Kinetic Energy and Potential Energy: Definition, Derivation, and Examples

The energy of an object is defined as its capacity to do work and is measured by the total amount of work it can do. One of the most important physical concepts is the concept of energy. Energy is the capacity to do work. Life is impossible without energy. In this blog, you will get a grasp of Kinetic Energy and Potential Energy!

When we eat, our bodies digest the food to release energy, so that we can work. When we work or walk we do some physical work, so here again we use energy. Energy lights our cities move our vehicles and runs our industries. The ability to do work is called energy.

Unit of Energy

The SI unit of energy is the same as that of work i.e. Joules, which is symbolized using the symbol J.

Let’s learn about the two types of energy, Kinetic Energy and Potential Energy:

Potential Energy

Have you ever stretched a rubber band? What happens when you release your hand from one of the ends? The band will tend to regain its original length from where does it get the energy to regain its position? Similarly, take a toy car. Wind it using its key. Place the car on the ground and the car starts to move. Where does it get the energy from?

Water stored in the reservoirs at heights helps in generating electricity. From where does the water get the energy to move the turbines? In all these above illustrations, applied force does not change the velocity but instead changes its position or configuration.

The work done by the force gets stored up in another form of energy called potential energy.

The energy possessed by an object by virtue of its position or configuration is called its potential energy. The work done on the rubber band to stretch it is stored as the potential energy in the band.

The work done to move the spring is stored as the potential energy, which helps the car to move. Similarly, the water at the height also possesses potential energy due to gravitation and that’s why when it gets converted to kinetic energy it is able to move the turbine.

Kinetic Energy

You all must have played the game carom and must have hit the carom coin with the striker. When you move the striker it hits the carom coin and changes its position. A bullet fired from a gun, is able to penetrate some distance into the target. A body can break something on which it falls. Fast blowing wind can rotate the blades of a windmill. Water in motion can rotate the blades of a turbine.

All the above illustrations show that a moving object is capable of doing work because of its motion and the energy possessed by a moving object is called its kinetic energy.

The energy possessed by an object by virtue of its motion is called as kinetic energy. The kinetic energy of a body moving with a certain velocity is equal to the work done on it to acquire that velocity.

Expression for kinetic energy

Consider an object of mass ‘m’ which is moving with an initial velocity ‘u’ on a perfectly frictionless surface. Let us consider that an external constant force ‘F’ acts on an object and produces acceleration ‘a’ in it. If v is the final velocity of the object after having undergone a displacement ‘s’, then from the third equation of motion we have

v2 – u2 = 2as
which implies (v2 – u2 )/2a = S

Work done by the force in displacing the body through a distance ‘s’ i.e. w = F * S

Also from Newton’s second law of motion we have,

F = ma
Thus from equation (1), (2) and (3) we get-
W = ma * (v2 – u2)/2a
This implies W = m (v2 – u2 )/2
Which implies W = ½ (mv2 – mu2)
Which implies W = ½ mv2 – ½ mu2

If the object is initially at rest i.e. u = 0, we have

W = ½ mv2

Or we can say that the work done (W) in making the object to acquire a velocity v after starting from rest is in fact stored in the object as its kinetic energy.

Work stored in moving an object is called as the kinetic energy of the object.

The kinetic energy is denoted by Ek. Thus, the kinetic energy possessed by an object of mass m, moving with a uniform velocity v is Ek which is equal to ½ mv2

Difference between Kinetic Energy and Potential Energy