Work Done by a Variable Force - Graphical - Problem L1

In our day to day life, we see many situations where we can say that work is being done by the force.

For example, here, we can say that man is doing work on the car by applying some force.

But the work done by these forces also depends upon their nature.

So it’s important to learn about the nature of these forces.

Here the forces involved are basically of two types.

$These are, 1. Constant Force 2 . Variable Force$

$Constant Force : If both magnitude, as well as direction of the force, remains constant, then we can say that force is of constant nature.$

$Variable Force: If either magnitude, direction or both changes, then we can say that force is of variable nature.$

So in this story, we will understand work done by variable force through graphs.

Consider a horizontal force is used to pull a block placed on the floor.

In this example, a horizontal force is used to pull the block.

This force varies with change in position coordinate x.

A horizontal force pulling the block is varying as shown in the figure.

We have to calculate work done by the force in moving the block from x=0 m to x= 30 m.

Solution

We know that work done is equal to the product of force and displacement.

But in this case product of force and displacement gives the area under the force-position graph.

So we can say that in rectilinear motion work done by a force equals to area under force-position graph and position axis.

Work done in displacing the block from x=0 m to x= 30m is equal to area of trapezium.

$So, work done can be given as W = \frac{1}{2} (20 + 30) \times 100 = 2500 J$

Revision

If either magnitude or direction or both changes then a force is said to be variable in nature.

In the case of rectilinear motion work done equals area under the force-position graph and position axis.

The End