Density

$ρ = \frac{m}{V}$

Where:
- ρ (the Greek letter rho) = density in kilograms per metre cubed (kg m^-3)
- m = mass in kilograms (kg)
- V = volume in metres cubed (m³)

Gases are less dense than liquids, which are less dense than solids
This is because there are fewer particles, and therefore less mass, per unit volume

Density comparison, downloadable AS & A Level Physics revision notes

Gases are less dense than solids because they have fewer particles, and therefore less mass, per unit volume

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

Volume of shapes, downloadable AS & A Level Physics revision notes

Expressions for calculating the volume of a sphere, a cube and a cylinder

A paving slab has a mass of 73 kg and dimensions 40 mm × 500 mm × 850 mm.

Calculate the density, in kg m^-3 of the material from which the paving slab is made.

WE - Density question image, downloadable AS & A Level Physics revision notes

Answer:

Step 1: List the known quantities and convert to SI units

Step 2: State the equation for density

$ρ = \frac{m}{V}$

Step 3: Calculate the volume

$volume of a cuboid = length \times width \times height$

$V = l w h$

$V = 0.850 \times 0.500 \times 0.040$

$V = 0.017 m^{3}$

Step 4: Substitute the known values to calculate

$ρ = \frac{73}{0.017}$

$ρ = 4300 kg m^{- 3} (2 s . f .)$

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 = $\frac{5}{1000}$ = 0.005 or 5 × 10^-3 kg
When dealing with squared or cubic conversions, cube or square the conversion factor too
- E.g. 1 mm³ = $\frac{1}{1000^{3}}$ = 1 × 10^-9m³
- E.g. 1 cm³ = $\frac{1}{1000^{3}}$ = 1 × 10^-6m³

Density (CIE A Level Physics)