From Google:
PE_{\text G} = mg \Delta h
PE_G = potential energy due to gravity
g = acceleration due to gravity
m = mass
\Delta h = distance above a surface (such as the ground)
How do you calculate gravitational potential energy?
4 answers
Say I have a rock of mass m kilograms in my hand.
The weight of the rock pushing down is m g or about 9.81 m Newtons.
If it is not accelerating the force up from my hand is then m g Newtons.
Now
If I lift that rock up a distance z, the work I do with my hand is F z = m g z
If there are no losses to friction or radiation or heat or anything energy is conserved so that work I put in, m g z, is an increase of potential energy of the rock of amount m g z Newtons
or
increase in PE = m g z
Note, important ---- all I calculated with that m g z was increase in potential energy from moving up distance z
There was no starting z = 0, the original height of my hand defined
Therefore to say my potential energy is U = m g z
I must say where z = 0 and U = 0. Often one chooses the level of the earth for z =U = 0, but you can pick any other height for U = 0
This is true of any other potential, always it is relative to some defined zero point.
The weight of the rock pushing down is m g or about 9.81 m Newtons.
If it is not accelerating the force up from my hand is then m g Newtons.
Now
If I lift that rock up a distance z, the work I do with my hand is F z = m g z
If there are no losses to friction or radiation or heat or anything energy is conserved so that work I put in, m g z, is an increase of potential energy of the rock of amount m g z Newtons
or
increase in PE = m g z
Note, important ---- all I calculated with that m g z was increase in potential energy from moving up distance z
There was no starting z = 0, the original height of my hand defined
Therefore to say my potential energy is U = m g z
I must say where z = 0 and U = 0. Often one chooses the level of the earth for z =U = 0, but you can pick any other height for U = 0
This is true of any other potential, always it is relative to some defined zero point.
ah well, who am I to criticize Google ?
Now if you are not just working on the surface of earth but in the much larger universe you must use the more general form of gravitational effect
F = G m M /r^2
m is that mass you are moving
M is the planet or star or whatever
r is the distance between the center of gravity of your rock and that star or whatever.
G is Newton's universal gravitational constant
[ Note if near earth surface r is about constant earth radius and m is earth mass F = [G M/r^2] m where G M/r^2 = g pretty much constant 9.81 m/s^2]
now change in PE = [(GMm)/r^2] dr = (GMm) integral dr/r^2
= GMm/ [1/R1 - 1/R2]
that is
G M m [ R2 - R1] /R1 R2
if R1 is close to R2 like near surface of earth that is
(GmM/R^2 )*( change in height ) or the same old m g z
which is the same old m g * change in height
F = G m M /r^2
m is that mass you are moving
M is the planet or star or whatever
r is the distance between the center of gravity of your rock and that star or whatever.
G is Newton's universal gravitational constant
[ Note if near earth surface r is about constant earth radius and m is earth mass F = [G M/r^2] m where G M/r^2 = g pretty much constant 9.81 m/s^2]
now change in PE = [(GMm)/r^2] dr = (GMm) integral dr/r^2
= GMm/ [1/R1 - 1/R2]
that is
G M m [ R2 - R1] /R1 R2
if R1 is close to R2 like near surface of earth that is
(GmM/R^2 )*( change in height ) or the same old m g z
which is the same old m g * change in height