Pressure

1. Overview

Pressure is a measure of how concentrated a force is on a surface. Understanding pressure allows us to explain why heavy vehicles need wide tires to avoid sinking and how deep-sea submarines withstand the immense weight of the ocean above them.

Key Definitions

• Pressure: The force acting per unit area on a surface.
• Pascal (Pa): The SI unit of pressure, equivalent to one Newton per square metre ($1\text{ N/m}^2$).
• Density ($\rho$): The mass per unit volume of a substance.

Core Content

The Pressure Equation

Pressure depends on two factors: the size of the force applied and the area over which that force is spread.

• Large Area: Spreads the force, resulting in lower pressure.
• Small Area: Concentrates the force, resulting in higher pressure.

Everyday Examples

• High Pressure: A sharp knife has a very small surface area at the edge, creating enough pressure to cut through materials with little force.
• Low Pressure: Skis or snowshoes have a large surface area to spread the wearer's weight, preventing them from sinking into soft snow.

Pressure in Liquids (Qualitative)

The pressure in a liquid behaves differently than in solids:

• Depth: Pressure increases as depth increases. This is because there is a greater weight of liquid acting downwards on the layers below.
• Density: Pressure increases if the density of the liquid increases, as a denser liquid is heavier for the same volume.
• Direction: Pressure in a fluid acts equally in all directions.

Worked Example (Core)

A box weighs $200\text{ N}$ and has a base area of $0.5\text{ m}^2$. Calculate the pressure exerted by the box on the floor.

1. State the formula: $P = F / A$
2. Substitute values: $P = 200 / 0.5$
3. Answer: $400\text{ Pa}$

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Extended Content (Extended Only)

Calculating Pressure in a Liquid

To calculate the change in pressure beneath the surface of a liquid, we use the density of the liquid and the depth.

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

Where $g$ is the acceleration due to gravity (usually $9.8\text{ m/s}^2$ or $10\text{ m/s}^2$ in IGCSE).

Worked Example (Extended)

Calculate the pressure exerted by water at the bottom of a swimming pool $3\text{ metres}$ deep. (Density of water = $1000\text{ kg/m}^3$; $g = 9.8\text{ m/s}^2$).

1. State the formula: $p = \rho g h$
2. Substitute values: $p = 1000 \times 9.8 \times 3$
3. Answer: $29,400\text{ Pa}$ (or $29.4\text{ kPa}$)

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Key Equations

Equation	Symbols	Units
$p = \frac{F}{A}$	$p$ = Pressure, $F$ = Force, $A$ = Area	$p$ (Pa), $F$ (N), $A$ ($\text{m}^2$)
$\Delta p = \rho g \Delta h$	$\rho$ = Density, $g$ = Gravitational field strength, $h$ = Depth	$\rho$ ($\text{kg/m}^3$), $g$ (N/kg), $h$ (m)

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Common Mistakes to Avoid

• ❌ Wrong: Calculating pressure using $\text{cm}^2$ but giving the answer in Pascals (Pa).
• ✅ Right: Always convert $\text{cm}^2$ to $\text{m}^2$ before calculating Pascals. (Remember: $1\text{ m}^2 = 10,000\text{ cm}^2$).
• ❌ Wrong: Thinking that if the weight stays the same, the pressure stays the same.
• ✅ Right: If the weight (force) is constant, but you reduce the contact area (e.g., standing on one foot instead of two), the pressure increases.
• ❌ Wrong: Multiplying force by area ($F \times A$).
• ✅ Right: Pressure is force divided by area ($F / A$).
• ❌ Wrong: Assuming that halving the area and doubling the force cancels out.
• ✅ Right: This actually makes the pressure four times greater ($2F / 0.5A = 4P$).

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Exam Tips

1. Unit Conversion is Key: Examiners love to give the area in $\text{cm}^2$. To convert $\text{cm}^2$ to $\text{m}^2$, divide by $10,000$ (or $100^2$). If you just divide by $100$, your answer will be off by a factor of $100$.
2. Total Pressure: In "Extended" liquid pressure questions, if the question asks for the total pressure at a certain depth, you must add the atmospheric pressure (usually $1 \times 10^5\text{ Pa}$) to the liquid pressure you calculated ($p = \text{atmospheric pressure} + \rho gh$).
3. Rearranging the Formula: Practice using the formula triangle for $P=F/A$ so you can easily calculate Force ($F = P \times A$) or Area ($A = F / P$).