We could also have solved this problem using Newton’s Second Law and some kinematics, but the work-energy theorem gives us a quicker route to the same answer.

 

    Potential Energy

 

    As we said before, work is the process of energy transfer. In the example above, the kinetic energy of the puck was transferred into the heat and sound caused by friction. There are a great number of objects, though, that spend most of their time neither doing work nor having work done on them. This book in your hand, for instance, is not doing any work right now, but the second you drop it—whoops!—the force of gravity does some work on it, generating kinetic energy. Now pick up the book and let’s continue.

 

    Potential energy, U, is a measure of an object’s unrealized potential to have work done on it, and is associated with that object’s position in space, or its configuration in relation to other objects. Any work done on an object converts its potential energy into kinetic energy, so the net work done on a given object is equal to the negative change in its potential energy:

    Be very respectful of the minus sign in this equation. It may be tempting to think that the work done on an object increases its potential energy, but the opposite is true. Work converts potential energy into other forms of energy, usually kinetic energy. Remove the minus sign from the equation above, and you are in direct violation of the law of conservation of energy!

 

    There are many forms of potential energy, each of which is associated with a different type of force. SAT II Physics usually confines itself to gravitational potential energy and the potential energy of a compressed spring. We will review gravitational potential energy in this section, and the potential energy of a spring in the next chapter.

 

    Gravitational Potential Energy

 

    Gravitational potential energy registers the potential for work done on an object by the force of gravity. For example, say that you lift a water balloon to height h above the ground. The work done by the force of gravity as you lift the water balloon is the force of gravity, –mg, times the water balloon’s displacement, h. So the work done by the force of gravity is W = –mgh. Note that there is a negative amount of work done, since the water balloon is being lifted upward, in the opposite direction of the force of gravity.

 

    By doing –mgh joules of work on the water balloon, you have increased its gravitational potential energy by mgh joules (recall the equation ). In other words, you have increased its potential to accelerate downward and cause a huge splash. Because the force of gravity has the potential to do mgh joules of work on the water balloon at height h, we say that the water balloon has mgh joules of gravitational potential energy.