# Basic Physics Lesson-21: Kinetic Energy

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## Introduction

We have read about energy in an earlier article (lesson-8: Force and Energy) in this series of basic Physics articles and now we would be learning more about different kinds of energies and their forms that exist around us. It could be mechanical energy, chemical energy, heat energy, potential energy, kinetic energy, electrical energy, nuclear energy etc. One of the nomenclatures for energy that is associated with a moving body is called kinetic energy. When a body is moving it has a velocity and due to that, it possesses some energy. Have you ever considered from where it got that energy? It is simply the work done on this body and pushing it to move with some velocity. It means that some force was applied to the body to move it and the force was applied for some time so that it accelerates and moves with even a bigger velocity. That time it possesses the maximum kinetic energy. Once the force is removed it starts to decelerate and then stops after some time and its kinetic energy reduces to zero.

## Force applied and movement of a body

When we apply a force on a body at rest the depending on the applied force the body would try to move. If the force is not sufficient then it would remain at its place and we say that force was not effective in moving the body from its resting position. If we try to push a big boulder alone then it won't move but if 2-3 people push it then the combined force is enough to move it in the desired direction. Please note that the big boulder is kept on the ground and there will be some friction between it and the ground and we must give sufficient force or push to it so that not only the frictional force is neutralised but some force is applied on the boulder to move it so that it acquires a velocity and starts moving. Frictional forces are opposite to the applied forces and play a very vital role in the movement of the bodies.

If friction is less then it is easier to move the heavy objects like moving bodies on a glass or marble floor. When friction is more then it becomes difficult to move the bodies like on loose sand or rough terrain.

Now whatever be the situation if we apply a sufficient force on a body and keep it for a longer time then the body would not only move but will accelerate also as per the fundamental equation F = ma where F is the applied force, m is the mass of the body on that force is applied, and a is the acceleration produced in it due to the applied force.

## Kinetic energy

When we apply a force on a body and the body moves and attains some velocity then it is very clear and obvious that we have done some work on that body and answer to the question as to where that work done has gone is the energy that the body has acquired by virtue of its movement and acquired velocity and that is what is termed as kinetic energy. If this moving body then collides against another body then what will happen? The other body might also start moving with that push or simply vibrate and come back to its normal position or due to collision some heat might be created there due to that impact and these are all examples of conversion of energy from one form to another. The one that a body possesses because of its mass and velocity in the form of energy called kinetic energy and for a body of mass m moving with a velocity of v its kinetic energy is in a mathematical form defined as mv2/2.

## Unit of kinetic energy

The unit of kinetic energy is the same as that of the energy and in MKS (metre-kilogram-second) system that is the joule. One joule is defined as the work done by a one-newton force acting over a one-metre distance. In a classical CGS (centimetre-gram-second) system the unit of energy is erg. The conversion between joule and erg is given by 1 joule = 107 erg. So, the erg is a small unit of energy. Interestingly, a flying mosquito or a flying fruit fly has a kinetic energy of the order of 1 erg.

Exercise:

Let us calculate the kinetic energy of a car having a mass of 1200 kg and a velocity of 40 km/hour.

Using the formula for the kinetic energy and keeping everything in MKS units, we have -

m = 1200 kg

v = 40 km/hour = 11.1 metre/second

So kinetic energy = (1200 x 11.1 x 11.1)/2 = 73926 joule

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That is quite a good amount of energy roughly equal to 100 horsepower from a classical scoary British view!

## Relation of kinetic energy to other forms of energy

As we observed earlier that energy can be transformed from one form to another, so kinetic energy also has the same characteristics. For example, a toy kept on the roof of a building has got gravitational potential energy by virtue of its position at such a height from the surface of the Earth and there is a formula for it which is -

Potential energy = mgh

where m is its mass, h is the height of the building, and g is the acceleration due to gravity. What happens when we let the toy fall down from the rooftop to the ground? Its gravitational potential energy is simply changed to the kinetic energy that it attains while moving down. Interestingly when it reaches the ground level its gravitational potential energy becomes zero and whatever potential energy it had at the rooftop had already been converted to kinetic energy by the time it reaches the ground.

## Rotational kinetic energy

In the simple case when a body is moving in a straight line it has linear kinetic energy. What happens when a body is moving in a rotational motion that is rotating around an axis? Then we say that the body has rotational kinetic energy and that is given by its moment of inertia (I) and rotational velocity (angular velocity) (ω) and the formula is -

Rotational kinetic energy = (I ω2)/2

If a body is having a complex motion like rotational as well as linear then the total kinetic energy is the sum of the linear kinetic energy plus rotational kinetic energy.

## Conclusion

By virtue of its mass and velocity, a body has kinetic energy which is a form of energy acquired by that body from the forces working on it.

## Kinetic energy

1. https://www.britannica.com/science/kinetic-energy