Learn4PH1Paper 1P · Paper 1 (core content)Solids, liquids and gasesPressure

Solids, liquids and gases · Subtopic 5 of 5

Pressure

Pressure is force per unit area, $p=\dfrac FA$ , measured in pascals ( $1$ Pa $=1$ N/m²). The same force on a smaller area gives a bigger pressure. In a liquid, pressure increases with depth and density: $\Delta p=\rho g\Delta h$ .

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Section 1 of 14

Learning objectives

Calculate pressure using $p=\dfrac FA$ , converting cm² to m².
Explain everyday examples of high and low pressure.
Explain why pressure in a liquid increases with depth.
Use $\Delta p=\rho g\Delta h$ .

Pause and think

Why does a drawing pin go into a board easily, but your thumb on the other end doesn't get hurt?

Section 2 of 14

Core idea

Start hereStilettos and snowshoes

A person in stiletto heels can dent a wooden floor that an elephant wouldn't. Snowshoes stop you sinking. It's not the force that matters but how concentrated it is: pressure.

The big idea

$p=\frac FA$ (Pa). In liquids, $p=\rho gh$ . Hydraulics transmit pressure to multiply force.

1. Solids

Same weight, different areas

600 N on 0.06 m² gives 10 000 Pa; on 0.0001 m² it gives 6 000 000 Pa. That is why knives are sharp and tractors have wide tyres.

p=\frac FA

$p$: pressure (Pa = N/m²).
$F$: force (N).
$A$: area (m²).

Worked exampleA 600 N person

Two feet (0.04 m²) vs one heel (0.0001 m²).

Goal: Pressures.
Strategy: $F/A$ .

$600\div0.04=15000\text{ Pa}$
Feet.
$600\div0.0001=6000000\text{ Pa}$
Heel: 400 times the pressure.

Answer

15

kPa vs

6

MPa.

✓ CheckArea 400× smaller, pressure 400× larger ✓.

2. Liquids

Pressure increases steadily with depth in water

\rho g h=1000\times10\times10=100\,000

Pa at 10 m: about one extra atmosphere. Dams are thicker at the bottom for this reason.

p=\rho gh

$V=Ah$
Column of liquid of height $h$ above area $A$ .
$m=\rho Ah,\ W=\rho Ahg$
Mass, then weight.
$p=\frac WA=\rho gh$
Divide by area.

Worked example10 m under water

$\rho=1000$ kg/m³.

Goal: Pressure.
Strategy: $\rho gh$ , then add the atmosphere.

$1000\times10\times10=100000\text{ Pa}$
Water.
$+100000\approx200\text{ kPa}$
Total, with atmospheric pressure.

Answer

100

kPa from water; about

200

kPa total.

✓ CheckEvery 10 m of water adds about one atmosphere ✓.

3. Hydraulics

Worked exampleA hydraulic jack

50 N on a 0.01 m² piston; output piston 0.5 m².

Goal: Output force.
Strategy: Liquid transmits the same pressure.

$50\div0.01=5000\text{ Pa}$
Pressure.
$5000\times0.5=2500\text{ N}$
Force = pressure × area.

Answer

2500

✓ CheckArea 50× larger, force 50× larger (small piston moves 50× further) ✓.

Common misconceptioncm² vs m²

1

m²

=10\,000

cm²: convert before dividing.

Pause and think

Why are dams thicker at the bottom?

Summary

$p=F/A$ .
$p=\rho gh$ .
Hydraulics: same pressure, larger area, larger force.

Pascal: N/m².

HistoryPascal's barrel. Blaise Pascal is said to have burst a strong wooden barrel in about

1646

by filling it with water and adding a long, thin tube on top. Pouring just a little water into the tall tube raised the pressure enough to split the barrel, showing pressure depends on depth, not the amount of water.

Fun factYour ears on an aeroplane. Cabin pressure drops during take-off, so the air trapped inside your ear pushes the eardrum outwards. Swallowing or yawning opens a tube to let air out and equalise the pressure: "pop".

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