Pressure in Solids and Liquids
Senior 2 · Physics
Pressure in Solids and Liquids
Lesson 1 of 5
20 min
Let's begin
Why does a sharp panga cut sugar cane easily while a blunt one just bruises it? Why does a cow sink into a muddy path when a person does not? And why do lorries that carry heavy loads have so many wheels? The answer in every case is pressure: not just how big a force is, but how widely it is spread.
Pressure is the force acting perpendicularly (at right angles) on a surface, divided by the area of that surface:
P = F ÷ A
The SI unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m². A pascal is small, so kilopascals are common: 1 kPa = 1000 Pa. Pressure is a scalar: it has a size but no direction of its own.
A brick of mass 2.0 kg measures 0.20 m × 0.10 m × 0.050 m. Take g = 10 m/s², so its weight is F = 2.0 × 10 = 20 N.
| Face it rests on | Area (m²) | Pressure = 20 N ÷ A |
|---|---|---|
| 0.20 m × 0.10 m (largest) | 0.020 | 1000 Pa (lowest) |
| 0.20 m × 0.050 m | 0.010 | 2000 Pa |
| 0.10 m × 0.050 m (smallest) | 0.0050 | 4000 Pa (highest) |
The force is the same every time. Only the area changes. Smaller area means larger pressure.
A 60 kg student stands on two feet with a total sole area of 0.030 m² (g = 9.8 m/s²). Weight = 60 × 9.8 = 588 N. Pressure = 588 ÷ 0.030 = 19 600 Pa. On one foot, the area halves, so the pressure doubles to 39 200 Pa.
| We want a HIGH pressure, so we make the area small | We want a LOW pressure, so we make the area large |
|---|---|
| Sharp pangas, knives and axes; pointed nails, needles and drawing pins; the studs on football boots | Wide tyres and many wheels on heavy lorries; tractor tracks; wide straps on a heavy school bag; a wide base for a building (foundations) |
Tip
Pressure = "how concentrated" the force is
For the maximum pressure of a block, use its SMALLEST face. For the minimum, use its LARGEST face. Always convert cm² to m² first: 1 cm² = 0.0001 m².
A 5.0 kg block rests on a face of area 0.050 m² (g = 10 m/s²). Find the pressure on the table.
Solution: F = 50 N, so P = 50 ÷ 0.050 = 1000 Pa.
A farmer presses a panga onto a stem with a force of 40 N. The blade edge is 0.20 m long and 0.00020 m wide. What pressure does the edge exert?
Solution: A = 0.20 × 0.00020 = 4.0 × 10⁻⁵ m². P = 40 ÷ (4.0 × 10⁻⁵) = 1.0 × 10⁶ Pa. The tiny area gives an enormous pressure, which is why a sharp blade cuts.
A 400 kg cow stands on four hooves, each of area 0.0075 m² (g = 10 m/s²). Find the pressure on the ground.
Solution: F = 4000 N and A = 4 × 0.0075 = 0.030 m². P = 4000 ÷ 0.030 = 1.3 × 10⁵ Pa. That is far more than the student in Worked example 2, which is why cows sink into soft mud.
Why do heavy lorries have many wide tyres?
Solution: Spreading the weight over a larger area lowers the pressure on the road, so the lorry does not sink into soft ground or damage the road surface.
Summary
Sources and credits
The Rwandan examples, worked examples and practice items are written by Ganzaa.
