How do you calculate the work done by a variable force?

To calculate the work done by a variable force, you need to integrate the force over the displacement.

When a constant force is applied to an object, the work done can be calculated by multiplying the force by the displacement and the cosine of the angle between them. However, when the force is variable, this method cannot be used. Instead, the work done is calculated by integrating the force over the displacement.

To do this, you need to break up the displacement into small intervals and calculate the work done by the force over each interval. Then, you can add up all these small amounts of work to get the total work done by the force.

The integral that represents the work done by a variable force is given by W = ∫F(x)dx, where F(x) is the force at a given displacement x. This integral can be evaluated using calculus techniques such as substitution or integration by parts.

It's important to note that the displacement must be in the same direction as the force for work to be done. If the force and displacement are perpendicular, no work is done. If the force and displacement are in opposite directions, the work done is negative.

In summary, to calculate the work done by a variable force, you need to integrate the force over the displacement. This involves breaking up the displacement into small intervals and adding up the work done over each interval. The displacement must be in the same direction as the force for work to be done.