Work Done by a Variable Force

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 car by applying some force.

But the work done by these forces also depend upon its nature.

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

Here the forces involved are basically of two types.

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

Consider a force which varies with change in position coordinate x.

We have to calculate the work done by this force while displacing the particle.


We know work done by a constant force is equal to the product of force and displacement.

But in this situation force is not constant.

So the question is, how to consider force in calculating work in this case.

So in this type of problem, we will consider very small displacement almost close to zero.

For infinitesimally small-displacement we can say the force is almost constant.

Hence for infinitesimally small displacement, we can calculate work done.


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

In case of variable force first, we calculate work done by the force for infinitesimally small displacement.

Then we add all these small-small work done to get total work done throughout the total displacement.

Since this is a continuous function so we use integral operation for addition.

The End