Edexcel IGCSE Physics · Spec 4.6-4.7
Kinetic & Gravitational Potential Energy
Kinetic energy and gravitational potential energy.
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Kinetic & Gravitational Potential Energy
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Explained
Two energy stores, and the transfer between them
Kinetic energy is the energy an object has because it is moving. It equals one half multiplied by the mass multiplied by the speed squared.
Gravitational potential energy is the energy an object has because of its height in a gravitational field. The change in it equals the mass multiplied by the gravitational field strength multiplied by the change in height.
Both are measured in joules, mass is in kilograms, speed is in metres per second and height is in metres. In the United Kingdom the gravitational field strength is about 10 newtons per kilogram, and 9.8 or 9.81 are accepted equally.
Why the squared matters
Kinetic energy depends on the square of the speed, and this is the single most tested consequence in the topic.
Double the mass and the kinetic energy doubles. Double the speed and the kinetic energy quadruples, because the speed is squared before the multiplying begins.
That is why braking distance grows so sharply with speed, why a small increase in a speed limit has a large effect on the severity of a crash, and why a light fast object can carry more energy than a heavy slow one.
It also means the square is applied to the speed only, never to the mass or the one half. Squaring the whole expression is a common slip and it produces an answer that is wrong by a very large factor, which at least makes it easy to spot when checking.
The height in the GPE equation
It is the vertical height gained or lost, not the distance travelled.
An object sliding four metres down a ramp that drops one metre has lost the gravitational potential energy corresponding to one metre. The four is the path length and it does not appear in the calculation.
Questions give the ramp length deliberately, so read carefully for the word vertical or for a height marked on a diagram, and check the units, since heights are often quoted in centimetres.
The transfer
A falling object loses gravitational potential energy and gains kinetic energy. If air resistance is ignored, all of it transfers, so the kinetic energy at the bottom equals the gravitational potential energy lost from the top.
Setting the two expressions equal gives one half m v squared equals m g h. The mass cancels from both sides, which is why, without air resistance, everything falls at the same rate regardless of how heavy it is.
Rearranged, v equals the square root of 2 g h. That gives the speed at the bottom from the height alone, and it is the quickest route through most fall questions.
The same idea run backwards gives the height something reaches when thrown upwards: all its kinetic energy becomes gravitational potential energy, so h equals v squared divided by 2 g.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme takes a candidate through a fall in stages: state the kinetic energy equation, substitute to get 860 J, and then, for the next part, give the gravitational potential energy.
The answer it wants for that third part is 860 J again. Its instruction reads: identical answer to the previous part, expect 860 J, allow an error carried forward.
One mark for writing the same number twice. That is not a gift, it is the physics: if all the kinetic energy came from gravitational potential energy, the two values must be equal, and recognising that is what is being tested. A candidate who starts calculating from scratch here has missed what the question was asking.
The part that follows asks for the height, using that energy in m g h, and the mark scheme adds a note worth having: it allows the use of v squared equals u squared plus 2 a s for full marks.
So the energy route and the motion equation route both earn everything. Two ways of thinking about the same fall, and the mark scheme does not prefer one. Where a question can be done either way, use whichever equation you can rearrange with more confidence.
Elsewhere the same series gives a mark simply for stating each equation before any numbers appear, allowing velocity in place of speed in the kinetic energy formula and instructing examiners to ignore the word gravity written in place of g.
When the transfer is not complete
In real situations some energy is transferred to the thermal store of the surroundings by friction and air resistance, so the kinetic energy gained is less than the gravitational potential energy lost.
Nothing is destroyed. It has been transferred somewhere the question is not asking about, which is why the numbers do not match and why efficiency questions attach to this topic so naturally.
If a question says smooth, or asks you to ignore air resistance, it is telling you the two values will be equal. If it does not, expect a difference and be ready to say where the missing energy went.
Spec 4.6-4.7
What you need to know
- Describe kinetic energy and what it depends on
- Describe gravitational potential energy
- Recall the two equations
Active recall
Quick check
Answer each question before opening the answer.
What is the equation for kinetic energy?
KE = ½ × m × v².
What is the equation for change in gravitational potential energy?
GPE = m × g × h.
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