To see an example of work in a simple system, let us consider the work done by a gravitational force on a falling object. The gravitational force is simply mg, and let us denote the distance of the fall by h. Clearly if the object simply falls straight down, the work done is given by W = mgh. But what if the object falls at an angle θ from vertical, as seen below? If the object falls the same height, then the distance traveled is given by x = . The work, then, is given by:
Work is commonly misunderstood because of its common definition. Most people think that it takes a lot of work to hold a 100 pound weight in the air. The weight is not moving, though, so in the sense of physics no work is done. It is important to realize how our definition differs from a common one, and stick to the physical understanding of work. From this definition of work, we will be able to bring in a concept of energy, and greatly simplify many aspects of classical mechanics.