Gravitational potential energy

Some forces have an associated potential energy: a reservoir of energy tied to the position (or configuration) of bodies. Weight is the most familiar example. Lifting a body costs effort, and that effort is not lost: it is stored as gravitational potential energy, ready to convert back into kinetic energy as soon as the body is dropped.

Principle — Gravitational potential energy

$\ev{E_{\text{pot,grav}} = m\,g\,h}$ where $h$ is the height above a chosen reference level.

The delicate point is the reference level: the height $h$ is not an absolute value, but must be measured relative to a level we choose (the floor, sea level, the edge of a table). Consequently the value of $E_{\text{pot,grav}}$ also depends on the choice of zero. This is not a problem, because in physics what matters is never the absolute value of the potential energy, but only its change between two states: and the difference $mgh_B - mgh_A$ does not depend on where we placed the zero. We can therefore choose the reference in whatever way makes the calculation most convenient.

Climbing Everest on croissants

Mount Everest is $h = 8849\;\text{m}$ high. For an $80\;\text{kg}$ person, the gravitational potential energy at the summit is: $E_{\text{pot}} = 80 \cdot 9{,}81 \cdot 8849 = 6{,}94 \cdot 10^6\;\text{J}$ A cream-filled croissant contains about $52\,000\;\text{cal} = 217\,360\;\text{J}$. About $32$ croissants would therefore be needed just for the potential energy, without even accounting for friction, wind, and the fact that the human body has an efficiency of barely $25\%$!

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Topics: Lavoro ed energia Concepts: Energia potenziale gravitazionale · Forze conservative

Related exercises: Problem — Block on an inclined plane with spring (equilibrium and oscillations) · Worked exercise — apple and spring · Problem — Estimating the kinetic energy of a car