So far the only form of energy that we defined was kinetic energy which is a
function of velocity squared (or speed squared)
K = 1
2
mv2
. (7.1)
It turns out that it is also useful to define another form of energy which is a
function of position. This new physical quantity we will call potential energy. The process of
storing potential energy would most certainly require work to be done on the
object, but later on the potential energy can be released.
The most familiar example of potential energy is the gravitational potential
energy, when the work must be done on an object to lift it up. For
example, if on object has mass m and is lifted from height x1 to height x2,
then the work done by gravitational force is
Wgrav =
!
−mgˆi
" !(x2 − x1) ˆi
"
= mgx1 − mgx2 (7.2)
Then it is convenient to define a gravitational potential energy
Ugrav ≡ mgx (7.3)
and then the work done by gravitational force can be written as
Wgrav = −∆Ugrav = Ugrav,1 − Ugrav,2. (7.4)
