What Is Potential Energy?

Potential Energy

Mmm, yummy, says your stomach.

Legend says that Isaac Newton's theory of gravitation was inspired by an apple falling from a tree.

Indeed, the apple in the tree appears to have more potential energy: it has more potential to do work, which in this case, could be making your head hurt.

Let's go back to briefly review energy though.

In that case, it was easy to see that one object had a huge amount of energy, because it was moving, and hence with plenty of kinetic energy. Sometimes, objects have energy even though they aren't moving.

The wound-up mousetrap has great potential to do work (unfortunate for a mouse), and so it also possesses potential energy. Indeed, there are many types of potential energy, ranging from Chemical Potential Energy...

... to gravitational potential energy ...

... to elastic potential energy ...

In the next few sections, we'll dig deeper into some of the mechanical types of potential energy!

Potential energy is, simply speaking, the energy stored in an object, "waiting" to be released.

You can almost think of it as the ability of that object to cause damage, or as the amount of work that someone has "invested" in that object.

Potential energy is typically denoted as either $U$ or as the more descriptive but less common abbreviation $PE$.

Every type of potential energy has an associated force. An example would be gravity and gravitational potential energy. Another would be the spring force and spring potential energy.

Quite simply, the potential energy is there because there is a force. For example, if there were no gravity, there would be no difficulty in climbing up a flight of stairs---the job would be done effortlessly, so no work would be done. Thus, we would not build up any potential energy, and we would not have the potential to cause damage.

Potential energy is typically defined as the work that one has to do to go from infinity to a given point. Thus, for a given point $P$, we may write the following: $$U=\int_{\infty}^P\vec{F}\cdot\vec{dr}$$ Notice that the potential energy is $0$ at infinity. Note, however, that what really matters is not potential energy, but the difference in potential energy. Thus, you can define the zero point to be any convenient choice that you may wish. For example, we often define the ground as the zero point for gravitational potential energy.