# Potential Energy

**Potential energy** is the ability to do work, or stored energy. There are different kinds of
**potential energy.** For example:

**Chemical Potential Energy**– e.g. gasoline, batteries- Electric
**Potential Energy**– e.g. voltage **Elastic Potential Energy**– e.g. springs**Gravitational Potential Energy**– e.g. work done by or against gravity.

Our Symbol for potential energy will be PE. Occasionally, you will see the
symbol *U* used for potential energy. A subscript will denote the type. For example, gravitational potential energy will be *PE _{g}* or

*U*. Potential energy is always in relation to another potential surface. For example, gravitational potential energy can be chosen for a height above the ground, above a table, or at any low point that we will call h = 0. For our discussions here, we will talk about two forms of Mechanical Potential Energy: Gravitational Potential Energy and Elastic Potential Energy.

_{g}Gravitational potential energy is the energy available to an object due to
the object's position relative to a given point (height above a surface). It is the energy available to it if gravity were to do work on the object. Recall that Work =
**F****·**
**d**. Since the force required to lift an object at a constant velocity is its weight, mg, and
the distance is the height of the object, we say that the gravitational potential energy, *PE _{g} or U_{g}* = mgh.

*Example: What is PE _{g} of a 5 kg box sitting on
a shelf 2 meters above the floor? From above, PE_{g} = mgh =*

*(5kg)(9.8 m/s ^{2})(2m) = 98
Joules.*

Another example of how gravitational potential energy is calculated relative to a given position:

Elastic potential energy is the energy available in an elastic device such as a spring, a rubber band, a superball, or a bungee cord. To start with, we need to know Hooke's Law: The distance a spring is displaced is proportional to the force applied to the spring, or

F_{p} =
-*k*x,

where *k* is a spring constant (in N/m) and x is the displacement of
the spring in meters. The force is negative because the restoring force will always be opposite the direction of the spring's displacement. To compute the spring constant, we perform a Hooke's Law
Experiment. Once we know the spring constant, k, we can find the
elastic potential energy in a straightforward manner.

Often it is helpful to see what someone else has to say on the topic. Be sure to check out:

http://www.physicsclassroom.com/Class/energy/u5l1b.htmll

For Practice Problems, Try:

*From the University of Oregon:*

Potential energy change in a rollercoaster

Giancoli Multiple Choice Practice Questions (Select "Practice Problems) and try
some. *Don't worry - you won't be able to do all of them yet.
But we are getting close!*