Density

Density

Density of a substance is the mass per unit volume of a substance. We are used to saying things like a bag of cement is heavier than a bag of feathers. This is true and the reason is that a bag that holds 50kg of cement can hold less than 10kg of feathers. In scientific terms we say cement is denser than feathers since a certain volume of cement is heavier than the same volume of feathers.

Density (ρ) =
mass ÷ volume

The SI unit of density is kg/m³. However sometimes we use the subunit g/cm³. To convert the units of density from g/cm³ to kg/m³, we multiply by 1000.

Aluminium has a density of 2.7g/cm³ which means that 1cm³ of aluminium has mass of 2.7g. This density can be converted to 2700kg/m³ by multiplying by 1000. This still means 1cm³ of aluminium has a mass of 2.7g and conversely 1m³ of aluminium has a mass of 2700kg.

Simple density measurements

Knowing the mass m and volume V of a substance it is easy to find density with the formulae:

ρ = m/V

Regularly shaped solid

If the substance has a regular shape, we can find its volume by measuring its dimensions and calculating the volume. We then find its mass using a balance.

Irregularly shaped solid

The volume of an irregularly shaped solid, such as a small rock, can’t found by measuring the dimensions. To find the volume of an irregular solid:

• First you put a measured volume of water in a measuring cylinder.
• Then you slowly lower the solid into the measuring cylinder using a string to prevent breaking the bottom of the measuring cylider and also to prevent the water splashing out.
• Measure the new volume and then subtract the old volume from the new volume to get the volume of the solid.
• The mass of the solid is then measured by the balance.
• Then calculate the density.

Liquid

To find the mass of the liquid:

• measure the mass of an empty beaker using a balance.
• transfer a known volume of the liquid into the beaker and measure the new mass.
• subtract the mass of the beaker from the new combined mass to get the mass of the liquid.
• then calculate the density.

Floating and sinking

An object sinks in a liquid of lower density than its own and floats in a liquid of higher density than its own.

Questions

1. If the density of wood is 0.5 g/cm³ what is the mass of
   (i) 3 cm³,
   (ii) 23 cm³,
   (iii) 87 cm³?

2. What is the density of a substance of
   (i) mass 300 g and volume 90 cm³,
   (ii) volume 33 m³ and mass 66 kg?

3. The density of gold is 15 g/cm³. Find the volume of
   (i) 30 g,
   (ii) 90 g of gold.

4. A piece of steel has a volume of 22 cm³ and a mass of 44 g.
   What is its density in
   a. g/cm3,
   b. kg/m3?

5. What is the mass of 15 m³ of cement of density 3000 kg/m³?

6. What is the mass of air in a room measuring 10 m × 5.0 m × 2.0 m if the density of air is 1.3 kg/m³?

7. When a golf ball is lowered into a measuring cylinder of water, the water level rises by 30 cm³ when the ball is completely submerged. If the ball weighs 33 g in air, find its density.

8. Why does ice float on water?