Calculating density

In a nutshell

The density of an object is a measure of its 'compactness', in other words, how tightly packed its mass is.

Equations

Variable definitions

Density

The density of an object tells you how much mass is in each unit volume. The density of an object is calculated by dividing its mass by its volume:

​$$density={mass\over volume}$$

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​$$\rho={m\over V}$$.

Example

Gold has a density of $$19\, 300\,kg/m^3$$. Calculate the volume of $$5\,kg$$ of gold.

Write down the relevant information provided in the question (converting to base units where appropriate):

 $$\rho = 19\,300\,kg/m^3\\ \ \\ m=5\,kg$$   

Write down the relevant formula:

 $$\rho=\frac{m}{V}$$

Rearrange the relevant formula:

 $$V=\frac{m}{\rho}$$

Substitute the relevant information into the correct formula:

 $$V=\frac{5}{19300} \\ \ \\ V=\underline{0.00026\,m^3}$$

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So $$5\,kg$$ of gold occupies a volume of $$\underline{0.00026\,m^3}.$$

Density of solids, liquids and gases

​​The particle model of matter says everything is made of lots of tiny particles. Dense materials have their particles tightly packed together, so the mass of the object occupies a small volume. 

Less dense substances have their particles more far apart, so the mass of the substance is spread out over a large volume. Therefore, two objects of equal volume but different density will weigh different amounts.

For example, particles in a solid tend to be very close together, so solids are dense. Particles in a liquid tend to be more separated, so liquids tend to be less dense than solids. Particles in a gas have much more distance between them, so gases are far less dense than solids and liquids.

Curiosity: Did you know that solid gold is about $$20$$​ times more dense than liquid water? A $$500\ ml$$​ bottle of water weighs half a kilogram, but the same volume of solid gold weighs nearly $$10\ kg$$​. Even denser are neutron stars - just a teaspoon of one has a mass of one billion tonnes! 

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