Density as mass per unit volume, the equation rho = m / V, and experiments to measure the density of regular solids, irregular solids and liquids.

What this dot point is asking

CCEA wants you to define density as mass per unit volume, use and rearrange the equation rho = m / V, and describe experiments to measure the density of regular solids, irregular solids and liquids. Density is also a practical-skills topic, so the methods are examined.

The answer

What density is

Water has a density of $1000\ \text{kg/m}^3$, which is the same as $1.0\ \text{g/cm}^3$. Rearranging the equation gives $m = \rho V$ and $V = m / \rho$.

Measuring the density of a regular solid

For a regular solid such as a cube or cylinder:

1. Measure the mass on a balance.
2. Measure the dimensions with a ruler or vernier calliper and calculate the volume (for example length times width times height for a cuboid).
3. Use $\rho = m / V$.

Measuring the density of an irregular solid

For an awkward shape such as a stone, the volume is found by displacement:

Measure the mass with a balance, find the volume by displacement, then use $\rho = m / V$.

Measuring the density of a liquid

1. Measure the mass of an empty measuring cylinder.
2. Pour in a known volume of the liquid and read the level (at eye level, bottom of the meniscus).
3. Measure the mass of the cylinder and liquid, and subtract to find the mass of the liquid.
4. Use $\rho = m / V$.

Worked example: density of an oil

Examples in context

Example 1. Floating and sinking

An object floats if it is less dense than the fluid around it. Ice (density about $0.92\ \text{g/cm}^3$) floats on water, while a steel nail sinks because steel is far denser than water.

Example 2. Choosing materials

Aircraft use low-density metals such as aluminium and titanium alloys so they are strong but light, reducing the weight that must be lifted.

Example 3. Hot-air and helium balloons

A balloon rises when the gas inside it is less dense than the surrounding air. Heating the air inside a hot-air balloon lowers its density; a party balloon filled with helium, which is naturally far less dense than air, floats upward for the same reason.

A common source of error in density experiments is reading the measuring cylinder inaccurately, or trapping air bubbles on an irregular solid when it is submerged. To improve reliability, take repeat readings, ensure the object is fully under water, and read the scale at eye level from the bottom of the meniscus.

Try this

Q1. Write the equation for density and state the unit of each quantity in SI units. [2 marks]

• Cue. $\rho = m / V$; density in kg/m cubed, mass in kg, volume in m cubed.

Q2. A $0.50\ \text{kg}$ block has a volume of $0.000\,25\ \text{m}^3$. Find its density. [2 marks]

• Cue. $\rho = 0.50 / 0.000\,25 = 2000\ \text{kg/m}^3$.

Q3. How would you find the volume of an irregular stone? [1 mark]

• Cue. By displacement: the rise in water level when the stone is fully submerged.