AQA GCSE Combined Science (8464), Higher tier · Physics › Forces › Forces and their interactions
Practise Gravity. 13 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Weight is the force acting on an object due to gravity. You must recall and use W = m g, explain the difference between mass and weight, and know that weight acts at the centre of mass. Expect short calculations and explanations comparing weights on the Earth, the Moon and other planets.
Grade by grade
What you need to be able to do, from the first marks up to the top grade.
3
State that weight is a force due to gravityWeight is measured in newtons (N); mass is measured in kilograms (kg).
4
Calculate weight using W = m gFor example, 60 kg × 9.8 N/kg = 588 N.
5
Rearrange W = m g for mass or gm = W ÷ g and g = W ÷ m.
5
Describe how to measure weightHang the object from a calibrated spring-balance (a newtonmeter).
6
Explain why weight changes but mass does notWeight depends on the gravitational field strength where the object is; mass is the amount of matter and stays the same.
6
State that weight acts at the centre of massThe weight of an object can be treated as acting at a single point called its centre of mass.
7
Use the proportionality between weight and massW ∝ m, so a graph of weight against mass is a straight line through the origin with a gradient equal to g.
Notes
Mass and weight
Mass is the amount of matter in an object, measured in kilograms (kg). It is the same wherever the object is.
Weight is the force acting on an object due to gravity, measured in newtons (N).
Close to the Earth, the force of gravity is due to the gravitational field around the Earth.
Weight depends on the gravitational field strength (g) at the point where the object is. On the Moon, g is much smaller, so your weight is smaller, but your mass is unchanged.
Calculating weight
weight = mass × gravitational field strength: W = m g
W in newtons (N), m in kilograms (kg), g in newtons per kilogram (N/kg).
On Earth, g = 9.8 N/kg. Use the value given in the question.
Weight and mass are directly proportional (W ∝ m): in the same place, doubling the mass doubles the weight.
Convert grams to kilograms first: 250 g = 0.25 kg.
Centre of mass and measuring weight
The weight of an object can be considered to act at a single point, called its centre of mass.
For a uniform, symmetrical object, such as a ruler or a ball, the centre of mass is at its centre.
Weight is measured using a calibrated spring-balance, called a newtonmeter.
Cheatsheet
W = m g (weight = mass × gravitational field strength)
Units: W in N, m in kg, g in N/kg
g on Earth = 9.8 N/kg
Weight is a force (vector); mass is the amount of matter (scalar)
W ∝ m in a given gravitational field
Weight acts at the centre of mass
Measure weight with a newtonmeter (calibrated spring-balance)
How to answer each type of question
Calculate weight
2 marks4
Check the mass is in kg.
Write W = m g and substitute.
Give the answer in newtons.
Example. A suitcase has a mass of 23 kg. gravitational field strength = 9.8 N/kg Calculate the weight of the suitcase.
Show the model answer
W = 23 × 9.8 (1) W = 225.4 N (1)
Two-step: weight in a different gravitational field
3 marks6
Use the weight and g in the first place to find the mass: m = W ÷ g.
The mass is the same everywhere.
Use the new value of g to find the new weight.
Example. A piece of equipment has a weight of 96 N on the Moon, where the gravitational field strength is 1.6 N/kg. Calculate its weight on Earth, where the gravitational field strength is 9.8 N/kg.
Show the model answer
m = 96 ÷ 1.6 = 60 kg (1) W = 60 × 9.8 (1) W = 588 N (1)
Explain the difference between mass and weight
2 to 3 marks6
Say what happens to the mass and why (amount of matter unchanged).
Say what happens to the weight.
Give the reason: a different gravitational field strength.
Example. An astronaut travels from the Earth to the Moon. Explain what happens to her mass and to her weight.
Show the model answer
Her mass stays the same because the amount of matter in her body does not change (1). Her weight decreases (1) because the gravitational field strength on the Moon is smaller than on the Earth (1).
Interpret a weight–mass graph
2 to 3 marks7
A straight line through the origin means weight is directly proportional to mass.
Gradient = change in weight ÷ change in mass = g, in N/kg.
Example. A student hangs different masses from a newtonmeter and plots a graph of weight against mass. The line is straight and passes through the origin. A mass of 0.50 kg has a weight of 4.9 N. (a) What does the graph show about the relationship between weight and mass? (b) Determine the gradient of the line and state what it represents.
Show the model answer
(a) Weight is directly proportional to mass (1). (b) gradient = 4.9 ÷ 0.50 = 9.8 N/kg (1) It is the gravitational field strength (1).
Shortcuts and memory tricks
Quick check: weight in N is about ten times the mass in kg. A 70 kg person weighs about 700 N (686 N with g = 9.8 N/kg).
The units give the equation away: kg × N/kg = N.
Mass is the matter; weight is the pull on it.
Moon check: g on the Moon is about one-sixth of g on Earth, so weights there are about one-sixth as big.
Where marks are lost
Giving a weight in kg. Weight is a force, so its unit is N.
Forgetting to convert grams to kilograms before using W = m g.
Saying an object's mass changes on the Moon. Only its weight changes.
Using g = 10 N/kg when the question gives 9.8 N/kg.
Calling g 'gravity'. Its name is gravitational field strength.
Exam technique
W = m g is one you must recall: it is not on the equations sheet.
Write the equation, substitute the values, then give the answer with a unit. Each step can earn a mark.
When comparing places, say that g is different so the weight is different, but the mass is the same.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
Calculate the weight of the backpack on the Earth. gravitational field strength = 9.8 N/kg Use the equation: weight = mass × gravitational field strength
117.6 N (118 N) N
State the direction in which the weight of the boulder acts.
Towards the centre of the Earth (vertically downwards).
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy6 marks
An astronaut’s backpack has a mass of 12 kg.
(a) Calculate the weight of the backpack on the Earth. gravitational field strength = 9.8 N/kg Use the equation: weight = mass × gravitational field strength[2]
(b) The gravitational field strength on the Moon is 1.6 N/kg. Calculate the weight of the backpack on the Moon.[2]
(c) What is the mass of the backpack on the Moon?[1]
(d) Name the instrument used to measure weight.[1]
Show the answer and mark scheme
(a)Answer: 117.6 N (118 N) N
W = 12 × 9.8
117.6 (N)
(b)Answer: 19.2 N
W = 12 × 1.6
19.2 (N)
(c)Answer: 12 kg
12 (kg)
(d)Answer: A newtonmeter (calibrated spring balance).
newtonmeter / (calibrated) spring balance
Question 2Medium3 marks
(a) A student hangs a stone from a newtonmeter. In air, the newtonmeter reads 3.4 N. Calculate the mass of the stone. gravitational field strength = 9.8 N/kg[2]
(b) The student then lowers the stone, still hanging from the newtonmeter, until it is fully submerged in a beaker of water. The newtonmeter reading decreases. Suggest why.[1]
Show the answer and mark scheme
(a)Answer: 0.35 kg (0.347 kg) kg
m = 3.4 ÷ 9.8
0.35 (kg)
(b)Answer: The water exerts an upward force (upthrust) on the stone, so a smaller tension now supports it.
there is now an upward force (upthrust) from the water acting on the stone, in addition to its weight and the tension, so the tension needed to support it is less than its weight
Question 3Hard7 marks
An astronaut has a mass of 75 kg. The International Space Station (ISS) orbits about 400 km above the Earth’s surface. The gravitational field strength at the height of the ISS is 8.7 N/kg. Gravitational field strength at the Earth’s surface = 9.8 N/kg
(a) Calculate the weight of the astronaut on the surface of the Earth.[2]
(b) Calculate the percentage decrease in the weight of the astronaut when the astronaut is on the ISS, compared with on the surface of the Earth.[3]
(c) A student says: ‘Astronauts float inside the ISS because there is no gravity in space.’ Use the information to explain why the student is wrong.[2]
Show the answer and mark scheme
(a)Answer: 735 N
W = 75 × 9.8
735 (N)
(b)Answer: 11% (11.2%) %
weight on the ISS = 75 × 8.7 = 652.5 (N)
decrease = 735 − 652.5 = 82.5 (N)
(82.5 ÷ 735) × 100 = 11 (%)
(c)Answer: g at the ISS is 8.7 N/kg, so the astronaut still has a weight of about 650 N.
the gravitational field strength at the ISS is 8.7 N/kg, which is not zero
so the astronaut still has a (large) weight / a weight of about 650 N