Density (OCR Gateway GCSE Physics: Combined Science)

• 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:

• Where: 
  • ρ = density (kg/m³)
  • m = mass (kg)
  • V = volume (m³)

• 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

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