5.1, 5.3-5.4 - Units, density and density practical

Units for this topic

Physics answers are only complete when the number and the unit work together. Pearson Edexcel expects you to use the unit symbols in this topic accurately, including units that will also appear in nearby solids, liquids and gases work.

The powers on metre matter. A length is measured in $m$. An area is measured in $m^2$ because it covers a surface. A volume is measured in $m^3$ because it fills space.

For this lesson, the most important linked units are $kg$, $m^3$ and $kg/m^3$. If mass is measured in kilograms and volume in cubic metres, density will be in kilograms per cubic metre.

Classroom apparatus may display mass in grams or volume in millilitres or cubic centimetres. Use the unit asked for in the question; if a final answer must be in SI units, convert before calculating or convert the final density carefully.

What density means

Density tells you how much mass is packed into each unit volume of a substance or object. A material with a high density has a large mass in a small volume. A material with a low density has less mass in the same volume. For example, water has a density of about $1000\text{ kg/m}^3$: one cubic metre of water has a mass of about 1000 kg.

Think about two blocks with the same volume. If one has a larger mass, it has the larger density. Now think about two objects with the same mass. If one takes up a smaller volume, it has the larger density because the same mass is packed into less space.

Density is a property of the material, not of the size of the sample. Cutting a block in half halves both its mass and its volume, so each half has the same density as the whole block. The value you calculate from an object still depends on measuring both mass and volume correctly. A wrong mass reading, wrong volume reading or mixed units will give a wrong density.

In the formula, $\rho$ means density, $m$ means mass and $V$ means volume. The Greek letter $\rho$ is pronounced "rho".

Using the density equation

Use the density equation in the same way as other Physics equations: write the equation, substitute the values with units, calculate, then give the final answer with the correct unit.

For example, a regular block has a mass of $0.054\text{ kg}$. Its volume is $0.000036\text{ m}^3$.

The equation can also be rearranged:

These rearrangements do not change the Physics. They just let you find whichever quantity is missing.

Be careful with powers of ten in volumes. A small solid may have a volume such as $0.000040\text{ m}^3$, which is the same as $4.0 \times 10^{-5}\text{ m}^3$. Losing a zero can change the density by a factor of ten.

If you use common laboratory units, remember:

• $1\text{ g} = 0.001\text{ kg}$
• $1\text{ cm}^3 = 1\text{ mL}$
• $1\text{ cm}^3 = 0.000001\text{ m}^3$
• $1\text{ g/cm}^3 = 1000\text{ kg/m}^3$

For density in $\mathrm{kg/m^3}$, kilograms and cubic metres must match the equation. For example, $2.7\,\mathrm{g/cm^3}=0.0027\,\mathrm{kg}/10^{-6}\,\mathrm{m^3}=2700\,\mathrm{kg/m^3}$. The factor is 1000, not one million, because both mass and volume units change.