METRONMETHOD. REASON. LEARN.
Energy · 12 min

Gravitational potential energy

Lifting a book or pumping water uphill stores energy in the object–Earth system. That energy can later transfer into motion or heating.

01Why this matters

Lifting a book or pumping water uphill stores energy in the object–Earth system. That energy can later transfer into motion or heating.

02See it

mass 2 kgrise 1.5 mweight 19.6 Ngain 29.4 J
Read left to right: mass 2 kg → rise 1.5 m → weight 19.6 N → gain 29.4 J. Each panel connects one part of the example.

03Understand it

Near Earth’s surface, a change in gravitational potential energy is mass × gravitational field strength × change in height.

Use ΔEp = mgΔh when g is approximately constant. Height is vertical height, not distance travelled along a slope. Choose a reference level; changes in energy are what matter. In an ideal fall without air resistance, lost gravitational potential energy becomes kinetic energy.

04Guided example

Raise a 2 kg book by 1.5 m, using g = 9.8 N/kg.

  1. Identify the vertical change in height: Δh = 1.5 m.
  2. Calculate the weight: mg = 2 × 9.8 = 19.6 N.
  3. Multiply by height change: ΔEp = 19.6 × 1.5 = 29.4 J.

05Try it

Raise 1 kg by 2 m with g = 9.8. Energy gained?
A little hint

Multiply m, g and height change.

06Practise it

Raise 5 kg by 3 m using g = 10. Energy gained?
A little hint

Use the stated value of g.

Mass 2 kg loses 4 m in height, g = 10. Energy change?
A little hint

The height change is negative.

07Use it in the real world

Pumped storage moves water to a higher reservoir. The higher water has more gravitational potential energy, although practical systems lose some transferred energy to heating and other processes.

Go a little deeper

The formula is a near-surface approximation. Across large changes in distance from Earth, gravitational field strength changes and a more general gravitational potential formula is needed.

08Quick check

Gain 60 J with mass 3 kg and g = 10. Height gained?
A little hint

Divide energy by mg.

09Summary

Near Earth’s surface, a change in gravitational potential energy is mass × gravitational field strength × change in height. Multiply by height change: ΔEp = 19.6 × 1.5 = 29.4 J.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea

ΔEp = mgΔh

ΔEp: change in energy in J; m: kg; g: N/kg; Δh: vertical change in m.

Δh = ΔEp/(mg), for non-zero m and g

Find this in the formula library →