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Potential Energy

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Equation

(Eq2)     EP = mgZ

potential energy

Nomenclature

EP (or PE)	potential energy
m	mass
g	gravitational acceleration
Z	vertical distance
F	force
W	work

Derivation

Consider a control mass that is initially at rest and at the elevation of some reference level. Let this mass be acted on by a vertical force F of such magnitude that it raises (in elevation) the mass with constant velocity an amount dZ. Let the acceleration due to gravity at this point be g. From the first law, Eq5:

δW = −F dZ = −d E_P

F = ma = mg

Then:

d E_P = F dZ = mg dZ

Integrating gives:

∫

EP2   EP1 = 0

dEP = m

∫

Z2   Z1

g dZ

Assuming that g does not vary with Z (which is a very reasonable assumption for moderate changes in elevation), the following is obtained:

(Eq1)

EP2 − EP1 = mg(Z2 − Z1)

or:

(Eq2)

EP = mgZ