Density, Expansion and Contraction: Concept Map

Concept Map

Organise the vocabulary, quantities and relationships into a connected model.

This extension applies that lens specifically to Density, Expansion and Contraction.

Density tells you how much mass is packed into a given volume:

Mass is usually in grams and volume in cubic centimetres, giving density in g/cm³. Pure water has a density of about 1 g/cm³.

The floating rule: an object floats in water if its density is less than 1 g/cm³, and sinks if its density is more than 1 g/cm³.

Worked example. A block of jacaranda wood has a mass of 240 g and a volume of 300 cm³.

$0.8 < 1$, so the block floats. And it floats with 80% of itself under the water — which is why an iceberg, at about 0.92 g/cm³, hides almost all of itself.

Expansion and contraction. Heat a substance and its particles move faster and push slightly further apart, so the substance expands. Cool it and the particles slow, move closer, and it contracts. The number of particles never changes, so the mass stays the same — but because the volume changes, the density changes too.

Engineers plan for this everywhere in South Africa:

• Gaps are left between the concrete slabs of a bridge on the N1 so the slabs have room to expand on a 38 °C day.
• Overhead power lines are strung with a deliberate sag; on a hot afternoon they sag further, and on a cold Highveld night they pull tight.
• A metal jar lid that will not budge loosens after hot water is run over it — the metal lid expands more than the glass jar.