Work and Potential Energy

 Physicists tend to use a lot of words like work, potential energy, kinetic energy, etc. What we are doing is building a conceptual picture to help us organize a number of physical phenomena and related mathematical equations. You will find that when you see this picture, are familiar with the “jargon”, these concepts become easy to use and powerful in their applications. Much of this chapter is to introduce the jargon and develop the picture.
The ideas of work and potential energy are closely related and play critical roles in the picture of energy. Let us discuss some examples simply from the point of view of getting used to the jargon.
Suppose I pick a ball of mass m off the floor and slowly lift it up to a height h. While lifting the ball, I have to just barely overcome the downward gravitational force mg. Therefore I exert an upward directed force of magnitude mg, and I do this for a distance h. Since my upward force and the upward displacement are in the same direction, the work I do, call it W_me, is my force mg times the distance h, or W_me = mgh. Using the ideas of potential energy discussed earlier, we can say that all the energy W_me = mgh that I supplied lifting the ball went into gravitational potential energy mgh. While I was lifting the ball, gravity was pulling down. The downward gravitational force and the upward displacement were in opposite directions and therefore the work done by the gravitational force was negative. While we are storing gravitational potential energy, gravity does negative work. When we let go of the ball, gravity releases potential energy by doing positive work.

Let us consider another example where we store potential energy by doing work against a force. Suppose I tie one end of a spring to a post and pull on the other end as shown in Figure (1). As I stretch the spring, I am exerting a force and moving the end of the spring in the same direction. Therefore I am doing positive work on the spring, and this energy is stored in what we can call the “elastic potential energy” of the stretched spring. (We know that a stretched spring has some form of potential energy, for a stretched spring can be used to launch a ball up into the air.)

Figure 1: Doing work on a spring.