Changes in energy: height, h, in metres, m

The idea

Height in the gravitational potential energy equation is the vertical distance moved, measured in metres, and it must be vertical: a ramp 5 m long rising 2 m gives h = 2 m. The equation is Eₚ = m g h, with mass in kilograms and gravitational field strength g = 9.8 N/kg near the Earth surface. So lifting a 60 kg student 4.5 m up a staircase fills the gravitational store with 60 × 9.8 × 4.5 = 2646 J. Only the change in height counts, so a ball that rises 3 m and falls back to the start has no net change. On the Moon the same lift stores far less because g is about 1.6 N/kg. Height questions often pair with the kinetic store, as in a falling object where m g h becomes ½ m v² and the mass cancels from both sides.

What earns the marks

• Identifying the vertical height change rather than the distance travelled along a slope.
• Substituting mass in kilograms and g = 9.8 N/kg into Eₚ = m g h.
• The energy given in joules.
• A rearrangement to find height or mass when the energy is the quantity given.

Common mistakes and how to put them right

• Using the length of a ramp or the distance run rather than the vertical rise.

• Leaving the mass in grams, which makes the stored energy 1000 times too large.

• Quoting the height in centimetres so the answer is out by a factor of 100.

• Using a weight in newtons in place of the mass in kilograms, so g gets counted twice.

Exam tips

• Underline the vertical height in the question before you start, especially on ramp and staircase problems.
• Where a question gives weight rather than mass, use energy = weight × height, because weight already contains g.
• Keep g = 9.8 N/kg unless the paper tells you otherwise.