Section 9.2 introduced two key ideas: (1) a system has energy and (2) work is a mechanical process that changes the system’s energy. Now we’re ready to look more closely at how to calculate the work done in different situations. Although we’ll be focusing on the mathematical techniques of calculating work, it’s important to keep in mind that our real goal is to learn how the energy of a system changes when forces are applied to it.
“Work” is a common word in the English language, with many meanings. Work might refer to physical exertion, to your job or occupation, or even to a work of art. But set aside those ideas about work because they are not what work means in physics. Work, as we’ll use the word, is a process. Specifically, it is a process that changes a system’s energy by mechanical means—pushing or pulling on it with forces. We say that work transfers energy between the environment and the system.
Equation 9.6 defined work as
where, recall, is the component of in the direction of motion (the s-direction). We began by looking at a force that was parallel to the displacement, but such a restriction is not required because any force component perpendicular to the motion does no work. Equation 9.14 is, in fact, a general definition of work.
We’ll start by learning how to calculate work for constant forces, and we’ll introduce a new mathematical idea, the dot product of two vectors, that will allow us to write the work in a compact notation. Then we’ll consider the work done by a variable force that changes as the particle moves.