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Skill 7 of 13
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Gravitational potential energy

The flower pot falls down and smashes the green house’s glass roof. Much energy was clearly stored – some potential energy was present – which was then released as the pot slid off the window sill.

Why did it fall? Because of gravity, obviously. When an astronaut in outer space let’s go of an object, it doesn’t fall; no gravity means no energy being stored. So, let’s call this energy gravitational potential energy, and let’s use the previously chosen potential-energy symbol and add a subscript: $U_g$.

It turns out that gravitational potential energy has the formula:

$$U_g=mgh$$

where $m$ is mass, $g=9.8\,\mathrm{m/s^2}$ the gravitational acceleration and $h$ the height from start to impact.1 This formula is derived in Proof 36.

Note: if we chose to look at the height, not from the roof but from the ground to the pot, then we have a larger $h$ and thus a larger $U_g$, because more stored potential energy will be released over this longer fall. Let’s call the roof or the ground – the “zero-level” for the height – a reference, which we choose so it fits a particular scenario.2

Where exactly is this gravitational potential energy stored?

  • Is it in the flower pot? No not really, since that same flower pot out in space would not “contain” this energy without the Earth.
  • Is it in the Earth then? Also no, since without the flower pot there would be nothing to fall.

It seems that gravitational potential energy is not stored “within” any object but rather “between” two objects or within the system made up of two objects. $U_g$ is energy stored in the Earth-and-flower-pot configuration.3

Note: There is more general version of this formula that can be used between large objects, such as between the Earth and the moon. It is relevant when the two objects are close to the same size. We’ll learn about that in the Space discipline.4