Gravitational field strength and weight
Key idea: Weight is the gravitational force on a mass: W = mg. Moving to a different gravitational field changes an object's weight while its mass stays the same.
Loading guide controls…
Guided lessons · coming soon
Guided lesson
How Guide me works
Work through examples, try questions and get help when you need it. You stay in this lesson throughout.
- Read the short instruction beside the current activity.
- Try the question using its usual answer controls, or work on paper.
- Compare your answer, revisit an explanation if needed, and return to the same question.
A preview uses the public lesson and no guided start. Guided sessions are unscored. Free accounts get 2 starts a day; Premium includes unlimited starts in covered courses. You confirm before a new session starts.
Steps in this guide
These links open parts of the lesson. Use the guide’s actions to continue your session.
More
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Guided steps
- Read how masses attract through a gravitational field.
- Explain what gravitational field strength measures.
- Read weight per kilogram from the graph and check the units.
- Convert grams to kilograms, then calculate weight.
- Rearrange W = mg and calculate the bag’s mass.
- Calculate g from the stationary spring-balance reading.
- Write the definition of gravitational field strength.
- Compare mass and weight, including units and measuring instruments.
- Enter the astronaut’s mass and weight using the Moon’s field strength.
- Explain what each balance would read on the Moon.
- Follow why weight alone gives acceleration g.
- Show the unit cancellation and explain when acceleration equals g.
On this page
You stopped at:
ContinueRevision Mode is on. Worked examples are hidden.
Let go of an apple and it falls, although nothing touches it. The Earth pulls on it across the gap, and that pull is the apple’s weight. How large the weight is depends on two things: how much mass the apple has, and how strong gravity is where the apple is. The relationship W = mg joins them.
Gravitational fields
A gravitational field is a region in which a mass experiences a force due to gravitational attraction.
Every mass has a gravitational field around it. The Earth’s dominates ordinary near-surface weight measurements, although other bodies also have gravitational fields. The field idea explains how gravity acts without contact: the Earth sets up the field, and any mass placed in the field is pulled towards the Earth.
Gravitational field strength
The gravitational field strength, g, at a point is the gravitational force per unit mass on a mass placed at that point:
where F is the gravitational force on a mass m. Its unit is the newton per kilogram, N kg⁻¹.
A field strength of 9.8 N kg⁻¹ means that every kilogram placed there is pulled with a force of 9.8 N. Near the Earth’s surface g ≈ 9.8 N kg⁻¹, and many questions use 10 N kg⁻¹. On the Moon, g ≈ 1.6 N kg⁻¹. Always use the value the question gives.
Weight: W = mg
Weight is the gravitational force on an object. If each kilogram is pulled with a force g, then m kilograms are pulled with m times that force:
with W in newtons, m in kilograms and g in N kg⁻¹. Near the Earth, weight acts vertically downwards, towards the centre of the Earth. Convert any mass in grams to kilograms before you substitute.
Weight vs mass (near Earth)
A straight-line graph of weight against mass near Earth. The gradient is the gravitational field strength g.
Scroll across the figure to read all labels.
View figure data
| Mass (kg) | W = mg (g ≈ 10 N kg⁻¹) |
|---|---|
| 0 | 0 |
| 1 | 10 |
| 2 | 20 |
| 3 | 30 |
| 4 | 40 |
| 5 | 50 |
Worked example 1
Find weight from mass
Problem
A bag of rice has mass 3500 g. Take g = 10 N kg⁻¹. Find its weight.
Show full solution
Convert the mass to kilograms
Method
Write the mass in kilograms.Reason
g is a force per kilogram, so the mass must be in kilograms.
Working
Answer
m = 3500/1000 = 3.5 kgApply the weight relationship
Reason
Weight is the gravitational force on the whole mass: g newtons for every kilogram.
Working
Answer
W = mg = (3.5)(10) = 35 N downwards
Quick check
Guided practice 1
Find mass from weight
Problem
A force meter shows that the weight of a bag is 48 N on Earth. Take g = 9.8 N kg⁻¹. Find the mass of the bag.
Try it before opening the hints
Hints
Hint 1
identify the known quantities
The force-meter reading is the weight W, not the mass.
Hint 2
rearrange the equation
From W = mg, use m = W/g.
Show solution step by step
Make mass the subject
Method
Rearrange the weight relationship.Reason
The unknown is the mass; the weight and the field strength are given.Working
Answer
m = W/gCalculate the mass
Reason
Dividing newtons by newtons per kilogram leaves kilograms.Working
Answer
m = 48/9.8 = 4.9 kg (to 2 s.f.)
Quick check
Exam-style question 1
Define g and find it from measurements
Examination question
(a) Define gravitational field strength. [1 mark]
(b) A 2.0 kg mass hangs at rest from a spring balance, which reads 19.6 N. Calculate the gravitational field strength. [2 marks]
Write the definition, then calculate g
Check your understanding 1 Define gravitational field strength
Write the definition asked for in part (a). Say which force is involved and what “per unit mass” means.
Show answer
Gravitational field strength is the gravitational force per unit mass on a mass placed at that point. It tells you the force on each kilogram there; its unit is N/kg. Check both “gravitational force” and “per unit mass”.
Show solution step by step
State the definition
1 markMethod
Give g as a force per unit mass.Reason
The definition must say which force and per what.Working
Answer
Gravitational field strength is the gravitational force per unit mass on a mass placed at that point.Use the reading as the weight
1 markMethod
Take the spring-balance reading as the gravitational force.Reason
The mass hangs at rest, so the balance pulls up with a force equal to the weight.Working
Answer
g = W/mCalculate with the correct unit
1 markReason
The force is in newtons and the mass in kilograms.Working
Answer
g = 19.6/2.0 = 9.8 N kg⁻¹
Self-mark with the mark scheme
Tick each mark point that your answer includes.
Self-mark the definition, the relationship and the result with its unit separately.
Common mistake
Answering “acceleration due to gravity” for the definition loses that mark: give the gravitational force per unit mass.
Mass and weight are different
Mass is a measure of the amount of matter in a body. Moving a body to another place, such as the Moon, does not change how much matter it has, so its mass stays the same. Its weight changes, because g is different there. Mass also measures inertia: how hard the body is to speed up or slow down.
| Mass | Weight |
|---|---|
| Amount of matter; measures inertia | Gravitational force on the body |
| Scalar | Vector: towards the attracting body (locally downwards) |
| Unit: kilogram (kg) | Unit: newton (N) |
| Same everywhere | Changes with g |
| Measured with a beam balance | Measured with a spring balance (force meter) |
Try it yourself 1
An astronaut on the Moon
Changed gravitational field
The gravitational field strength on the Moon is about 1.6 N kg⁻¹. An astronaut has mass 60 kg on Earth. Find the astronaut’s mass and weight on the Moon.
Try it before opening the hints
Hints
Hint 1
decide what changes
Which quantity measures the amount of matter, and which measures gravitational force?
Hint 2
calculate the weight
Use W = mg with the Moon’s value of g.
Show solution step by step
Keep the mass unchanged
Method
The astronaut’s mass on the Moon is 60 kg.Reason
Mass is the amount of matter, which does not depend on the gravitational field.Working
Answer
m Moon = 60 kgCalculate the weight on the Moon
Reason
Weight is the gravitational force, so it uses the Moon’s smaller g.Working
Answer
W = mg = (60)(1.6) = 96 N downwards on the Moon
Quick check
Check your understanding 2 A beam balance on the Moon
Would a beam balance give the correct mass of an object on the Moon? Would a spring balance calibrated in kilograms on Earth? Explain.
Show answer
The beam balance would. It compares the weight of the object with the weight of standard masses on the other side. On the Moon both weights are smaller by the same factor, because both use the same g, so the balance still levels when the masses are equal.
The spring balance would not. It measures the force pulling on its spring. On the Moon the object’s weight is about one sixth of its weight on Earth, so the balance would read about one sixth of the true mass.
Why g is also an acceleration
You also met g in kinematics as the acceleration of free fall, about 9.8 m s⁻². In free fall, weight is the only force. Combining F = ma with W = mg gives ma = mg, so a = g in the downward direction. These equivalent units connect field strength with acceleration when gravity is the only force.
Spot the mistake 1
Are N kg⁻¹ and m s⁻² the same?
Learner response
On Earth, g ≈ 9.8 N kg⁻¹. A student claims that this cannot equal 9.8 m s⁻² because the units look different. Find the error and show the unit conversion. State the condition under which an object in this field accelerates at this value.
Use the definition of the newton
Show the unit cancellation and explain when acceleration equals g.
Show solution step by step
Write the newton in base units
Method
Replace N by kg m s⁻².Reason
A newton is defined as the force that gives 1 kg an acceleration of 1 m s⁻².Working
Answer
1 N = 1 kg m s⁻²Cancel the kilograms
Reason
The kilogram in the newton cancels the “per kilogram”.Working
Answer
9.8 N kg⁻¹ = 9.8 (kg m s⁻²)/kg = 9.8 m s⁻²
Common mistake
Common mistakes
- Giving mass in newtons or weight in kilograms.
- Writing “weight = mass”. Weight is a force; mass is an amount of matter.
- Substituting a mass in grams into W = mg.
- Defining g as “the force of gravity”. It is the gravitational force per unit mass.
- Saying an astronaut’s mass changes on the Moon. Only the weight changes.
- Leaving out the unit of g: N kg⁻¹, or m s⁻².
Spotted an error? Report a correction