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Unlock This CourseIn everyday life people say things like "I weigh 60 kg". In physics that sentence is wrong. Kilograms measure mass, not weight. Mass and weight are two different quantities with two different units, and examiners expect you to keep them apart.
Remember, weight is the gravitational force that pulls an object towards the Earth. Because it is a force, it is measured in newtons and it has a direction: downwards, towards the centre of the Earth.
Key terms:
Mass is the amount of matter in an object.
It is measured in kilograms (kg), using a balance.
Mass has size only, so it has no direction.
The mass of an object is the same everywhere. Moving an object to a new place does not change how much matter is in it.
Weight is a force: the pull of gravity on an object.
It is measured in newtons (N), using a newton meter.
Weight has size and direction. It acts downwards.
The weight of an object depends on where it is, because it depends on the gravitational field strength there.
A bathroom scale is a good example of the mix-up. It shows a reading in kilograms, so it is telling you your mass. Your weight is the force with which gravity pulls you down, and it is a number of newtons.
Weight, mass and gravitational field strength are linked by one equation:
weight = mass × gravitational field strength
W = m × g
You must learn this equation. It is not given on the formulae page of the exam paper.
| Quantity | Symbol | Unit |
|---|---|---|
| Weight | W | newton (N) |
| Mass | m | kilogram (kg) |
| Gravitational field strength | g | newton per kilogram (N/kg) |
On Earth, g = 10 N/kg. This is the value used in Edexcel exam papers. It means that gravity pulls on every kilogram of mass with a force of 10 N. So a 1 kg mass has a weight of 10 N, a 2 kg mass has a weight of 20 N, and so on. Weight is directly proportional to mass.
The value of g is different on the Moon and on other planets. That is why an object's weight changes when it leaves the Earth, even though its mass stays the same. If a question is set somewhere else, it will give you the value of g to use.
You can rearrange W = m × g to find any one of the three quantities:
A sack of potatoes has a mass of 5 kg. Calculate its weight on Earth.
W = m × g
W = 5 × 10
W = 50 N
A bar of chocolate has a mass of 250 g. Calculate its weight on Earth.
The mass must be in kilograms: 250 / 1000 = 0.25 kg
W = m × g
W = 0.25 × 10
W = 2.5 N
A suitcase has a weight of 180 N on Earth. Calculate its mass.
m = W / g
m = 180 / 10
m = 18 kg
A rover on the surface of Mars has a mass of 900 kg. Its weight on Mars is 3330 N. Calculate the gravitational field strength on Mars.
g = W / m
g = 3330 / 900
g = 3.7 N/kg
Notice that the mass of the rover is still 900 kg on Mars. Only its weight is different from its weight on Earth, which would be 900 × 10 = 9000 N.
A quick check. On Earth, the weight in newtons is always ten times the mass in kilograms. A handy fact to remember is that a mass of 100 g (0.1 kg) has a weight of 1 N. A medium apple weighs about 1 N.
You measure weight with a newton meter. Hold the newton meter by its top ring so that it hangs straight down. Check that it reads zero with nothing on the hook. Then hang the object from the hook. The weight of the object stretches the spring inside, and a marker moves along a scale marked in newtons. Wait until the object is still, then read the scale with your eye level with the marker.
A student hangs different masses from a newton meter and records the readings:
| Mass in g | Mass in kg | Weight in N |
|---|---|---|
| 100 | 0.1 | 1.0 |
| 200 | 0.2 | 2.0 |
| 300 | 0.3 | 3.0 |
| 400 | 0.4 | 4.0 |
If you plot weight (up the side) against mass in kilograms (along the bottom), the points make a straight line through the origin. This shows that weight is directly proportional to mass. The gradient of the line is weight divided by mass, which is g. Here the gradient is 4.0 / 0.4 = 10 N/kg.
Weight is a force, so it can be combined with other forces to find a resultant force. Questions often give you a mass and expect you to work out the weight yourself.
A model rocket has a mass of 0.5 kg. Its engine gives an upward thrust of 20 N. Ignore air resistance. Calculate the acceleration of the rocket as it leaves the ground.
Step 1: find the weight.
W = m × g = 0.5 × 10 = 5 N downwards
Step 2: find the resultant force.
F = 20 − 5 = 15 N upwards
Step 3: use a = F / m.
a = 15 / 0.5
a = 30 m/s2 upwards
An astronaut has a toolbox with a mass of 12 kg.
(a) State the equation linking weight, mass and gravitational field strength. [1 mark]
(b) Calculate the weight of the toolbox on Earth. Use g = 10 N/kg. [2 marks]
(c) The astronaut takes the toolbox to the Moon. On the Moon the toolbox has a weight of 19.2 N. Calculate the gravitational field strength on the Moon. Give the unit. [3 marks]
(d) State the mass of the toolbox on the Moon. Give a reason for your answer. [2 marks]
(a) weight = mass × gravitational field strength, or W = m × g (1)
(b) W = 12 × 10 (1)
W = 120 N (1)
(c) g = W / m = 19.2 / 12 (1)
g = 1.6 (1)
N/kg (1)
(d) 12 kg (1) The mass is the amount of matter in the toolbox, and this does not change when the toolbox is moved to a different place. (1)
In part (c) the unit has its own mark, so write N/kg even if you are unsure of your number. In part (d) do not be tempted to calculate anything. The mass was given at the start of the question and it is the same on the Moon as on Earth.