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Pressure

Section 1.8: Force and pressure

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Pressure Defined

P = F / A

where: P = pressure (Pa or N/m²), F = force (N), A = area (m²)

Key insight: Pressure is force spread over an area. Smaller area = greater pressure for same force.

Real-world examples (IGCSE-examinable):

Knife (sharp point) → small area → high pressure → cuts easily

Snowshoes → large area → low pressure → doesn't sink

Heel shoes → tiny contact → very high pressure

Force vs Pressure

Key difference:
• Force: Measured in Newtons (N) — push or pull
• Pressure: Measured in Pascals (Pa) — force concentrated on area

The same force can create different pressures:

Push with open hand = large area = low pressure = no damage

Push with fingertip = tiny area = high pressure = penetrates

Exam insight: Examiners often ask: "How does area affect pressure?" Always explain using P = F/A.

Worked Example 1: Box on Table

Question:
A box (weight 500 N) sits on a table. Contact area = 0.05 m².
What is the pressure on the table?

Solution:

P = F / A

P = 500 / 0.05

P = 10,000 Pa (or 10 kPa)

Key point: Pressure is inversely proportional to area. Smaller area → higher pressure.

Worked Example 2: Person Standing

Question:
A person (weight 600 N) stands on one foot. Foot area = 0.015 m².
Calculate pressure exerted on ground. Then find pressure if standing on both feet (0.03 m²).

On one foot: P = 600 ÷ 0.015 = 40,000 Pa

On both feet: P = 600 ÷ 0.03 = 20,000 Pa

Exam note: Double-check units! If area is in cm², convert to m² first (1 m² = 10,000 cm²).

Pressure Varies with Force AND Area

Increasing Force → Pressure increases:

P ∝ F (if area constant)

Increasing Area → Pressure decreases:

P ∝ 1/A (if force constant)

Combined: P = F/A means:
• Double the force at same area = double the pressure
• Double the area with same force = halve the pressure

Pressure in Liquids — The Formula

Δp = ρgΔh

where: Δp = pressure increase (Pa), ρ = density (kg/m³), g = 9.8 m/s², Δh = depth (m)

Key insight: Pressure in liquids increases with depth. The deeper you go, the greater the pressure from the weight of liquid above.

Why? Imagine a column of water pushing down from above. Deeper = taller column = heavier = more pressure.

Pressure in Liquids — Worked Example

Question:
A diver is 20 m below the surface of seawater.
Density of seawater = 1025 kg/m³, g = 9.8 m/s².
Calculate the pressure increase due to the water.

Solution:

Δp = ρgΔh = 1025 × 9.8 × 20

Δp = 200,900 Pa ≈ 201 kPa

Real-world: At 20 m depth, water pressure alone is ≈200 kPa (plus ≈101 kPa atmospheric = ≈301 kPa total). Submarine hulls must be extremely strong!

Pressure in Liquids: Key Properties

Pressure increases with depth (qualitative understanding):

✓ Acts in all directions (sideways, up, down)

✓ Depends on liquid density: denser liquid = higher pressure at same depth

✓ Independent of container shape

Exam tip: If a question asks "why do submarines have thick hulls?" Answer: "Pressure increases with depth (Δp = ρgΔh). At great depth, pressure is very high."

Atmospheric Pressure

Atmospheric pressure at sea level ≈ 101,000 Pa (101 kPa)

Why? It's the weight of the entire air column (≈20 km) pressing down on Earth's surface. Imagine a column of air pushing from above!

Real-world everyday examples:

Suction cups work because atmospheric pressure pushes them on

Drinking from a straw: you lower mouth pressure → atmospheric pressure pushes liquid up

At higher altitudes, atmospheric pressure is lower → water boils at lower temperatures

Summary: The 4 Syllabus Objectives

1. p = F/A
Pressure equals force divided by area.

2. Pressure varies with force and area
More force → higher P. Larger area → lower P.

3. Pressure in liquids changes with depth (qualitative)
Deeper → higher pressure (weight of liquid above).

4. Δp = ρgΔh (quantitative)
Calculate pressure increase with depth.

Exam Technique: P = F/A Questions

Step 1: Identify force (F) in Newtons. If given weight, that's the force.
Step 2: Identify area (A) in m². If in cm², divide by 10,000.
Step 3: Calculate: P = F ÷ A
Step 4: State units: Pa or N/m² (they're the same!)

Common pitfall: Area given in cm²? Convert: 1 cm² = 0.0001 m² (divide by 10,000)

Exam Technique: Δp = ρgΔh Questions

Step 1: Identify density (ρ) in kg/m³. If not given, water ≈ 1000 kg/m³.
Step 2: Use g = 9.8 m/s² (or 10 for approximation).
Step 3: Identify depth change (Δh) in metres. If in cm, divide by 100.
Step 4: Calculate: Δp = ρ × g × Δh
Step 5: State units: Pa

Exam question clue: "Pressure increases..." or "deeper underwater" → use this formula!

Key Takeaways

✅ P = F / A — pressure is force per unit area

✅ Pressure increases with force, decreases with area

✅ Δp = ρgΔh — pressure increases with depth in liquids

✅ Atmospheric pressure ≈ 101 kPa at sea level

✅ Pressure acts in all directions in liquids

✅ Real examples: sharp objects (small area), submarines (deep = high pressure), straws (atmospheric pressure)

Master these 4 objectives — crush the pressure questions! 💪