What you need to know
Cambridge IGCSE Physics 0625 · Syllabus 1.3 Mass and weight, and 1.4 Density. Tick each one when you can do it. Your ticks are saved on this device.
Core
- 1.3.1State that mass is a measure of the quantity of matter in an object at rest relative to the observer.
- 1.3.2State that weight is a gravitational force on an object that has mass.
- 1.3.3Define gravitational field strength as force per unit mass; recall and use g = W / m, and know it equals the acceleration of free fall.
- 1.3.4Know that weights (and masses) may be compared using a balance.
- 1.4.1Define density as mass per unit volume; recall and use ρ = m / V.
- 1.4.2Describe how to find the density of a liquid, a regular solid and an irregular solid that sinks (by displacement), with calculations.
- 1.4.3Decide whether an object floats from density data.
Extended (Supplement)
- 1.3.5Describe, and use the idea of, weight as the effect of a gravitational field on a mass.
- 1.4.4Decide whether one liquid will float on another from density data, given that they do not mix.
Contents
3.1Mass Core
How much "stuff" is in an object.
Mass is a measure of the quantity of matter in an object (at rest relative to the observer).
The SI unit of mass is the kilogram (kg). Small masses are measured in grams (1 kg = 1000 g) and very large ones in tonnes (1 tonne = 1000 kg). Mass is a scalar.
The key fact: an object's mass does not change when you move it somewhere else. A 70 kg astronaut is still 70 kg on the Moon, because they are made of exactly the same amount of matter.
- A 5 kg bag of rice from a shop in Mumbai is still 5 kg in London, on a plane, or on the Moon. You still get the same amount of rice to eat.
- Doctors and nurses record a baby’s mass in kg to check that it is growing, because mass measures how much body the baby has.
- The "kg" on bathroom scales, shopping bags and recipe books is always a mass.
3.2Weight Core
The pull of gravity on a mass.
Weight is the gravitational force on an object that has mass.
Because weight is a force, it is measured in newtons (N), and it is a vector: it has a direction, towards the centre of the Earth (or whichever planet you are on).
We calculate weight from mass using the gravitational field strength g (on Earth, g ≈ 9.8 N/kg):
W = m × g weight (N) = mass (kg) × gravitational field strength (N/kg)Weight is measured with a newton meter (spring balance). The weight pulls the spring down, and the more it weighs, the more the spring stretches.
Mass and weight are different
| Mass | Weight | |
|---|---|---|
| What it is | Quantity of matter | Gravitational force on the mass |
| Unit | kilogram (kg) | newton (N) |
| Scalar or vector? | Scalar | Vector (acts towards the centre of the planet) |
| Changes on the Moon? | No | Yes: about 1/6 of its Earth value |
| Measured with | Balance | Newton meter (spring balance) |
- Astronauts on the Moon bounce along in big hops. Their mass hasn’t changed, but their weight is only about one-sixth of what it is on Earth, so their legs push them much higher.
- In everyday speech people say "I weigh 50 kg". In physics that is your mass; your weight is about 50 × 9.8 = 490 N.
- A lift (elevator) has a maximum load sign such as "8 persons, 544 kg". Engineers design the cables to hold the weight of that mass: about 544 × 9.8 ≈ 5300 N.
3.3Gravitational field strength Core
How strongly a planet pulls on each kilogram.
Gravitational field strength, g, is the force per unit mass: the weight of each 1 kg.
On Earth g ≈ 9.8 N/kg, so every kilogram is pulled down with a force of 9.8 N. The units N/kg and m/s2 are equivalent, so g is the same number as the acceleration of free fall you met in Chapter 2. That's why every object falls with the same acceleration: double the mass means double the weight, so the acceleration stays the same.
Weight as the effect of a gravitational field Extended
A planet is surrounded by a gravitational field: a region where any mass feels a force. Your weight is simply the effect of this field on your mass. The bigger the mass, the bigger the force; the stronger the field (the bigger g), the bigger the force. Far out in space, away from planets and stars, the field is very weak, so an object has almost no weight, even though its mass is unchanged.
- Jupiter’s field is about 2.5 times stronger than Earth’s, so a 60 kg student would weigh about 1500 N there and could hardly stand up.
- Astronauts on the International Space Station seem "weightless", but the station is only about 400 km up, where g is still about 8.7 N/kg. They float because they and the station are falling around the Earth together.
- Engineers use W = mg to work out the force on bridges, shelves and lift cables from the masses they must hold.
3.4Comparing masses with a balance Core
Beam balances, spring balances and electronic balances.
A beam balance compares the weight of an object with the weight of known standard masses. When the beam is level, the two weights are equal. Both pans are in the same gravitational field, so equal weights mean equal masses. That is why we say weights (and masses) can be compared using a balance.
A spring balance (newton meter) measures weight directly, so its reading changes if g changes. A beam balance compares two weights in the same field, so it gives the same answer anywhere.
In the lab you will usually use an electronic (top-pan) balance. It measures the force on its pan and displays the mass in grams, set up for Earth's value of g. Press tare (zero) first if you are using a container.
- Vegetable sellers in Indian markets still use the traditional tarazu, a beam balance with two pans and iron weights. It works exactly like Fig 3.7.
- Jewellers weigh gold on very sensitive electronic balances that read to 0.001 g, because even a tiny mass of gold is valuable.
- Airline check-in scales show your suitcase in kg, so passengers can check it is under the 23 kg limit.
3.5Density Core
How tightly the mass is packed.
Density is the mass per unit volume.
ρ is the Greek letter "rho". The units are g/cm3 or kg/m3. Water has a density of 1.0 g/cm3 = 1000 kg/m3.
1 g/cm3 = 1000 kg/m3. So to go from g/cm3 to kg/m3, multiply by 1000: aluminium 2.7 g/cm3 = 2700 kg/m3.
Every pure substance has its own density, so density helps identify materials:
- Racing bicycles are made from aluminium or carbon fibre rather than steel. These materials have a much lower density, so the frame has a smaller mass for the same size.
- Gold is very dense (19.3 g/cm³). A gold bar the size of a mobile phone has a mass of about 1.5 kg.
- A pillow and a brick can have similar sizes, but the brick is far denser, so it is much harder to lift.
3.6Measuring density Core
Three methods you must be able to describe, with calculations.
For every method you need two measurements: the mass (from a balance) and the volume. Only the way you find the volume changes.
Method 1: a regular solid (cube, cuboid, cylinder)
- Measure the mass on a balance.
- Measure the sides with a ruler and calculate the volume (cuboid: V = l × w × h).
- Calculate ρ = m / V.
Method 2: a liquid
- Measure the mass of an empty measuring cylinder.
- Pour in some liquid and read its volume at the bottom of the meniscus.
- Measure the mass of the cylinder with the liquid. Mass of liquid = second reading − first reading.
- Calculate ρ = m / V.
Method 3: an irregular solid that sinks
- Measure the mass on a balance.
- Find the volume by the displacement method (Chapter 1): read the water level, lower the object in on a thread, read the new level. V = V2 − V1.
- Calculate ρ = m / V.
- Read measuring cylinders at eye level, at the bottom of the meniscus.
- Lower the object gently on a thread so no water splashes out, and make sure it is completely under the water.
- Repeat the measurements and take an average.
- A famous story says the Greek scientist Archimedes checked whether a king’s crown was pure gold by measuring its volume from the water it displaced. If the crown’s density was lower than gold’s, cheaper metal had been mixed in.
- Jewellers and gold buyers still use density tests to check the purity of gold.
- Milk dairies check milk with a density meter (lactometer). Milk with water added has a lower density than pure milk.
Measure the density of liquids in our Density of Liquids simulator, and of irregular solids in the Displacement Method simulator.
3.7Floating & sinking Core
Predicting whether something floats from its density.
Compare the density of the object with the density of the liquid:
- Object less dense than the liquid → it floats.
- Object denser than the liquid → it sinks.
A floating object that is only a little less dense than the liquid floats low, with most of it under the surface. Ice (0.92 g/cm3) floats with about nine-tenths below the water.
How does a steel ship float?
Steel is about 8 times denser than water, so a steel block sinks. A ship, though, is a hollow shell full of air. What matters is the average density of the whole ship: its total mass divided by its total volume, including all the air inside. That average is less than the density of water, so the ship floats.
Liquids floating on liquids Extended
If two liquids don't mix, the less dense liquid floats on top of the denser one. Use the density data to put them in order: lowest density at the top, highest at the bottom.
- Ice cubes float in your drink, and icebergs float in the sea, because ice is less dense than water. About 90% of an iceberg is hidden under the water, which makes icebergs very dangerous to ships.
- When an oil tanker leaks, the oil spreads out as a thin layer on top of the sea, because oil is less dense than sea water.
- In the Dead Sea the water is so salty, and so dense, that people float easily without swimming.
- A hot-air balloon rises because the hot air inside is less dense than the cooler air around it.
Key terms & formulae
Learn these word for word. Definitions earn easy marks.
Formulae
Worked examples
Try each one yourself first, then open the solution.
1A suitcase has a mass of 23 kg. Calculate its weight on Earth (g = 9.8 N/kg). Coresolution
2A rock weighs 32 N on the Moon, where g = 1.6 N/kg. What is its mass? What would it weigh on Earth? Coresolution
3A metal block measures 4.0 cm × 3.0 cm × 2.0 cm and has a mass of 189.6 g. Find its density in g/cm³ and in kg/m³. Coresolution
4An empty measuring cylinder has a mass of 85.0 g. With 40 cm³ of cooking oil in it, the mass is 121.8 g. Will the oil float on water? Coresolution
5A stone of mass 75 g is lowered into a measuring cylinder. The water level rises from 50 cm³ to 80 cm³. Find the density of the stone. Will it float in sea water (1.03 g/cm³)? Coresolution
6What mass of air is in a classroom 10 m × 8.0 m × 3.0 m? (Density of air = 1.2 kg/m³) Coresolution
Exam tips & common mistakes
Where students most often lose marks on this topic.
- Giving weight in kg. Weight is a force, so its unit is the newton (N).
- Saying mass changes on the Moon. Only weight changes; mass stays the same.
- Mixing units in density: grams with m³, or kg with cm³. Use g with cm³ (g/cm³) or kg with m³ (kg/m³).
- In the liquid method, forgetting to subtract the mass of the empty cylinder.
- Using the final water level as the volume in the displacement method. The volume is the rise: V2 − V1.
- Saying "heavy things sink". It's density, not mass, that decides: a huge ship floats and a small coin sinks.
- Mass: "quantity of matter".
- Weight: "gravitational force on a mass".
- Gravitational field strength: "force per unit mass".
- Density: "mass per unit volume".
- Floating: "the object is less dense than the liquid".
Try it in the 3D lab
The IGCSE practicals for this chapter. Ready simulators open straight away.
Chapter 3 quiz
10 exam-style multiple-choice questions. Choose an answer for each, then check your score.