Syllabus coverage
- State that mass is a measure of the quantity of matter in an object at rest relative to the observer
- State that weight is a gravitational force on an object that has mass
- Define gravitational field strength as force per unit mass, and recall and use the equation g = W/m, knowing that this is equivalent to the acceleration of free fall
- Know that weights and masses may be compared using a balance
- Describe, and use the concept of, weight as the effect of a gravitational field on a mass
Part of the IGCSE Physics syllabus 0625.
Mass and weight are two different quantities
Mass is a measure of the quantity of matter in an object at rest relative to the observer. It tells you how much stuff the object is made of, and it is measured in kilograms (kg). Mass is a scalar quantity, so it has a size but no direction, and it is the same wherever the object happens to be - on the Earth, on the Moon or floating in deep space.
Weight is the gravitational force acting on an object that has mass. Because it is a force, weight is measured in newtons (N) and it is a vector, so it always acts in a particular direction: straight down towards the centre of the Earth. Weight is not a property of the object on its own - it depends on the object and on the gravitational field the object is sitting in.
This is where most marks are lost. People say 'my weight is 60 kg', but that is a mass, not a weight. A 60 kg student has a weight of about 600 N on the Earth. The two quantities have different units, different symbols and different meanings, and an examiner will not accept one in place of the other.
- Mass is measured in kilograms (kg) and is a scalar; it does not change from place to place.
- Weight is measured in newtons (N) and is a vector; it acts towards the centre of the Earth.
- Mass is the amount of matter; weight is the gravitational force on that matter.
Gravitational field strength and the equation g = W/m
Gravitational field strength, given the symbol g, is defined as the force per unit mass. In other words, it is the weight that acts on each kilogram of an object. Its unit follows straight from the definition: newtons divided by kilograms, written N/kg. Near the surface of the Earth g is about 10 N/kg, which means that every kilogram of mass is pulled downwards with a force of about 10 N.
Because g is the weight of each kilogram, the weight of an object is simply its mass multiplied by g. The two forms of the equation you must know are:
g = W / m and W = m x g, where W is the weight in newtons, m is the mass in kilograms and g is the gravitational field strength in N/kg. Use the first form when a question gives you the weight and asks for g, and the second when it gives you a mass and asks for the weight.
Put some numbers in. A student of mass 60 kg standing on the Earth, where g = 10 N/kg, has weight W = m x g = 60 x 10 = 600 N. The same student standing on the Moon, where g = 1.6 N/kg, has weight W = 60 x 1.6 = 96 N. The mass is still 60 kg in both places; only the weight has changed, because g has changed.
Weight on different planets and moons
The value of g is not fixed. It depends on the mass of the planet or moon and on its radius, so it is different at the surface of every body in the Solar System. A large, massive planet such as Jupiter has a much stronger gravitational field than the Earth, and a small body such as the Moon has a much weaker one.
Because W = m x g, the weight of an object changes in proportion to g, while the mass stays exactly the same. An astronaut who weighs 600 N on the Earth weighs only 96 N on the Moon, but still has a mass of 60 kg and still needs exactly the same force to be accelerated in space. This is why astronauts bounce easily on the Moon but their bodies behave the same way they would on the Earth.
The table shows how the weight of the same 60 kg student changes from place to place. Every value is found from W = m x g, so you can check any line for yourself.
| Place or body | g / N/kg | Weight of a 60 kg student / N |
|---|---|---|
| Moon | 1.6 | 96 |
| Mercury | 3.7 | 222 |
| Mars | 3.7 | 222 |
| Venus | 8.9 | 534 |
| Earth | 10 | 600 |
| Saturn | 10.4 | 624 |
| Jupiter | 25 | 1500 |
Measuring mass and weight: balances and newton meters
You compare masses with a balance. A beam balance has two pans, and you place the objects on the pans and see which side goes down. The object with the greater mass pushes its pan down further, and when the beam is level the two masses are equal. A balance works by comparing masses, so it gives the same answer on the Earth and on the Moon: both pans are pulled by the same value of g, so g cancels out of the comparison.
You measure weight with a newton meter or spring balance. The object pulls on a spring and stretches it, and the scale is marked in newtons. Because the reading depends on g, a newton meter gives a different reading on the Moon from the one it gives on the Earth, even for the same object. A digital bathroom scale is really a newton meter that has been calibrated to display mass in kilograms, which is why you must set the right 'gravity' on it.
The practical rule is easy to remember: a balance compares masses, a newton meter measures weight. If a question asks you to compare the masses of two objects, use a balance; if it asks you to measure the weight of an object, use a newton meter.
- Balance: compares masses; reading is the same wherever g is, because both pans feel the same g.
- Newton meter (spring balance): measures weight in newtons; reading changes when g changes.
- Digital scales show a mass in kg by dividing the measured weight by a built-in value of g.
Free fall: why g is also an acceleration
Drop a coin and it speeds up as it falls, with an acceleration of about 10 m/s2 near the Earth's surface. If we ignore air resistance, the only force acting on the coin is its weight, so the coin is said to be in free fall. The acceleration it gains is called the acceleration of free fall.
Now apply Newton's second law to the coin. The resultant force is its weight W, so the acceleration is a = W / m. But the definition of gravitational field strength is g = W / m, so the acceleration of free fall is numerically equal to g. This is why g can be written either as 10 N/kg or as 10 m/s2, and why the two units are really the same thing: 1 N/kg means 1 N of force on each kilogram, and 1 N acting on 1 kg gives it an acceleration of 1 m/s2.
The equivalence explains a surprising result. Two objects of different mass dropped together in a vacuum hit the ground at the same time. The heavier object has a bigger weight, but it also has more mass to accelerate, and the two effects cancel exactly. In air, a feather falls more slowly than a stone only because air resistance affects the feather much more.
Weight as the effect of a gravitational field
A gravitational field is a region in which a mass experiences a force. The Earth is surrounded by a gravitational field, and any object with mass placed inside that field is pulled towards the centre of the Earth. That pull is what we call the weight of the object. Weight is therefore the effect of the gravitational field on a mass.
Thinking of weight this way explains everything about the topic. The field strength g tells you how strong the pull is at each point: a strong field means a large force on each kilogram, so a large weight. The Moon has a weaker field because it has less mass than the Earth, so an object on the Moon feels a smaller pull and has a smaller weight. Far out in space, where the field is extremely weak, the same object would feel almost no weight at all, yet its mass would be completely unchanged.
The direction matters too. The weight always acts towards the centre of the body that creates the field, so on the Earth every weight acts vertically downwards. When you draw a weight on a diagram, draw it as an arrow from the centre of the object pointing straight down, and label it W or weight.
Key terms you must be able to define
- Mass
- A measure of the quantity of matter in an object at rest relative to the observer, measured in kilograms (kg); it is a scalar and does not change with position.
- Weight
- The gravitational force acting on an object that has mass, measured in newtons (N); it is a vector acting towards the centre of the Earth.
- Gravitational field strength (g)
- The force per unit mass, measured in newtons per kilogram (N/kg); defined by g = W / m and equal to the acceleration of free fall.
- Newton (N)
- The unit of force; one newton is the force that gives a mass of 1 kg an acceleration of 1 m/s2.
- Acceleration of free fall
- The acceleration of an object when the only force acting on it is its weight, about 10 m/s2 near the Earth's surface and numerically equal to g.
- Balance
- An instrument that compares masses by balancing objects against each other, so its reading is the same wherever g has any value.
- Newton meter (spring balance)
- An instrument that measures weight in newtons from the extension of a spring; its reading changes when the value of g changes.
- Gravitational field
- A region in which a mass experiences a force; the weight of an object is the effect of the gravitational field on its mass.
Applied to the real world
Cambridge sets physics in unfamiliar contexts - a car braking, a power station, a hospital scanner, a satellite. Use these as models for how to apply the physics, then write your own.
To compare the masses of two metal blocks you place them on the pans of a beam balance. The pan that goes down holds the greater mass, and when the beam is level the masses are equal. This works on the Earth or on the Moon, because both pans are pulled by the same value of g, so the comparison does not depend on where you are. To find the weight of a block instead, you hang it from a newton meter and read the force in newtons.
An astronaut has a mass of 80 kg. On the Earth the astronaut's weight is W = m x g = 80 x 10 = 800 N. On the Moon, where g is only 1.6 N/kg, the weight is W = 80 x 1.6 = 128 N. The mass is still 80 kg, so the astronaut still has to push the same mass around, but the weaker gravitational field means far less force is needed to lift the body, which is why astronauts can jump so high.
A patient is weighed on a balance that compares the patient against known masses, which gives the mass in kilograms no matter where the hospital is. A digital scale instead measures the weight and divides it by a stored value of g to display a mass. If a digital scale is used on the Moon without being recalibrated, it shows the wrong mass, because the weight it measures is smaller while the mass has not changed.
A crane is rated by the weight it can lift, not the mass, because the weight is the force the cable and hook must carry. A load of mass 500 kg on the Earth has weight W = m x g = 500 x 10 = 5000 N. The crane operator needs the weight in newtons to check that the cable is strong enough, and would use W = m x g to convert the mass on the delivery note into the force the crane must support.
Mission planners must know the gravitational field strength at the surface of every body they visit. A rover of mass 200 kg weighs 2000 N on the Earth but only 200 x 3.7 = 740 N on Mars. The smaller weight means the rover's wheels need less grip to support it, but its mass of 200 kg is unchanged, so the rocket that launched it had to accelerate exactly the same mass on the way out.
Flashcards
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Exam-style questions
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Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Exam technique for this topic
- Check the unit before you write the answer. Mass is always in kilograms (kg), weight is always in newtons (N) and g is always in newtons per kilogram (N/kg). A weight given in kg scores nothing.
- Learn both forms of the equation, g = W/m and W = m x g. Use W = m x g to find a weight from a mass, and g = W/m to find the field strength or the mass from a weight.
- Unless a question gives you a different value, use g = 10 N/kg for the Earth. If a question gives g = 9.8 N/kg, use 9.8 exactly, and if it gives another planet's value, use that value.
- For a question about moving an object to another planet, say clearly that the mass is unchanged and only the weight changes, because g has changed. The mark is for the link between weight, mass and g.
- Remember that g has the same numerical value as the acceleration of free fall, so it can be written as 10 N/kg or 10 m/s2. If a question asks why the two are the same, refer to W = m x g and a = W/m.
- For instruments, say that a balance compares masses and a newton meter measures weight. Do not claim that a balance measures weight, because a balance gives the same reading on the Moon as on the Earth.
Why students lose marks here
Where this fits in IGCSE Physics
This page is one topic of Cambridge IGCSE Physics 0625. IGCSE Physics is the course home: every area and every topic in Cambridge's own order, the papers you sit and what each one tests, and the exam-practice tools. The full topic list, with each topic linked to its revision page, is on the IGCSE Physics syllabus page.