# 16.44 Density

Which has the greatest mass 1 kg of steel or 1 kg of wood? (If you’re not sure what “mass” means see posts 16.12 and 16.13.) I hope that you immediately realised that both have the same mass of 1 kg.

But we all believe that steel is “heavier” (it has a higher mass) than wood. Why? Because steel sinks in water but wood floats. Let’s be clearer about what we believe – that if we have a lump of steel, and a lump of wood with the same volume, the lump of steel has a higher mass than the lump of wood. So, for example, 1 m3 of steel has a higher mass than  1 m3 of wood.

Density is simply the mass of 1 m3 of something. (Strictly speaking this is the definition of density using SI units, see post 16.12; other measurement systems are based on a unit of length that is not a metre so the fundamental measure of volume is not the m3.)

Suppose that we have a lump of stuff that has a mass m and a volume V. Then the mass of 1 m3 of this stuff is its mass, m, divided by its volume – so its density, ρ, can be defined by    ρ = m/V. Because we measure mass in kg and volume in m3, we measure density in kg.m-3 (kg/m3). The densities of some common substances are tabulated below; you can see that steel has a higher density than water but wood has a lower density than water – so steel sinks and wood floats.

Anything with a lower density than water will float in water; anything with a higher density will sink. Mercury is also a liquid. So, if you look at the table, you will see that iron, steel and lead will all float on mercury. Of the substances listed, only gold and platinum will sink in it.

Density is a much easier concept to understand than most of the topics in recent posts. The reason for writing about it now is because I’ll be using it in the next post.

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Follow-up posts