat energy is produced as a result of internal friction. Heat energy not being a type of mechanical energy, we can say that kinetic energy is not conserved during the event of inelastic collision and hence, mechanical energy is not conserved in an elastic collision.

Is total mechanical energy conserved in an inelastic collision?

Kinetic energy and potential energy together constitute what we known as mechanical energy. During an inelastic collision, some amount of mechanical energy is dissipated and converted to heat energy or some times this energy is used in deforming the object.

Hence we can say that total mechanical energy is not conserved during inelastic collision as the energy is converted in to some other form.

Where does mechanical energy go in an elastic collision?

We all know this fact about energy that it cannot never be created nor be destroyed. What we can do with energy is that we can only convert it from one from to another.

In inelastic collision, the kinetic energy reduces as it gets dissipated in to heat energy or gets used up in deforming the shape of body. So we can say that mechanical energy gets converted to heat energy or gets used up in deforming the object after collision.

What is perfectly inelastic collision?

When the object loses maximum or all of its kinetic energy, it can be said that it underwent a perfectly inelastic collision.

The value of e or co efficient of restitution for a perfectly inelastic collision is zero. This implies that kinetic energy after collision is zero. That means the kinetic energy is completely dissipated into heat or used up in deformation of shape of object.

Examples of inelastic collision

A collision can be said inelastic when we can see the value of kinetic energy decreasing after the collision.

Let us see some examples of inelastic collision. They are given below-

  • Mud ball thrown on wall- The mud ball sticks on the wall. The kinetic energy of the mud ball becomes zero. Entire energy is used up in deformation of the mud ball.
  • Cricketer hitting a ball– When a cricketer hits a ball, the kinetic energy of the ball may increase or decrease depending upon the impact of both.
  • Ball dropped from a height– A ball loses some energy after striking from the ground, it does not necessarily bounces back to same height. Thus we can say that some kinetic energy of the ball is lost implying it is an inelastic collision.
  • Striking of insect with car– When an insect strikes a car, there is no significant change in car’s velocity. But the insect’s velocity becomes equal to the car’s velocity. This is an example of perfectly inelastic collision.
  • Two people of different sizes running into each other– When two people of different sizes hit each other, the final kinetic energies of both people will be decreased as some amount of energy is used up in balancing themselves.
  • Mobile phone falling on the ground– When a mobile phone slips out of pocket and falls down, the phone does not bounce back to the same height as that of pocket. The kinetic energy is lost in cracking or breaking of phone. Hence it is an inelastic collision. Even the phone having soft covers don’t come back to same height because the soft covers absorb the impact.

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