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 = [math]\displaystyle{ \vec F }[/math] ∙ [math]\displaystyle{ \vec x }[/math]. This will often be the formula used in this course. Keep in mind that this is a dot product, so if these two vectors are perpendicular to one another, the dot product (and therefore the work) will equal zero. This is a key connection to be made about work.