Forces, mass and weight
Key idea: Mass is the amount of matter; weight is the gravitational force on it. Weight equals mass times gravitational field strength, so moving to the Moon changes weight, not mass.
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Guided lesson
Guided steps
- Name each force before deciding whether contact is needed.
- Identify the balloon’s force and whether the objects must touch.
- Compare mass with the gravitational pull on it.
- Find field strength as gravitational force per kilogram.
- Keep mass unchanged and use the local field to find weight.
- Convert grams to kilograms before calculating weight.
- Find mass on Mars, then weight on Earth.
- Compare mass and weight units and their measuring instruments.
- Explain why the balance and spring readings change differently.
- Keep mass unchanged when calculating weight on the Moon.
- Find weight and name the supporting force in each situation.
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ContinueAn astronaut on the Moon can leap far higher than on Earth, yet she is made of exactly the same matter. Her mass has not changed; her weight, the pull of gravity on her, is only about a sixth of her weight on Earth. Weight is one of several forces, some of which act only when objects touch and some of which act across a gap.
Contact and non-contact forces
A force is a push or a pull that one object exerts on another. Every force comes from an interaction between two objects. To describe a force, name the specific force first, then decide whether the two objects must touch for it to act.
- A contact force acts only while the objects touch.
- A non-contact force acts across a distance: the objects need not touch.
| Force | What it does | Type |
|---|---|---|
| friction | opposes one surface sliding, or trying to slide, over another | contact |
| air resistance | opposes an object moving through air | contact |
| tension | pulls along a taut string, rope or cable | contact |
| normal force | pushes out from a surface, at right angles to it | contact |
| gravitational force | attracts any two masses towards each other | non-contact |
| electrostatic force | attracts or repels charged objects | non-contact |
| magnetic force | attracts or repels magnets, and attracts magnetic materials | non-contact |
A book resting on a table has two forces on it: its weight, a gravitational force pulling it down, and the normal force from the table pushing it up. Lift the book off the table and the normal force disappears, because the book no longer touches the table. The gravitational force is still there.
“Contact force” is a type of force, not the name of one. When a situation shows which force acts, write its name: “normal force”, “friction”, “tension” or “air resistance”.
Check your understanding 1
A rubbed balloon pulls small pieces of paper up from a desk without touching them. Name the force and classify it.
Show answer
It is an electrostatic force: the rubbed balloon is charged. It acts without the balloon touching the paper, so it is a non-contact force.
Mass: the amount of matter
Mass is a measure of the amount of matter in a body. Its symbol is m and its SI unit is the kilogram (kg). Small masses are often given in grams: 1 kg = 1000 g.
The mass of an object changes only if matter is added or removed. Taking an object somewhere else does not add or remove matter, so a 70 kg astronaut still has a mass of 70 kg on the Moon, on Mars or in a spacecraft. Mass has a size but no direction, so it is a scalar.
Gravitational fields
Every mass attracts every other mass. The force is far too weak to notice between everyday objects, but the Earth has so much mass that its pull on everything near it is strong.
A gravitational field is a region in which a mass experiences a force due to gravitational attraction. The Earth is surrounded by a gravitational field. Any mass placed in the field is pulled by a gravitational force.
You cannot see a field. You detect it by the force it exerts on a mass: let go of a stone and it falls; hang it from a spring and the spring stretches.
Near the Earth, the gravitational force on a mass points towards the centre of the Earth. That is what “down” means. For a person in Singapore and a person in Brazil, “down” points in different directions in space, but both point to the Earth’s centre.
The Moon and other planets have gravitational fields of their own. The field strength at a surface depends on both the body’s mass and its radius. The Moon’s surface field is weaker than Earth’s; less mass alone is not enough to compare two bodies, because their sizes also matter.
Gravitational field strength
The gravitational field strength, g, at a point is the gravitational force per unit mass placed at that point.
Its unit is newtons per kilogram (N/kg). Near the Earth’s surface, g is about 10 N/kg: every kilogram placed there is pulled towards the Earth with a force of about 10 N. (The measured value is about 9.8 N/kg; this course uses 10 N/kg unless a question gives another value.)
| Place | g at the surface / N/kg (approximate) | Force on each 1 kg |
|---|---|---|
| Earth | 10 | 10 N |
| Moon | 1.6 | 1.6 N |
| Mars | 3.7 | 3.7 N |
| Jupiter | 25 | 25 N |
Worked example 1
Field strength on the Moon
Problem
A 2.0 kg rock sample hangs from a spring balance on the Moon. The balance shows a gravitational force of 3.2 N. Find the gravitational field strength there.
Show full solution
Choose the relationship
Method
Use g = gravitational force ÷ mass.Reason
Gravitational field strength is force per unit mass.Working
Answer
g = F ÷ m
Check the units
Method
Look at the units of the data.Reason
The force is in N and the mass in kg, so no conversion is needed.Working
Answer
N and kg
Substitute
Method
Divide the force by the mass.Reason
This gives newtons per kilogram.Working
Answer
g = 3.2 ÷ 2.0 = 1.6 N/kg
Check
Working
Answer
The table gives about 1.6 N/kg on the Moon, and N ÷ kg gives N/kg.
Weight: W = mg
The weight of an object is the gravitational force acting on it. Weight is a force, so it is measured in newtons (N), and it has a direction: towards the centre of the body that attracts it. Rearranging the definition of g gives
- Convert the mass to kilograms.
- Use the value of g for the place where the object is.
- Calculate W = mg and give the answer in newtons.
To find a mass from a weight, use m = W ÷ g. To find a field strength, use g = W ÷ m.
Worked example 2
Mass and weight on another world
Problem
A rover has a mass of 75 kg. On Mars, g = 3.7 N/kg. Find its mass and its weight on Mars.
Show full solution
Mass
Method
Keep the mass the same.Reason
Mass is the amount of matter, which does not depend on place.Working
Answer
Mass on Mars: 75 kg
Weight
Method
Use W = mg with the Martian field.Reason
Weight depends on the field strength where the object is.Working
Answer
W = 75 × 3.7 = 277.5 N
Round
Method
Give the answer to two significant figures.Reason
The data are given to two significant figures.Working
Answer
Weight on Mars: 280 N
Check
Working
Answer
On Earth the rover weighs 75 × 10 = 750 N. The Martian field is weaker, so a smaller weight makes sense.
Worked example 3
Weight with a conversion
Problem
An apple has a mass of 150 g. Find its weight on Earth.
Show full solution
Convert the mass
Method
Change grams to kilograms.Reason
W = mg gives newtons only from kilograms.Working
Answer
m = 150 ÷ 1000 = 0.150 kg
Find the weight
Working
Answer
W = 0.150 × 10 = 1.5 N. Using 150 without converting would give 1500 N, the weight of a large adult.
Check your understanding 2
A probe weighs 37 N on Mars, where g = 3.7 N/kg. Find its mass and its weight on Earth, where g = 10 N/kg.
Show the steps Optional working
Show answer
m = W ÷ g = 37 ÷ 3.7 = 10 kg. On Earth, W = 10 × 10 = 100 N.
Mass and weight are different quantities
| Mass | Weight |
|---|---|
| the amount of matter in a body | the gravitational force on the body |
| measured in kilograms (kg) | measured in newtons (N) |
| the same everywhere | changes when the gravitational field strength changes |
| has no direction | a force, directed towards the centre of the attracting body |
| measured with a beam balance | measured with a newton meter (spring balance) |
A balance and a newton meter measure different things
A newton meter measures weight. The object stretches a spring until the spring’s pull balances the object’s weight, and the scale reads the force in newtons. Take it to the Moon and the same object stretches the spring less, because its weight is less.
A beam balance measures mass. It compares the object with standard masses on the other side. Both sides are in the same gravitational field, so if they balance on Earth they also balance on the Moon: the balance gives the same mass in both places. This comparison needs a nonzero field acting equally on the two sides; freely floating pans do not provide a mass comparison in this way.
An electronic balance actually senses the force on its pan and converts it to a mass using the value of g it was set up for. On the Moon it would need to be set up again to read mass correctly.
Worked example 4
A bag of rice on Earth and on the Moon
Problem
A 5.0 kg bag of rice is measured on Earth and then on the Moon (g = 1.6 N/kg), first with a beam balance and then with a newton meter. Predict each reading.
Show full solution
Beam balance
Method
Compare the rice with standard masses.Reason
A beam balance compares masses, and the field acts equally on both pans.Working
Answer
5.0 kg on Earth and 5.0 kg on the Moon
Newton meter
Method
Use W = mg in each place.Reason
A newton meter measures the gravitational force on the rice.Working
Answer
Earth: 5.0 × 10 = 50 N; Moon: 5.0 × 1.6 = 8.0 N
Explain the difference
Working
Answer
The mass reading does not change because the amount of rice does not change. The weight reading falls because the Moon’s field is weaker.
Check your understanding 3
An astronaut weighs 800 N on Earth, where g = 10 N/kg. Find the astronaut’s mass and weight on the Moon, where g = 1.6 N/kg.
Show the steps Optional working
Show answer
Mass stays the same, so find it first: m = W ÷ g = 800 ÷ 10 = 80 kg. On the Moon her mass is still 80 kg, and her weight is W = mg = 80 × 1.6 = 128 N, about 130 N.
Check your understanding 4 The support changes while the mass stays
A 2.0 kg sample rests on a table where g = 6.0 N/kg. It is then hung at rest from a string in the same place. Calculate its weight. Which force balances that weight in each situation?
Show answer
On the table, the upward force is the normal force; after lifting, it is tension from the string. Both are contact forces. Weight is 2.0 × 6.0 = 12 N downwards towards the attracting body, and is a non-contact gravitational force in both situations. Removing table contact removes that table’s normal force; it does not remove gravity or change the sample’s mass.
Common mistakes
- Giving a weight in kilograms. The kilogram is a unit of mass: a 5 kg bag has a weight of 5 × 10 = 50 N on Earth.
- Saying an astronaut’s mass is less on the Moon. No matter is removed; her weight is less because g is smaller.
- Saying a non-contact force means no force acts. It means the objects need not touch.
- Saying a book resting on a table has no weight. Its weight still acts down; the normal force from the table acts up.
- Using grams in W = mg. A 200 g mass weighs 0.200 × 10 = 2.0 N, not 2000 N.
- Saying a newton meter reads the same anywhere. It measures weight, which depends on g; a beam balance compares masses where the same nonzero field acts on both sides.
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Syllabus and review details
- SEC G3 Combined Science Physics component 2027 · 2027
Physics section, PDF pages 8–24
Last reviewed: