Cambridge Syllabus Notes

1.7.1 Energy – Gravitational Potential Energy

Objective:

Recall and use the equation for the change in gravitational potential energy: $$\Delta E_p = m g \Delta h$$

What is Gravitational Potential Energy?

Think of a ball held at the top of a hill. The higher it is, the more “energy” it has stored, ready to be released if it rolls down. This stored energy is called gravitational potential energy (GPE). The amount of GPE depends on three things: the mass of the object, the height above the ground, and the strength of gravity.

Key Variables

Symbol	Meaning	Units
$m$	Mass of the object	kg
$g$	Acceleration due to gravity (≈9.8 m s⁻² on Earth)	m s⁻²
$\Delta h$	Change in height (final height – initial height)	m

Analogy: The Water Tank

Imagine a water tank at the top of a hill. The higher the tank, the more potential energy the water has. When you open the tap, the water rushes down, turning that potential energy into kinetic energy (motion). The same principle applies to any object lifted against gravity.

Quick Example

Mass of a book: $m = 2.0\;\text{kg}$
Height lifted: $\Delta h = 1.5\;\text{m}$
Calculate ΔE_p:

$$\Delta E_p = (2.0\;\text{kg})(9.8\;\text{m s}^{-2})(1.5\;\text{m}) = 29.4\;\text{J}$$

So the book now has 29.4 J of gravitational potential energy.

Exam Tips

Always write the full equation: ΔE_p = m g Δh.
Check units: kg × m s⁻² × m = J (joules).
Remember that Δh is positive when the object is raised and negative when lowered.
Use the symbol “Δ” to indicate a change (e.g., Δh = h_final – h_initial).
When working out a problem, first identify the given values, then plug them into the formula.

Recall and use the equation for the change in gravitational potential energy ΔE_p = m g Δh