Gravity is the attractive force of the Earth, or of any other celestial body, which pulls objects towards its centre. Weight is the force with which the Earth pulls an object towards its centre, and it is found by multiplying the mass of the object by the acceleration due to gravity.
Newton and the falling apple
Look at a waterfall and at a stone dropped from the top of a house. Is the direction of the two motions the same? It is, and both go the same way: downwards. In the middle of the seventeenth century Newton saw an apple fall from a tree and went looking for the answer to exactly that sort of curiosity. He identified the Earth's attractive force as the cause of an object falling towards the Earth's surface, and this attractive force of the Earth is called gravity.
People had watched things fall for as long as there have been people, so noticing that an apple falls was not the discovery. Everybody already knew that. What Newton did was to ask a stranger question: is the force that pulls the apple down the same force that keeps the Moon going round the Earth? Before him, the sky and the ground were treated as two different worlds with two different sets of rules. He proposed that they were one world with one rule, and that the same pull reaches from a tree in an orchard all the way out to the Moon. That is why his idea mattered. He did not find a new fact. He noticed that two things nobody had connected were the same thing.
Gravity and gravitation are not the same word
These two are easy to mix up and the textbook keeps them apart, so it is worth being careful.
| Term | What it means |
|---|---|
| Gravitation | Newton also found that every object in the universe pulls every other object towards its centre with an attractive force. That universal force is called gravitation. It works between any two objects at all, including you and your chair. |
| Gravity | The attractive force belonging to a celestial body such as the Earth is called gravity, and it acts towards the centre of that body. So gravity is the particular case of gravitation that involves a planet, a moon or a star. |
Notice the phrase towards the centre, because it explains something you may never have thought about. Down is not a fixed direction in space. Down means towards the centre of the Earth, so a person in Nepal and a person on the far side of the world are both being pulled downwards and are being pulled in opposite directions as seen from outside. Nobody is upside down, because down is always defined by wherever the centre happens to be.
What gravity is doing for you right now
The reason the atmosphere is able to stay wrapped around the Earth is the Earth's gravity. Without it the air would simply drift away into space, and that is exactly what has happened to the Moon, which has almost no atmosphere. In the same way, it is because of the Earth's gravity that water, hail and snow fall from the sky towards the Earth's surface.
Because of gravity, when an object is thrown upwards or falls downwards, a change happens in its velocity. The change in velocity in unit time is called acceleration. In an object that has gone up or is falling down, the acceleration is produced by the Earth's gravity, and because it is produced in the object by the Earth's gravity it is called acceleration due to gravity. The average value of acceleration due to gravity, written as g, is 9.8 metres per second squared. And it is because of the Earth's gravity that any object has weight at all.
Mass and weight: the pair everybody confuses
This is the most muddled pair of words in school physics, and the muddle is built into ordinary speech. People say my weight is fifty kilograms, and that sentence is wrong twice over, which is why it is worth taking slowly.
| Mass | Weight | |
|---|---|---|
| What it is | How much matter the object contains, that is, how much stuff there is | How hard a particular planet is pulling on that stuff |
| Does it change if you move? | No. It is the same on the Earth, on the Moon and in deep space | Yes. It depends entirely on where you are standing |
| Is it a force? | No. It is a quantity of matter | Yes. Weight is a kind of force, which is why it is measured in newton |
| Unit | Kilogram (kg) | Newton (N) |
| Scalar or vector | Scalar. A magnitude alone describes it | Vector. Its direction is always towards the centre of the Earth |
| Measured with | A beam balance, which compares one mass against another | A spring balance, which measures how hard the pull is |
Here is the thought experiment that separates the two for good. Suppose you travel to the Moon. Not one atom of you has been left behind, so the amount of matter in your body is exactly what it was: your mass has not changed at all. But the Moon is much smaller than the Earth and pulls far more weakly, so its value of g is about one sixth of ours. Since weight is mass multiplied by g, your weight on the Moon is about one sixth of your weight here. Same person, same body, same breakfast, and the spring balance now reads a completely different number. That is the proof that weight is not a property of you. It is a relationship between you and whatever large body you happen to be standing near.
Weight, and how it is measured
The force with which the Earth pulls an object towards its centre is the weight of that object. In mathematical form, the product of an object's mass and the acceleration due to gravity is its weight. More gravity acts on an object with more mass, and less gravity acts on an object with less mass, so the object on which more gravity acts has more weight. A spring balance is used for measuring weight. Since weight is itself a kind of force, it is measured in newton.
| Weight = mass × acceleration due to gravity, that is, \( W = m \times g \) |
Worked example 1: from mass to weight
Calculate the weight of an object whose mass is 50 kg, taking g as 9.8 metres per second squared.
| Mass (m) = 50 kg, and g = 9.8 m/s². Weight (W) = ? |
| W = m × g = 50 × 9.8 = 490 N |
So the weight of the object is 490 N. Look at that answer next to the everyday sentence my weight is fifty kilograms and you can see both mistakes at once. Fifty is a mass and not a weight, and the kilogram is a unit of mass and not of force. What a bathroom scale really does is measure the pull and then quietly convert it back into kilograms for you, because that is the number people expect to see.
Worked example 2: from weight to mass
Calculate the mass of an object whose weight is 1200 N, taking g as 9.8 metres per second squared.
| Weight (W) = 1200 N, and g = 9.8 m/s². Mass (m) = ? |
| From W = m × g, rearrange to \( m = \dfrac{W}{g} = \dfrac{1200}{9.8} = 122.45 \) kg |
A mass answer must end in kg and a weight answer must end in N, and swapping them costs a mark even when the arithmetic is perfect. There is an easy way to tell which way round a calculation has gone. If your answer is a bigger number than you started with, you have almost certainly multiplied by g and found a weight in newton. If it is a smaller number, you have divided by g and found a mass in kilograms. On the Earth, the weight in newton is always about ten times the mass in kilograms, so if those two numbers come out close to each other, something has gone wrong.
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