Potential Energy

In particular, for a conservative force one can always find what is
called a **potential energy** such that the work done by this force is
given by

where the ``change'' in some quantity ``X'' is defined as

Note that only changes in potential energy have physical relevance.

If we now use the fact that the work done on an object equals the change in that object's kinetic energy, we then have

or, in other words,

We now define for this situation the **total energy** of the system as

for which we can then say

Two very fundamental concepts arise out of these considerations:

- The total energy of a system is
**conserved**, or independent of time. - The forms of energy (e. g., kinetic and potential)
which comprise the total energy may be
**transformed**into one another.

We now illustrate these concepts with three forms of potential energy.

1999-09-29