# 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 lessons on basic Physics and now we would be learning in this article about a form of the energy called as kinetic energy. It is the energy that is associated with a moving body and 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 by some force which had pushed 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 more time so that the body accelerates and moves with even a greater 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. While moving if it collides with another body then due to its energy it can damage or even move the other body which was earlier at rest. In such a case it would transfer some of its kinetic energy to the other body. With remaining energy it will move for some distance and eventually come to a rest.

## Force applied and movement of a body

When we apply a force on a body at rest then 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 act 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 heavy bodies on a glass or marble floor. When friction is more then it becomes difficult to move the bodies. For example it is difficult to move them on loose sand or rough terrain.

Now, whatever be the situation if we apply an adequate 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, and a is the acceleration produced in it due to the applied force.

So, under the force applied the body will acquire some velocity and if the force continues to be there then the velocity will further increase and it is obvious that the kinetic energy which is proportional to its velocity will also increase.

## 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 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. If the first body is able to move the second body then a part of the kinetic energy of the first body is transferred to the second body. In this process the first body loses a part of its kinetic energy while the second one which was at rest gains that much of kinetic energy.

The formula for kinetic energy that a body possesses because of its mass and velocity at a particular instant of time is given as -

Kinetic energy = mv2/2 where m is the mass and v is its velocity.

## 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 joule. One joule is defined as the work done by a one-newton force acting over a one-metre distance. In 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

That is quite a good amount of energy roughly equal to 100 horsepower from a classical British units of energy angle.

## 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 -

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Potential energy of the toy = 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.

When the toy comes to a stop where does its kinetic energy go? It is simply used up in the collision that it had with ground and the toy and the ground get some heat generated. Energy is never lost and we have to remember that it only changes its form from one form to other.

Electricity generators in big dams utilise the kinetic energy of falling water from a good height on the turbines of the electric generators to produce electricity. The continuously falling water on the turbine blades move them to give the desired rotation of coils in the generator.

## 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 in analogy to the formula for linear kinetic energy (mv2/2) the formula for rotational kinetic energy is -

Rotational kinetic energy = (I ω2)/2 (note that m has been replaced by I and v is replaced by ω)

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 possesses kinetic energy which is a form of energy. The body acquires it from the forces working on it and moving it. The quantitative value of kinetic energy depends on the mass and velocity of the body. If a body is at rest then its kinetic energy is zero.

## Other Physics lessons in this series

Lesson-1: Distance and Displacement.

Lesson-2: Speed and Velocity.

Lesson-3: Acceleration.

Lesson-4: Mass and Weight.

Lesson-5: Gravity.

Lesson-6: Volume and Density.

Lesson-7: Momentum.

Lesson-8: Force Work Done and Energy.

Lesson-9: Heat and Temperature.

Lesson-10: Circular Motion.

Lesson-11: Friction.

Lesson-12: Rotational Motion.

Lesson-13: Simple Harmonic Motion

Lesson-14: Voltage and Current.

Lesson-15: Magnetism.

Lesson-16: Light.

Lesson-17: Sound.

Lesson-18: Electrical Resistance.

Lesson-19: Capacitance.

Lesson-20: Atomic Structure.

## References

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