Force-Displacement Plot
The above concept can be understood more clearly using the force-displacement plot. The plot below shows a variable force with the displacement it is producing. It is known that the integrals represent the area under the curve. So, in this case, the area under the curve gives the work done by the force on the body. The area under the curve is divided into many rectangles which represent the displacement.
The area of a single rectangle is . This represents the work done by the force for an infinitesimally small displacement. The total sum of the area of all the rectangles gives the total work done.
W =
⇒ W = ∫Fdx
Work Done by a Variable Force
Usually, a dancing person is considered to be more energetic compared to a sitting person. A security guard who has been standing at his place the whole day has been working for hours. In real life, this seems obvious, but these terms and definitions work differently when it comes to physics. In physics, work has been defined as the product of force and displacement. This means, that if there is no displacement, work done is zero, no matter how much force or time was spent. This definition builds up concepts like the work-energy theorem. Let’s see this in detail.