Work/Energy

The Main Idea

Up until this point, we've worked in applying the Energy Principal in situations where there is no work. Therefore, the right side of the energy equation (EQN) is zero. But what if there is work? In this section we will cover what work is and how we will use it.

Work is a movement of an object in the direction of the force applied to it. A person pushing a box, jogging to work, and pulling a wagon are all doing work. We will be using work in the context of The Energy Principal in a moment but first lets look at the mathematical definition of work.

A Mathematical Model

The best definition of work is as an integral. It can be expressed as: [math]\displaystyle{ \int{F}\, dx }[/math]. This is the integral (evaluated over bounds from initial to final position) of the force times the change in position.

Under a constant force, this can be expressed as W = F ∙ x. This will often be the formula used in this course. Keep in mind that for this to be true, the force must be in the same direction