Edexcel IGCSE Physics · Spec 4.6-4.7
KE & GPE: Using the Equations
Worked examples using the kinetic and gravitational potential energy equations.
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KE & GPE: Using the Equations
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Explained
Kinetic and gravitational potential energy, separately and together
Two equations, and then one idea that links them.
Kinetic energy is a half times mass times speed squared. Gravitational potential energy is mass times gravitational field strength times height. Both give an answer in joules when the mass is in kilograms, the speed in metres per second and the height in metres.
The square is the interesting part
In the kinetic energy equation only the speed is squared, and the half applies to the whole product rather than to the mass alone.
Squaring the speed has a consequence worth understanding rather than memorising. Double the speed and the kinetic energy is four times larger, not twice. Triple it and the energy is nine times larger. That is why stopping distances grow so sharply with speed, and it is a favourite point for an explain question.
The most common calculation error is squaring the whole expression, or forgetting to square at all. Work out the speed squared first, on its own, then multiply by the mass and halve it.
Height means vertical height
In the potential energy equation, height is the vertical distance moved, not the distance travelled. A ball rolling 5 m up a gentle slope that rises 2 m has gained potential energy corresponding to 2 m.
It is also always a change in height. Where you measure from does not matter, provided you are consistent, because only the difference has any physical meaning.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme gives a mark simply for stating each equation, before any numbers appear. It allows standard symbols, and for the kinetic energy equation it allows velocity written in place of speed.
For gravitational potential energy it allows the standard symbols and, in its notes, instructs the examiner to ignore the word gravity written for g. It also allows the use of 9.8 or 9.81 as well as the value given in the paper, so a slightly different constant does not cost the mark.
The interesting part comes next. Having asked for the kinetic energy at the bottom of a fall, the paper asks for the potential energy at the top, and the mark scheme says the answer should be identical to the previous one, allowing an error carried forward.
That is the whole conservation of energy idea expressed as a marking instruction. If the question tells you to ignore air resistance, the potential energy lost equals the kinetic energy gained, so you already have the answer and do not need to calculate it again.
Combining them
For a falling object with no air resistance, m g h at the start equals a half m v squared at the end. The mass appears on both sides and cancels, which is why the speed a dropped object reaches does not depend on how heavy it is.
Cancelling gives v squared equals 2 g h. Dropping something 5 m with g at 10 N/kg gives v squared equals 100, so the speed on landing is 10 m/s.
If the question does mention air resistance, the two are no longer equal. Some of the potential energy has been transferred to the surroundings by heating, so the kinetic energy at the bottom is less than the potential energy at the top, and saying where the difference went is usually the final mark.
Spec 4.6-4.7
What you need to know
- Use kinetic energy equals a half m v squared
- Use gravitational potential energy equals m g h
- Combine them for falling objects
Active recall
Quick check
Answer each question before opening the answer.
What is the kinetic energy of a 2 kg mass moving at 3 m/s?
KE = ½ × 2 × 3² = 9 J.
How much GPE is gained lifting 5 kg by 2 m (g = 10 N/kg)?
GPE = m × g × h = 5 × 10 × 2 = 100 J.
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