Work done by a variable force
The work done by a constant force of magnitude F on a point that moves a displacement d in the direction of the force is the product.
W = Fd
When a force varies as it pushes or pulls an object, one cannot simply calculate work as the product
work = force * distance
Doing work on an object is a simple concept: we apply a certain force over a certain distance. But in real life, that force is rarely constant.
Therefore, we need to understand variable forces and be able to calculate them accurately.
If the force varies we need to use calculus to find the work done.
The graph shows a variable force with the displacement it is producing.
The area under the curve gives the work done by the force on the body. The area under the curve is divided into a number of rectangles that represent dx displacement.
If the force is given by F(x) then the work done by the force along the x-axis from a to b is:
