Density

After many weeks at sea, this ship arrives at the harbor. The captain orders the anchor to be lowered. Hmm, obviously, something is not right about this anchor, looks like it's made of wood. Wood floats so it's not a good material to make an anchor with. Change the material to steel and the anchor sinks to the bottom of the sea holding the ship in place.

Why does a wooden anchor float while a steel one sinks? Let's look at it on a smaller scale. The wooden cube floats in water while the steel one sinks, even though they are of the same size the steel one has more mass - it's heavier. Now compare this to water of the same size, that size or volume of wood has less mass than the volume of water. This causes it to float in water.

The steel cube has greater mass than water of the same volume, so it sinks. The mass of the material compared to its volume is called its density. The steel and wooden anchors are the same volume but the steel one has more mass, so it has higher density. ​ ​To find density, you have to find out how much mass is in the material based on its volume. How many kilograms are there per cubic meter of that material? It's the mass of the material divided by its volume.

We represent density with the Greek letter rho which looks like a p. We measure it in kilograms per cubic meter. That's the SI unit for density. It's made up of the SI units for mass and volume. Density tells you how many kilograms there are in 1 cubic meter of a material.

All you need in order to measure the density of a material is its volume and mass. Any material with a higher density than water will sink and anything with a lower density than water will float. There's a simple equation you can use to test if a material will float in water. Divide the density of the material by the density of the water. The density of water is 1,000 kilograms per cubic meter.

The density of the wood is 900 kilograms per cubic meter. This gives you the density of wood in relation to the density of water. It's the relative density of the wood. ​ ​Materials with relative density lower than 1 will float. Materials with relative density higher than 1 will sink. The relative density of wood is lower than 1 so it floats in water.

Now compare this to the relative density of steel. Steel has a density of 7,900 kilograms per cubic meter. The relative density of steel is 7,900 divided by 1,000, which is 7.9. The relative density of steel is higher than 1, steel will sink in water. which means the Relative density is a ratio, so it does not have a unit.

You can measure the relative density of any material. All you need to know is its density. Understanding relative density allows engineers to pick the best materials for building things. If the person who made the anchor knew how to measure relative density, they would never have made an anchor out of wood. The ship could have anchored properly.