Objective:

• To understand the physical term ‘density’.
• To be able to determine the density of a material using the equation;  $\rho = \frac{m}{V}$

Simply put, density is how much mass there is of a substance in a certain amount of volume. In other words, if you had a specific volume, say a box to fill…

If filled with air it would have very little mass – as you can imagine!

If filled with water (sure… a cardboard box was a stupid image decision), the mass would increase by quite a significant amount compared to the air.

If instead sand was used to fill up the box (a solid that will easily fill up most of the space provided), it will have an even higher mass again!

In other words, for the same volume of space there is a small mass with gas, a medium mass with liquid and a much larger mass with a solid. Mass is a property of a substance, density however is how much of this property can fit into a certain volume.

It is defined as the mass per unit volume and the following equation can be written to determine it;

$\rho = \frac{m}{V}$

where;

$\rho$  is the density, which is preferably measured in  $kg/m^{3}$
$m$  is the mass, which is preferably measured in   $kg$
$V$  is the volume, which is preferably measured in   $m^{3}$

Convenience

Density is a much more useful property than we give credit. It helps to explain how things float, it explains our atmospheres composition, helps to describe why a flame points upwards and why some gases rise.

The units we use when calculating density are preferably as shown previously (or below);

$m$  is the mass, which is preferably measured in   $kg$
$V$  is the volume, which is preferably measured in   $m^{3}$
$\rho$  is the density, which is preferably measured in  $kg/m^{3}$

However, if you are trying to measure the density of small items (like an ice cube or magnet) then the idea of measuring their dimensions in metres and their mass in kilograms is a little inconvenient. It would make much more sense to measure them in centimetres and grams and hence the units would need to change;

$m$  is the mass, measured in  $gg$
$V$  is the volume, measured in  $cm^{3}$

When used in the equation $\rho = \frac{m}{V}$, we now obtain a different unit for density than outlined above. The new unit would be $g/cm^{3}$ .

The way to determine the final unit of density is determined by substituting whatever units you use for volume and mass into the equation.

If your job were to calculate the densities of different materials, you could be really irritating to your peers or colleagues…
You could either use non-conventional units like ‘feet’ or ‘yards’ along with ‘ounces’ or ‘slugs’ (an American unit). This could give you a density in terms of $slugs/feet^{3}$ , but practically this is just not helpful!

In your GCSE’s the only units you should use are $kg/m^{3}$ and/ or $g/cm^{3}$.

How do somethings float but others sink?Different substances have different densities; Take a piece of wood that floats on water, this happens because the wood is of lower density than the water. Take a stone that when thrown into the sea sinks, this is because it has a greater density than the water.

So, the greater the density the more likely it will take the lower position and vice versa.

This can be shown in the following video;

Click for a video link

The following is another video that demonstrate five facts about density…