Introduction to Work Energy Theorem & its Application - JEE PDF Download

Introduction

According to this theorem, the net work done on a body is equal to the change in kinetic energy of the body. This is known as Work-Energy Theorem. It can be represented as:

K_f – K_i = W
Where K_f = Final kinetic energy
K_i = Initial kinetic energy
W = net work done
So the above equation follows the law of conservation of energy, according to which we can only transfer energy from one form to another. Also, here the work done is the work done by all forces acting on the body like gravity, friction, external force etc. For example, consider the following figure.

According to Work energy theorem,
Work done by all the forces = Change in Kinetic Energy
W_g + W_N + W_f  =K_f – K_i
Where W_g = work done by gravity
W_N = work done by a normal force
W_f = work done by friction
K_f = final kinetic energy
K_i = initial kinetic energy

Work done by a constant force

A constant force will produce constant acceleration. Let the acceleration be ‘a’.
From the equation of motion,
v² = u² + 2as
2as = v² – u²

Multiplying both sides with mass ‘m’

Comparing the above equation, we get,
Work done by force (F) = F.s
Where ‘s’ is the displacement of the body.

Work done by Non-Uniform Force

Now the equation,
W = F.ds
This is only valid when force remains constant throughout the displacement. Suppose we have a force represented below,

For these kinds of forces, we can assume that force remains constant for a very small displacement and then integrate that from the initial position to the final position.

This is work done by a variable force. A graphical approach to this would be finding the area between F(x) and x from x_i  to x_f.

The shaded portion represents the work done by force F(x).