The potential energy formula
The previous page found one answer by doing the arithmetic. Replacing each number with the quantity it stood for turns that arithmetic into a formula.
work done = weight × vertical height raised
weight = mass × acceleration due to gravity
work done = mass × acceleration due to gravity × height
Gravitational potential energy
Ep = m g h
- m — the mass of the object, in kilograms
- g — the acceleration due to gravity, taken as 10 m s-2
- h — the vertical height the object was raised through, in metres
Three factors, and only three
Gravitational potential energy depends on the mass, on g, and on the height — and on nothing else. Two of the three are worth dwelling on.
Mass and height are yours to change
Lift twice the mass, or lift it twice as high, and the stored energy doubles. Both enter the formula plainly, neither is squared.
g is fixed wherever you are
On the surface of the earth g does not change, so in every problem in this chapter it is simply 10 m s-2.
h is the vertical height, not the distance travelled
A child climbing a staircase walks much further than they rise. Only the vertical gain goes into h, because gravity is a vertical force and only displacement along a force counts as work against it.
Potential energy is m g h
Ep = m g h — mass in kilograms, g as 10 m s-2, and h the vertical height in metres. The answer comes out in joules.