The change in gravitational potential energy

Why focus on the change?

In physics, what often matters is not the absolute value of Epp but its change between two positions, denoted by delta Epp. This change does not depend on the choice of reference point, unlike Epp itself.

The formula

delta Epp = Epp(final) - Epp(initial) = m * g * (h_final - h_initial) = m * g * delta h

• If the object rises (delta h > 0), then delta Epp > 0: the potential energy increases.
• If the object falls (delta h < 0), then delta Epp < 0: the potential energy decreases.

Example

A climber with a mass of 65 kg climbs a height of delta h = 300 m on a cliff (g = 10 N/kg):

delta Epp = 65 * 10 * 300 = 195,000 J = 195 kJ

This energy was supplied by the climber’s muscular work against their weight.

Link to the work done by weight

The work done by weight during a movement is given by W(weight) = –delta Epp = m * g * (initial h – final h). When the object descends, the weight does positive work (it aids the movement); when the object ascends, the weight does negative work (it opposes the movement).

Common pitfall

Do not confuse the sign of delta h with that of the work done by the weight: a descent results in a negative delta h but positive work done by the weight, due to the negative sign in the relationship W = -delta Epp.