Life is impossible without energy. The energy demand is ever increasing.
The Sun is the most significant natural source of energy for us. Many of our sources of energy are derived from the Sun. We can also take energy from the nuclei of atoms, the inside of the earth, and the tides.
An object having the ability to do work is said to possess energy. The object which does the work loses energy, and the object on which the work is done gains energy.
Therefore, the unit of energy is the same as that of work: \(joule (J)\).
\(1\ J\) is the energy required to do \(1\ joule\ of\ work\). Sometimes a larger unit of energy called kilojoule (kJ) is used. \(1\ kJ\) equals \(1000\ J\).
Energy can exist in two basic mechanical forms
- Kinetic Energy - which is the energy of motion, and
- Potential Energy - which is the stored energy due to position or state.
In this section, we will derive the formula to find the kinetic energy of an object.
Kinetic energy is the energy contained by an object due to its motion. The kinetic energy of an object increases with its speed.
The kinetic energy of a body moving with a certain velocity is equal to the work done on it to make it obtain that velocity.
Let us now represent the kinetic energy of an object in the form of an equation.
Consider an object of mass (m) moving with a uniform velocity (u).
Let it now be displaced through a distance \(s\) when a constant force \(F\), acts on it in the direction of its displacement.
From the equation of work done, We know that,
\(Work\ done\ =\ F\ \times s\)
The work done on the object will cause a change in its velocity. Let its velocity change from initial velocity (u) to final velocity (v).
Let a be the acceleration produced.
We studied three equations of motion. The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration (a), and the displacement (s) is,
\(v^2\ -\ u^2\ =\ 2as\)
Rearranging it to gets, \(s\ =\ \frac{v^2\ -\ u^2}{2a}\)
We also know that,
\(Force\ (F)\ =\ Mass\ (m)\ \times\ Acceleration(a)\)
Substitute the equation s and F in work done,
\(Work\ done\ =\ F\ \times s\)
\(=\ F\ \times \frac{v^2\ -\ u^2}{2a}\)
\(=\ F\ \times \frac{v^2\ -\ u^2}{2a}\)
Simplifying it weget,= \(\frac{1}{2}\ \times\ m\ \times\ (v^2\ -\ u^2)\)
If the object starts from its stationary position, that is, \(u\ =\ 0\), then,
\( Work\ done (W)\ =\ \frac{1}{2}\ \times\ m\ \times\ (v^2)\)
It is clear that the work done is equal to the change in the kinetic energy of an object.
If \(u\ =\ 0\), the work done will be \(\frac{1}{2}\ \times\ m\ \times\ (v^2)\).
Thus, the kinetic energy possessed by an object of mass (m) and moving with a uniform velocity (v) is,
\(E_k\ =\ \frac{1}{2}\ \times\ m\ \times\ (v^2)\)
Objects in motion contain energy. We define this energy as kinetic energy.
A coconut is falling from the tree, a speeding car, a rolling stone, a flying aircraft, running water, blowing wind, a running athlete etc., possess kinetic energy.
Potential Energy is the stored energy due to position or state. It is represented by
Potential energy, \(E_p\ =\ mgh\)
The power is represneted as rate of doing work, \(P\ = \frac{E}{T}\)