Pressure
Pressure — definition and calculations
Defining pressure
Pressure is the force acting per unit area on a surface, acting at right angles (perpendicularly) to it.
\[ P = \frac{F}{A} \]
1 pascal = 1 newton per square metre (1 Pa = 1 N/m²).
| Symbol | Quantity | Unit |
|---|---|---|
| \( P \) | Pressure | pascal, Pa (= N/m²) |
| \( F \) | Force acting perpendicular to the surface | newton, N |
| \( A \) | Area over which the force acts | square metre, m² |
What affects pressure:
- A larger force on the same area → greater pressure.
- The same force spread over a larger area → smaller pressure.
Pressure in everyday design
| Example | Explanation |
|---|---|
| Knife blade (sharp) | Very small contact area → very high pressure → cuts easily |
| Snowshoes (wide) | Large area distributes weight → low pressure → walker does not sink into snow |
| Drawing pin (sharp tip) | Small tip area → high pressure enough to pierce surface |
| Tractor tyres (wide) | Large contact area → low pressure → does not sink into soft soil |
| Stiletto heel | Tiny heel area → very high pressure on flooring |
| Camel's padded feet | Wide feet spread weight → low pressure on desert sand |
Worked examples
Example 1 — calculate pressure
A block of weight 240 N rests on a floor. Its base area is 0.060 m². Calculate the pressure on the floor.
\( P = \dfrac{F}{A} = \dfrac{240}{0.060} = 4000\,\text{Pa} \)
Example 2 — find area from pressure and force
A person of weight 600 N exerts a pressure of 15 000 Pa on the ground. What is the total contact area of their feet?
\( A = \dfrac{F}{P} = \dfrac{600}{15\,000} = 0.040\,\text{m}^2 = 400\,\text{cm}^2 \)
Example 3 — compare two scenarios
A woman (weight 550 N) wears flat shoes (contact area 150 cm²) or stiletto heels (contact area 2.0 cm², combined). Compare the pressures.
Flat shoes: \( P = \dfrac{550}{0.0150} = 36\,700\,\text{Pa} \)
Stilettos: \( P = \dfrac{550}{0.000200} = 2\,750\,000\,\text{Pa} \)
The stiletto heels exert about 75 times greater pressure — enough to damage wooden floors.
Always convert area to m² before using \( P = F/A \). Common errors: using cm² instead of m² (1 cm² = 0.0001 m²), or using mass instead of weight for \( F \) (remember: \( F = mg \), weight in N not kg).
"Explain why…" pressure questions need two steps: (1) state what happens to the area (larger/smaller), then (2) link area to pressure using \( P = F/A \). One mark per step. Never just say "more pressure" — say why in terms of force and area.