Density

If a forest is 'dense' the trees are closely packed together. Dense objects have their particles packed tightly together. The more you can pack into a smaller space the greater the density will be! Density therefore involves how much 'stuff' you have (mass) and how much space it takes up (volume).
Take a look at the two boxes on the right. Each box has the same volume. If each ball has the same mass, which box would weigh more? Why? The box that has more balls has more mass per unit of volume would weigh the most. This property of matter is called density.

The density of a material helps to distinguish it from other materials. We can list the mass of a cubic metre of lots of materials and compare them. Small items made of the densest materials would still be quite ‘heavy’ whereas large items made of the least dense materials would still be quite light!

THE GENERAL EQUATION

Density tells you how much mass has been packed into a given volume of space.

At KS3 this is abbreviated to:

but at A level we use the symbol 'ro' for density ( ) making the equation:

UNITS

It is usually expressed in how much mass (in kilogrammes) you can pack into one cubic metre:

Values for densities are listed in tables using this unit, so that people can look them up and use them.

In exams and tests you will sometimes find it expressed in how much mass (in grammes) you can pack into one cubic centimetre:

Work in whatever units you are given.... don't change from one to another unless you are told to. However there is a relationship between the two units.

A kilogramme is a thousand grammes and a cubic metre is a million cubic centimetres, therefore the density in kg/m³ is always a thousand times bigger than the density expressed in g/cm³

PERFORMING CALCULATIONS

Always lay your calculations out carefully.

• Extract information from the question and list it on the right hand side of the page
• Ensure that you write in the units for the values too!
• Write out the basic equation
• If necessary work out values required from the information given
• Substitute the numbers into the equation
• Calculate the answer
• Put in the correct units

The density of an object determines whether it will float or sink. See the Archimedes Principle.

TO FIND THE DENSITY OF AN OBJECT

1. Use a set of scales to find its mass (in grammes or kilogrammes)

2. Find its volume.

• If it is regular you can work it out from measurements.
• If it is irregular you will need to use a displacement can or Eureka can (together with a measuring cylinder) to measure the volume.

3. Calculate its density (as shown above).

Related topics:

• Floating and sinking
• Archimedes Principle