Density & Pressure Notes

Edexcel IGCSE Physics: Revision notes

Key facts

Density $\rho = \dfrac{m}{V}$ , in kg/m³.
Pressure $p = \dfrac{F}{A}$ , in pascals (Pa): the same force on a smaller area gives a larger pressure.
Pressure in a fluid acts equally in all directions.
Pressure in a liquid increases with depth: $p = h\rho g$ .
Convert units before substituting: cm³ to m³ (÷ 1 000 000) and g to kg (÷ 1000).

Density

Density is the mass packed into each unit of volume: mass divided by volume.

Density $\rho$ is in kg/m³, mass $m$ in kg and volume $V$ in m³. A dense material has a lot of mass in a small volume.

On a graph of mass against volume, the gradient is the density.

Mass against volume: the gradient is the density.

Density $\rho = \dfrac{m}{V}$

1
Mass
measure with a balance
2
Volume
measuring cylinder or displacement; calculate for regular solids
3
Calculate
apply $\rho = m \div V$

Investigating density

Worked example

A block has a mass of 540 g and a volume of 200 cm³. Find its density in kg/m³.

1
Convert: 540 g $= 0.54$ kg and 200 cm³ $= 0.0002$ m³.
2
$\rho = \dfrac{0.54}{0.0002}$ .

A 3 kg block has a volume of 0.001 m³. What is its density?

Pressure

Pressure is the force acting on each unit of area, so the same force on a smaller area gives a bigger pressure.

Pressure $p$ is in pascals (Pa), force $F$ in N and area $A$ in m².

This is why a sharp blade cuts easily and snowshoes stop you sinking into snow.

Pressure $p = \dfrac{F}{A}$

Small area Large area Effect Large pressure Small pressure Example Knife blade, nail Snowshoes, tractor tyres

	Small area	Large area
Effect	Large pressure	Small pressure
Example	Knife blade, nail	Snowshoes, tractor tyres

Small area

Effect:: Large pressure
Example:: Knife blade, nail

Large area

Effect:: Small pressure
Example:: Snowshoes, tractor tyres

Worked example

A 60 N force acts over an area of 0.02 m². Find the pressure.

1
$p = \dfrac{F}{A}$ .
2
$p = \dfrac{60}{0.02}$ .

The same force acts on half the area. The pressure

Pressure in fluids

In a fluid at rest, pressure acts equally in all directions and increases with depth.

Fluid molecules move randomly and hit surfaces from every direction, so pressure acts equally in all directions.

Pressure in a liquid increases with depth, because more liquid lies above. $h$ is depth (m), $\rho$ the liquid's density and $g$ the gravitational field strength (N/kg).

Pressure from water increases steadily with depth.

Pressure due to a liquid $p = h \times \rho \times g$

Worked example

Find the pressure due to water at a depth of 5 m ( $\rho = 1000$ kg/m³, $g = 10$ N/kg).

1
$p = h\rho g$ .
2
$p = 5 \times 1000 \times 10$ .

A diver goes from 5 m to 10 m deep in water. The pressure due to the water

Try an exam question

A diver is 20 m below the surface of a lake. The density of water is 1000 kg/m³ and the gravitational field strength is 10 N/kg. Calculate the pressure due to the water at this depth, and explain why pressure increases with depth.

[4 marks]

That's the notes covered.

Carry on to the next subtopic.