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:
W = Fx cosθ = (mg)()(cosθ) = mgh
As long as the object falls h distance, the work done on the object falling at
an angle is the same as if the object were falling straight down. This fact,
special to gravity and other forces, is significant in the study of energy, but
for now suffices to demonstrate how to calculate work.
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.