GCSE · Physics · Edexcel · Spec 1PH0

Gravitational PE equation

Carry a heavy bag up three flights of stairs and your legs feel every metre. Physics can put an exact number on that — and soon, so can you.

Lift it higher, make it heavier — watch the energy climb

01.252.53.755062.5125188250Change in vertical height Δh (m)Change in GPE (J)80 JGain in GPE for a 4 m liftlift ↑ = heavier
Mass m 2 kg

Mass m: 2 kg. Gain in GPE for a 4 m lift: 80 J

Each line shows the gain in GPE for one mass. Here g, the pull of gravity on each kilogram, is taken as 10 N/kg. Read the energy for any lift straight off the line. Then grab the point at 4 m and lift it: that swaps in a heavier object, and the whole line tilts steeper.

Exam line: Double the height and ΔGPE doubles. Double the mass and ΔGPE doubles. That is what a product like m × g × Δh does.
Watch out: Read the line backwards too: lower the object by the same height and its store loses exactly the energy it gained on the way up.

One equation, four ways to use it

ΔGPE = m × g × Δh

Three things multiplied together: mass (kg), gravitational field strength g (N/kg) and change in vertical height (m). The answer is in joules. On Earth g is about 9.8 N/kg, and questions often round it to 10 N/kg — use the value you're given.

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Your turn

Finish the calculation: find the mass

A climber hauls a bag 25 m up a cliff. The bag's gravitational store gains 1470 J. Taking g = 9.8 N/kg, calculate the mass of the bag.

  1. Known: ΔGPE = 1470 J, g = 9.8 N/kg, Δh = 25 m. Want: m.Before any sums, sort out what you've got and what you're after. The unknown is the mass.
  2. missing step
Which line is step 2?

Exam line: Write the rearranged equation before you touch the numbers, and divide by the whole bottom line, not just part of it.

Spot the slip

Where does this answer go wrong?

A 750 g book is lifted from the floor onto a shelf 180 cm above the floor. Taking g = 10 N/kg, calculate the gain in the book's GPE.

A student's answer — which line goes wrong?

Exam line: Scan the question for g and cm before you substitute anything: grams ÷ 1000 gives kg, centimetres ÷ 100 gives m.

Which height?

The ramp question

Mia pushes a 20 kg trolley up a ramp. The ramp is 12 m long. The bottom of the ramp is on a platform 3 m above the ground, and the top of the ramp is 4.5 m above the ground. Take g = 10 N/kg.

Which height should go into ΔGPE = m × g × Δh?
How sure are you?

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Lift something up and you fill its gravitational store. One multiplication tells you by how much.

What you need to know

  • Raise an object and the energy in its gravitational potential energy store goes up; lower it and the energy goes down.
  • ΔGPE = m × g × Δh: change in GPE (J) = mass (kg) × gravitational field strength (N/kg) × change in vertical height (m).
  • To find m, g or Δh, divide ΔGPE by the other two quantities multiplied together.
  • Convert first: grams to kilograms and centimetres to metres, before anything goes into the equation.
  • Δh is the change in VERTICAL height — how much higher or lower the object ends up, whatever route it took.

The big picture

Raising an object transfers energy into its gravitational potential energy (GPE) store; lowering it transfers energy out. The change is ΔGPE = m × g × Δh, with mass in kilograms, gravitational field strength in newtons per kilogram and the change in vertical height in metres, which gives the energy in joules. To find any one of m, g or Δh, divide ΔGPE by the other two multiplied together.

Key points

1Raising an object increases its GPE store; lowering it by the same height decreases the store by the same amount.
2ΔGPE (J) = m (kg) × g (N/kg) × Δh (m) — a product, so doubling any one quantity doubles ΔGPE.
3g is the gravitational field strength: about 9.8 N/kg at the Earth's surface, often rounded to 10 N/kg. Use whichever value the question gives.
4Rearranged: m = ΔGPE ÷ (g × Δh), g = ΔGPE ÷ (m × Δh), Δh = ΔGPE ÷ (m × g).
5Grams ÷ 1000 → kg and centimetres ÷ 100 → m, before substituting.
6Δh is the vertical change between start and finish — not the length of a slope, and not the height above the ground unless it started on the ground.

Worked example

Problem

A 1.2 kg drone rises straight up until its gravitational store has gained 180 J. Taking g = 10 N/kg, how much higher is the drone than where it started?

⚠ Watch out

Putting the wrong height into the equation — the distance along a slope or staircase, or the final height above the ground when the object didn't start on the ground. Δh is only the change in vertical height.

🧠

Memory hook

Heavier, stronger gravity, or higher: ΔGPE = m × g × Δh, so double any one of them and the energy doubles.

✓

Check yourself

A 0.5 kg ball is lowered 0.8 m from a table to the floor, with g = 10 N/kg. Does its GPE store go up or down, and by how much? (Down, by 4 J.)

Flashcards

(9)
What happens to an object's GPE store when it is raised? And when it is lowered?
Raised: energy is transferred into the store, so it increases. Lowered: energy is transferred out, so it decreases.
Write the equation for the change in gravitational potential energy.
ΔGPE = m × g × Δh
Give the unit of each quantity in ΔGPE = m × g × Δh.
ΔGPE in joules (J), m in kilograms (kg), g in newtons per kilogram (N/kg), Δh in metres (m).
What is g, and what value is it on Earth?
The gravitational field strength — the force of gravity on each kilogram. About 9.8 N/kg at the Earth's surface, often rounded to 10 N/kg.
How do you rearrange ΔGPE = m × g × Δh to find any one of m, g or Δh?
Divide ΔGPE by the other two multiplied together, e.g. g = ΔGPE ÷ (m × Δh).
Which height goes into the GPE equation?
The change in vertical height: how much higher or lower the object ends up than where it started, whatever route it took.
A question gives the mass in grams and the height in centimetres. What do you do first?
Convert: grams ÷ 1000 to get kg, centimetres ÷ 100 to get m. Then substitute.
For the same mass, what happens to ΔGPE if the height lifted is doubled?
ΔGPE doubles — for a fixed mass and g, ΔGPE is directly proportional to Δh.
Why do N/kg × kg × m give an answer in joules?
N/kg × kg leaves newtons, and newtons × metres is newton-metres. One newton-metre is one joule.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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