Pressure
Force spread out: how area matters, why depth counts, and why sharp things pierce surfaces.
Core Idea
Pressure = Force ÷ Area. Smaller area = bigger push. Bigger area = smaller push.
In Liquids
Pressure gets stronger deeper down because of the weight of water above. Δp = ρgΔh
Real Life
Tractors use big tyres to reduce pressure. Drawing pins use sharp points to increase it. High heels sink.
Pressure & Forces
📖 What Is Pressure?
Imagine pushing with the same force, but through a thin needle instead of your palm. The needle hurts more—not because you're pushing harder, but because the force is crammed into a tiny space.
Pressure is the force pushing on a surface, divided by how big that surface is.
Think of it this way:
- A normal shoe spreads your weight over a large area → low pressure → your foot doesn't sink into mud
- A high heel concentrates your weight into a tiny area → high pressure → it punches into soft ground
- A bulldozer has huge tyres to spread its massive weight → low pressure → it doesn't sink even though it weighs tonnes
🔑 Remember: 1 Pascal = 1 Newton per square metre
A pascal (Pa) is a tiny unit. A N/m² is just another name for it. You'll often see pressures in kPa (kilopascals). 1 kPa = 1000 Pa.
Worked Example: Lifting Machine
Question
A pump creates a pressure of 5.28 × 10⁵ Pa in a liquid. This liquid pushes on a piston with a cross-sectional area of 2.73 × 10⁻² m². Calculate the force the liquid applies to the piston.
Step 1: List Known Quantities
Pressure (p) = 5.28 × 10⁵ Pa
Area (A) = 2.73 × 10⁻² m²
Step 2: Write the Equation
p = F ÷ A
Rearrange: F = p × A
Step 3: Substitute & Calculate
F = (5.28 × 10⁵) × (2.73 × 10⁻²)
F = 14,414.4 N
Step 4: Final Answer (3 sig figs)
F = 14,400 N or 14.4 kN
💡 The Key Relationship
The bigger the area, the lower the pressure (for the same force).
This is why:
- Tractors have huge tyres. A tractor weighs tonnes, but its big tyres spread that weight over a massive area. This keeps pressure low, so it doesn't sink into mud or soft soil.
- Drawing pins have sharp points. You press down with your thumb (a big area), but the pin funnels all that force into a tiny needle-like tip. This creates huge pressure that pierces the wall.
- High heels have small contact areas. Your weight is concentrated on a 1 cm² heel, creating high pressure. This is why they sink into soft surfaces (and why they're uncomfortable on tile!).
💭 Exam Insight: Pressure Questions Often Ask…
Why does X happen? The answer is always about comparing areas. A wider tyre = larger area = lower pressure.
Practice Question 1
Practice Question 2