GCSE · Maths · AQA · Spec 8300 · Foundation
Compound units — density and pressure
High heels can press on a floor harder than an elephant, and a one-metre box holds a million centimetre cubes. Both surprises come down to one small word: 'per'.
Density · mass per cubic centimetre
Drag to change how much of the metal you have. Volume and mass both change, but the mass of each single cubic centimetre stays at 8 g. Try it: before you drag to 6 cm³, predict the mass. Then go the other way: which volume gives 40 g?
Predict, then check
Pressure is the other compound unit in this lesson. Commit to an answer first.
A person in high-heeled shoes and an elephant both stand on a wooden floor. Which presses on the floor with the greater pressure?
The formula triangle
Force goes on top because force = pressure × area. Density fits the very same triangle: mass on top, density and volume underneath. Tap the quantity you want to find.
Tap the quantity you want to find. The triangle shows you the formula.
Cover force, pressure or area to reveal its rearranged formula, then plug in numbers to solve.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Grams per cubic centimetre. Newtons per square metre. Read the unit properly and it tells you what to divide.
What you need to know
- A compound unit is a 'per': density is mass per unit of volume, and pressure is force per unit of area.
- Read the unit and it tells you the calculation: g/cm³ means grams ÷ cubic centimetres, and N/m² means newtons ÷ square metres.
- Get every quantity into matching units before you divide, and before you compare two answers.
The big picture
Density and pressure are compound units: each one is a 'per'. Density is the mass in each unit of volume (density = mass ÷ volume) and pressure is the force on each unit of area (pressure = force ÷ area). The unit is built from the units you divided, each formula rearranges to find the other two quantities, and every mass, volume, force and area must be in matching units before you calculate or compare.
Key points
Worked example
Problem
Change a density of 8 g/cm³ into kg/m³.
⚠ Watch out
Dividing the numbers straight out of the question when the units don't match, such as a mass in kg with a volume in cm³, or converting cm² to m² (or cm³ to m³) by dividing by 100.
Memory hook
Heel beats elephant: a small area makes a big pressure. And a cubic metre hides a million cubic centimetres.
Check yourself
Cover the page and try this: a pebble has a mass of 50 g and a volume of 20 cm³. What is its density in g/cm³, and what is that density in kg/m³?
Flashcards
(11)Density: what does it measure, and how do you calculate it?
Pressure: what does it measure, and how do you calculate it?
Rearranging density: how do you find a mass, and how do you find a volume?
Rearranging pressure: how do you find a force, and how do you find an area?
How do you know what unit a density or pressure answer has?
Converting an area: one square metre is how many square centimetres?
Converting a volume: one cubic metre is how many cubic centimetres?
The same force acts on a smaller area. What happens to the pressure?
What must you check before comparing two densities?
You cut a block of metal in half. What happens to its density?
A density is in g/cm³. How do you turn it into kg/m³?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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