Force, work, power and energy

Kinetic Energy

The world requires a lot of energy. To satisfy this demand, we have natural energy sources such as the sun, wind, water present at great heights, tides, etc. We also have artificial energy sources such as coal, petroleum, natural gas, etc.



Energy exists in various forms such as light, sound, motion, etc.

Forms of energy

Some forms of energy are

Light

Sound

Heat

Mechanical

Electrical

Chemical

Nuclear

In this section, we will consider only mechanical energy
Mechanical energy

It is the form of energy possessed by an object having the potential to do work. It is caused by the motion, or the position and configuration of the object. Mechanical energy is of two types.

(i) Kinetic energy (caused by the motion of an object)

(ii) Potential energy (caused by the position and configuration of an object)

Kinetic energy


A body possesses kinetic energy by virtue of its motion. A moving arrow can be made to go through an object. Hence, it is said that the arrow possesses kinetic energy.


The elastic string of a catapult is stretched to throw a stone. The work done is stored in the stone and the string. After its release, the stone is said to possess kinetic energy.


Take a long cardboard and fold it so that it has two hump-like peaks with a valley in between them (see figure). Mark point I at the top of the hump, and points II, III, and IV at respective distances of 10 cm, 20 cm and 30 cm from point I. Now, allow a ball to roll down from each of these marked points, one by one. Measure the vertical height attained by the ball on the second hump in each case. Compare these heights. What do you observe?


You will observe that the ball will reach its highest point when it is dropped from point I. It will reach its lowest height when it is dropped from point IV. What causes the ball to go up? Discuss the results with your friends.

A stone dropped from a height has the capability to create a depression in wet ground. Hence, the dropped stone has some amount of kinetic energy. A fired bullet can get embedded in a wall or a wooden block. Hence, it is said that a moving bullet possesses kinetic energy. Can you find out how much energy is possessed by a moving object because of its motion?

For this, let us derive a formula for kinetic energy.

Formula for kinetic energy

Kinetic energy of a moving body is equal to the work required to change its velocity from u to v.

Let a body of mass m be moving with a uniform velocity u. Let an external force be applied to it, such that it gets displaced by a distance s, and its velocity becomes v.

We have velocity−position relation as

v2 = u2 + 2as

Where, a = Acceleration of the body during the change of velocity

Or … (1)

Hence, the work done on the body by the force is given by

W = F × s

F = ma

W =




If the body is initially at rest, i.e., u = 0, then

W

Since kinetic energy is equal to the work done on the body to change its velocity from 0 to v, we obtain

Kinetic energy,


Hence, the kinetic energy of a body increases with its velocity.

Its SI unit is Joule (J).

Kinetic energy of a body is directly proportional to

(i) Its mass (m)

(ii) The square of its velocity (v2)

It is the kinetic energy of the wind that is used in windmills for generating electricity.