Density
Forces in Action - OCR A-Level Physics
Key Definition
Density
Mass per unit volume of a substance. It is a property of the material, not of the object. The SI unit is $\text{kg m}^{-3}$.
Mass per unit volume of a substance. It is a property of the material, not of the object. The SI unit is $\text{kg m}^{-3}$.
$$\rho = \frac{m}{V}$$
- Common densities: water $1000 \text{ kg m}^{-3}$, air $1.2 \text{ kg m}^{-3}$, steel $7800 \text{ kg m}^{-3}$, aluminium $2700 \text{ kg m}^{-3}$, mercury $13\,600 \text{ kg m}^{-3}$.
- Unit conversions: $1 \text{ cm}^{3} = 1 \times 10^{-6} \text{ m}^{3}$ and $1 \text{ litre} = 1 \times 10^{-3} \text{ m}^{3}$.
- An object floats if its average density is less than the density of the surrounding fluid.
- To find the volume of an irregular object, fully submerge it in a measuring cylinder of water. The change in liquid level gives the displaced volume, which equals the object's volume.
Common Mistake
MEDIUM
Students often: forget to convert $\text{cm}^{3}$ to $\text{m}^{3}$ when the volume is given in $\text{cm}^{3}$ but mass in $\text{kg}$, giving an answer a million times too big.
Instead: always convert both quantities to SI base units before substituting into $\rho = m/V$.
Instead: always convert both quantities to SI base units before substituting into $\rho = m/V$.
Examiner Tips and Tricks
- Quote density to the unit given in the question. If the data sheet gives water as $1000 \text{ kg m}^{-3}$, use that, not $1.00 \text{ g cm}^{-3}$.
- Check the order of magnitude before writing your final answer: solids are typically $10^{3}$ to $10^{4} \text{ kg m}^{-3}$, gases $\sim 1 \text{ kg m}^{-3}$.