Pressure

CORE VS EXTENDED GUIDE

• Core students study only the unlabelled sections.
• Extended students must study everything, including Extended Extended points.
• Extended = Core + Supplement.

Defining Pressure

Pressure is a measure of how concentrated a force is over an area.

Pressure: the force per unit area.

When the same force acts over a smaller area, the pressure increases. When the same force spreads over a larger area, the pressure decreases.

A drawing pin pushed into a board illustrates this clearly: the sharp point has a tiny area, so the pressure there is very large, which is why it pierces the board. The flat head has a much larger area, so the pressure on your thumb remains small enough to avoid injury.

Pressure is a scalar quantity — it acts equally in all directions at a point and has no specific direction.

Reading the equation

In physics equations, each letter represents a measurable quantity. A fraction means "divided by," so p = F/A reads as "pressure equals force divided by area." Whenever a quantity sits in the denominator (bottom of the fraction), increasing that quantity decreases the result.

Key Equations

Pressure:

$$p=\frac{F}{A}$$

Variables:

• $p$ = pressure, in pascals (Pa)
• $F$ = force acting perpendicular to the surface, in newtons (N)
• $A$ = area over which the force acts, in metres squared (m²)

SI unit: Pa (1 Pa = 1 N m⁻²)

Rearrangements

Starting from $p=\frac{F}{A}$:

Rearranging for force:

$$F=p\times A$$

Rearranging for area:

$$A=\frac{F}{p}$$

Proportionality

• Pressure is directly proportional to force when area is constant. Doubling the force doubles the pressure.
• Pressure is inversely proportional to area when force is constant. Doubling the area halves the pressure.

Worked Example

A crate weighing 600 N stands on the floor. The base of the crate has an area of 0.20 m². Calculate the pressure the crate exerts on the floor.

Equation used

$$p=\frac{F}{A}$$

Given

$$F=600\text{ N}$$

$$A=0.20{\text{ m}}^{2}$$

Substitution

$$p=\frac{600}{0.20}$$

$$p=3000\text{ Pa}$$

Answer

$$p=3000\text{ Pa}$$

MisconceptionStudents sometimes write the unit of pressure as N/m or forget to square the metre. The SI unit is the pascal (Pa), equivalent to N m⁻². Always check that area is in m², not cm².

Exam TipIf area is given in cm², convert to m² by dividing by 10⁴ before substituting.

Pressure in Everyday Contexts

The relationship between force, area, and pressure explains many everyday observations.

When designers want high pressure, they reduce the area on which a force acts. When they want low pressure, they increase the area. The table below summarises common examples.

In every case, the force involved (usually the weight of the person or object) stays the same. The change in pressure results entirely from the change in area.

Examiner InsightCIE frequently asks students to explain an everyday situation using the pressure equation. Always state three things: (1) what the force is, (2) whether the area is large or small, and (3) the effect on pressure using the word "inversely proportional" or the equation p = F/A.

Exam TipName the force (e.g. "weight") — do not just write "force."

Pressure Beneath a Liquid Surface

Liquid pressure increases with depth below the surface because a greater depth of liquid sits above the point, so a greater weight of liquid pushes down.

Three key facts describe how pressure in a liquid behaves:

1. Pressure increases with depth. The deeper the point beneath the surface, the greater the weight of liquid above it, so the greater the pressure.

2. Pressure increases with the density of the liquid. A denser liquid has more mass in the same volume, so the weight of liquid above a given depth is greater, which produces a greater pressure. Mercury (density ≈ 13 500 kg m⁻³) exerts a much higher pressure at the same depth than water (density ≈ 1000 kg m⁻³).

3. Pressure acts equally in all directions at a given depth. At any point in a liquid, the pressure pushes up, down, and sideways with the same magnitude.

A simple demonstration shows these ideas: a tall container of water with small holes at different heights leaks water furthest from the lowest hole, because the pressure is greatest at the greatest depth.

MisconceptionStudents sometimes state that pressure in a liquid depends on the total volume of liquid. Pressure at a point depends only on the depth below the surface and the density of the liquid, not on the shape or total volume of the container. Two containers with different widths but the same liquid and the same depth produce the same pressure at their bases.

Exam TipWrite "depth" not "amount of liquid."

Extended Calculating Pressure Change in a Liquid

Extended The pressure change beneath the surface of a liquid can be calculated using the equation Δp = ρgΔh.

Reading the equation

The symbol Δ (Greek capital delta) means "change in." So Δp means "change in pressure" and Δh means "change in depth." The equation tells us the additional pressure caused by a column of liquid of height Δh, not the total pressure (which would also include atmospheric pressure above the liquid surface).

Key Equations

Pressure change beneath a liquid surface:

$$\Delta p=\rho g\Delta h$$

Variables:

• $\Delta p$ = change in pressure, in pascals (Pa)
• $\rho $ = density of the liquid, in kilograms per metre cubed (kg m⁻³)
• $g$ = gravitational field strength, in newtons per kilogram (N kg⁻¹). Use $g=9.8$ N kg⁻¹ (or 10 N kg⁻¹ if the question states so).
• $\Delta h$ = change in depth below the surface, in metres (m)

SI unit: Pa

Rearrangements

Starting from $\Delta p=\rho g\Delta h$:

Rearranging for depth change:

$$\Delta h=\frac{\Delta p}{\rho g}$$

Rearranging for density:

$$\rho =\frac{\Delta p}{g\Delta h}$$

Proportionality

• Δp is directly proportional to Δh when ρ and g are constant. Doubling the depth doubles the pressure change.
• Δp is directly proportional to ρ when Δh and g are constant. A liquid twice as dense produces twice the pressure change at the same depth.