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Density (AQA GCSE Physics: Combined Science)
Revision Note
Density
- Density is defined as:
The mass per unit volume of a material
- Objects made from low density materials typically have a low mass
- Similarly sized objects made from high density materials have a high mass
- For example, a bag full of feathers is far lighter compared to a similar bag full of metal
- Or another example, a balloon is less dense than a small bar of lead despite occupying a larger volume
- Density is related to mass and volume by the following equation:
- Gases, for examples, are less dense than solids because the molecules are more spread out (same mass, over a larger volume)
Gases are less dense than solids
- This equation can be rearranged with the help of the formula triangle:
Density, mass, volume formula triangle
- The units of density depend on what units are used for mass and volume:
- If the mass is measured in g and volume in cm3, then the density will be in g/cm3
- If the mass is measured in kg and volume in m3, then the density will be in kg/m3
- This table gives some examples of densities on common materials
- If a material is more dense than water (1000 kg/m3), then it will sink
Approximate Densities of Materials Table
- The volume of an object may not always be given directly, but can be calculated with the appropriate equation depending on the object’s shape
Volumes of common 3D shapes
Worked example
A paving slab has a mass of 73 kg and dimensions 0.04 m × 0.5 m × 0.85 m.
Calculate the density, in kg/m3, of the material from which the paving slab is made.
Step 1: List the known quantities
- Mass of slab, m = 73 kg
- Volume of slab, V = 0.04 m × 0.5 m × 0.85 m = 0.017 m3
Step 2: Write out the equation for density
Step 3: Substitute in values
ρ = 73 ÷ 0.017 = 4294 kg/m3
Step 4: Round the answer to two significant figures
ρ = 4300 kg/m3
Examiner Tip
Make sure you are comfortable converting between units such as metres (m) and centimetres (cm) or grams (g) and kilograms (kg).
- When converting a larger unit to a smaller one, you multiply (×)
- E.g. 125 m = 125 × 100 = 12 500 cm
- When you convert a smaller unit to a larger one, you divide (÷)
- E.g. 5 g = 5 ÷ 1000 = 0.005 or 5 × 10-3 kg
Students can often confuse mass, weight and density.
- Mass is the amount of matter in a substance or an object, measured in kg
- Weight is the force that acts on that object in the presence of a gravitational field, measured in N
- Density is the amount of matter in a fixed volume, measured in kg / m3
To imagine density in a visual way, you can think about the number of particles in a cubic centimetre. The key to understanding this is recognising that at the atomic level of particles, the space between particles is empty space. Imagine you have 1 cm3 of liquid water and 1 cm3 of steam (which is just gaseous water). The liquid water will contain more particles in that 1 cm3 than steam, so liquid water is more dense. If we had 1 g of liquid water and steam, then less dense steam would take up a greater volume. With density you always have to consider both mass and volume.
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