## 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/m^{3}. However sometimes we use the subunit g/cm^{3}. To convert the units of density from g/cm^{3} to kg/m^{3}, we multiply by 1000.

Aluminium has a density of 2.7g/cm^{3} which means that 1cm^{3} of aluminium has mass of 2.7g. This density can be converted to 2700kg/m^{3} by multiplying by 1000. This still means 1cm^{3} of aluminium has a mass of 2.7g and conversely 1m^{3} 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

If the density of wood is 0.5 g/cm

^{3}what is the mass of

(i) 3 cm^{3},

(ii) 23 cm^{3},

(iii) 87 cm^{3}?What is the density of a substance of

(i) mass 300 g and volume 90 cm^{3},

(ii) volume 33 m^{3}and mass 66 kg?The density of gold is 15 g/cm

^{3}. Find the volume of

(i) 30 g,

(ii) 90 g of gold.A piece of steel has a volume of 22 cm

^{3}and a mass of 44 g.

What is its density in

a. g/cm3,

b. kg/m3?What is the mass of 15 m

^{3}of cement of density 3000 kg/m^{3}?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/m

^{3}?When a golf ball is lowered into a measuring cylinder of water, the water level rises by 30 cm

^{3}when the ball is completely submerged. If the ball weighs 33 g in air, find its density.Why does ice float on water?