S3.5.8 Chapter 8

Density

Why does oil float on water, and why does a stone sink?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

A Heavy things sink and light things float.
You picked A. Read on. At the end, the chapter comes back to your guess.
B A thing floats when it packs less mass into each cm³ than the liquid does.
You picked B. Read on. At the end, the chapter comes back to your guess.
C Big things float and small things sink.
You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

Explain density as how much mass is packed into a space
Explain why oil floats on water and a stone sinks
Calculate density from mass and volume

A stone sinks in water, but a big log floats. A little oil floats on water. So heavy things do not always sink. What decides it?

The mass of a thing is how much matter it holds. Its volume is the space it takes up. We measure mass in grams, and volume in cubic centimetres, written cm³. A cm³ is the space of a cube 1 cm wide.

The same space and the same number of particles. The box of heavy particles holds more mass.

Both boxes take up the same space. The box of heavy particles holds more mass in that space. We say it is more dense.

The same volume of different materials can have very different masses. 1 cm³ of water has a mass of 1 g. 1 cm³ of iron has a mass of about 8 g.

Density tells you the mass in each cm³. A dense material packs a lot of mass into a small space.

See it three ways

With things

Fill one cup with dry sand and an identical cup with cotton wool. Lift them. The cup of sand is far heavier. Sand is denser than cotton wool.

As a picture

In words

A dense material has a lot of mass in each cm³. A material with a low density has little. The table shows about how many grams are in 1 cm³. Real samples differ a little.

In symbols

density = mass ÷ volume. The unit is g/cm³.

Heavier particles make a material denser. A gas has very few particles in each cm³, because they are far apart. So a gas has a very low density. Water is hundreds of times denser than air. Cotton wool and cork are light because they hold pockets of air.

A block of wood. Its volume is 10 × 8 × 5 = 400 cm³, and its mass is 200 g.

To find a density, divide the mass by the volume. Here is a worked example with this block.

Worked example

A block of wood has a mass of 200 g and a volume of 400 cm³. What is its density?

Write the rule: density = mass ÷ volume.
Put in the numbers: 200 ÷ 400.
200 ÷ 400 = 0.5.

Answer: 0.5 g/cm³. This is less than the density of water, so the block floats.

Now the rule for floating. A thing floats in a liquid if it is less dense than the liquid. It sinks if it is denser. If the two are equal, it stays wherever you put it, neither rising nor sinking.

Oil floats on water because oil is less dense than water. Oil and water do not mix, so they stay in two layers. A ship is mostly air inside, so the whole ship is less dense than water. That is why it floats.

Most woods float, but a few very dense woods, such as ebony, sink. Most metals are denser than water, so a lump of iron sinks. Always compare the density of the thing with the density of the liquid.

The densest liquid is at the bottom. Each thing rests on the first layer that is denser than it.

How do you find the volume of a stone? A stone pushes water out of its way. We say it displaces water. The water level rises by exactly the volume of the stone. Remember that 1 mL is the same as 1 cm³.

Draw it first

Find the density of a stone

1 Put the stone on a scale. Read its mass in grams.
2 Pour water into a measuring cylinder. Read the level in mL.
3 Lower the stone in. Read the new level. The rise in the level is the volume of the stone.

Take the first level from the second to get the volume. Then divide the mass by the volume to get the density.

Try it

Sink or float

You need: a bowl of water, a stone, a piece of wood or cork, a spoon of cooking oil.

Be safe: Wipe up spilled oil, because it is slippery. Do not drink the water.

Write down which of the stone and the wood you think will float.
Put each into the water, one at a time. See which float and which sink.
Pour the spoon of oil onto the water. Watch where the oil goes.

What you will see: The stone sinks. The wood floats. The oil spreads in a thin layer on top of the water and stays there. The picture draws the oil layer thicker so that you can see it.

If you cannot try it, this is what happens.

A wrong idea many people have

Heavy things sink and light things float.

Why it feels right: A stone is heavy and sinks. A feather is light and floats.

The test that breaks it: A big log floats on a river. A tiny steel pin sinks in a cup. The log has far more mass than the pin.

What is true: Mass alone does not decide it. What counts is density, the mass in each cm³. A thing less dense than the liquid floats. A denser thing sinks.

Key words

mass: how much matter a thing holds. We measure it in grams.
volume: the space a thing takes up. We measure it in cm³ or mL.
density: the mass in each cm³: mass ÷ volume.
displaces: pushes water out of its way, so the level rises by the volume of the thing.

Back to your guess

The answer is B: A thing floats when it packs less mass into each cm³ than the liquid does.

What counts is how much mass is packed into each cm³. That is density. A thing less dense than the liquid floats. A denser thing sinks.

Keep it

Copy this into your exercise book.

Density is mass divided by volume, in g/cm³. A thing floats if it is less dense than the liquid and sinks if it is denser. Water is about 1 g/cm³.

Draw: Draw a jar with oil on top, water in the middle and honey below. Put a cork at the top and a stone at the bottom.