Energy

Kinetic Energy – definition and derivation

In the previous article we have discussed about the different forms of energy. In the current article, we will discuss about Mechanical Energy in more details.

Mechanical Energy is broadly classified into:

Kinetic Energy and
Potential Energy

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What is Kinetic Energy?

Kinetic energy of a moving body is defined as the energy it possesses by virtue of its motion. The work done by a moving body against external impressed forces, before coming to rest gives the measure of its kinetic energy.

Examples of Kinetic Energy

Let’s consider a huge reservoir of water of a hydel power project. Will it be able to drive a dynamo? No. But if there is a small hole at the bottom from where water gushes out, it can easily drive a dynamo. Due to high velocity of water flowing out, it has high kinetic energy, which is then used to drive the dynamo.
Another example can be a hammer driving a nail into a wooden plank. Now if we keep the hammer on the nail for eternity, will it drive the nail into the plank? No. But if we raise the hammer and hit the nail with high velocity, then the nail gradually goes in the plank. As the hammer comes down, it possesses kinetic energy which keeps on increasing with the increase in velocity and finally helps the nail to overcome the resistance of the wooden plank.

How kinetic energy is calculated

Let’s consider the last example of the hammer driving the nail. Say, the mass of the hammer is m and at any instant its velocity is u. If a constant force P opposing the motion be impressed upon it, the body decelerates and comes to rest after traversing a distance s. If then uniform retardation produced be f, then

P=mf (force = mass x retardation) –[1]

0=u²-2fs

Therefore : u² = 2fs

Since kinetic energy is measured by the work done against the force as the body comes to rest, so we can write

Kinetic energy of the body = E_k = force x distance = P.s = mf.s [From [1]]

= m(u²/2s).s = ½(mu²) (in absolute unit)

Thus to sum up – the kinetic energy of a moving body at any instant is given by half the product of its mass and the square of its velocity at that particular instant.

What is change in kinetic energy?

Change in kinetic energy is the work done by the impressed force. It can cause an increase in kinetic energy if the velocity increases or decrease if the velocity decreases.