- Calculate the pressure of a solid with p = F / S
- Find the pressure at a depth in a liquid and explain Pascal's law
- Explain how atmospheric pressure is measured and how it changes with height
Walking in snow in ordinary boots, your feet sink, but on skis you glide easily over the top. A sharp knife cuts bread easily, while a blunt one just squashes it. In both cases the force is the same — what makes the difference is pressure.
Pressure of solids
The force acting perpendicular to a surface divided by the area of that surface. Its unit is the pascal: 1 Pa = 1 N/m².
- ppressure, in pascals (Pa)
- Fforce acting perpendicular to the surface, in N
- Sarea of the surface, in m² (often written A in English books)
Leyla, who has a mass of 45 kg, stands on snow. The soles of her two boots have a total area of 300 cm², and her skis have an area of 0.3 m². Find the pressure she exerts on the snow in each case (g = 10 N/kg).
Show solutionHide solution
In boots: S = 300 cm² = 0.03 m², p = 450 N / 0.03 m² = 15 000 Pa (15 kPa).
On skis: p = 450 N / 0.3 m² = 1500 Pa.
On skis the pressure is 10 times smaller, so Leyla doesn't sink.
- To reduce pressure, the area is made larger: wide tractor tracks, broad building foundations, skis.
- To increase pressure, the area is made smaller: a sharp knife, a needle, a nail.
Pressure in liquids and Pascal's law
Because of its weight, a liquid presses on the bottom and walls of its container and on anything inside it. The deeper you go, the greater the pressure: the deeper a diver goes, the more pressure they feel in their ears.
- ρdensity of the liquid, in kg/m³ (1000 kg/m³ for water)
- gacceleration due to gravity, ≈ 9.8 N/kg
- hdepth below the surface, in m
Pressure at a depth in a liquid (hydrostatic pressure)
A diver goes down to a depth of 10 m. What pressure does the water exert on the diver? (ρ = 1000 kg/m³, g = 10 N/kg)
Show solutionHide solution
Interestingly, this is about the same as normal atmospheric pressure: every 10 m of water adds roughly one more “atmosphere”.
Pressure applied to a liquid or gas in a closed container is passed on unchanged to every point of it and in all directions.
In a hydraulic lift the small piston has an area of 5 cm² and the large one 500 cm². A force of 200 N is applied to the small piston. What force does the large piston exert?
Show solutionHide solution
F₂ = F₁ · S₂ / S₁ = 200 N · 500 / 5 = 20 000 N.
The force is multiplied by 100 — enough to lift a car with a mass of about 2 tonnes.
Atmospheric pressure
The air around the Earth also has weight, so it presses on everything. In 1643 the Italian scientist Evangelista Torricelli showed that atmospheric pressure can hold up a column of mercury about 760 mm high. Normal atmospheric pressure is 760 mmHg, which is about 101 300 Pa. It is measured with a barometer.
- As you go higher, the air gets thinner and the pressure drops: near the ground, by about 1 mmHg for every 12 m.
- When you drink juice through a straw, you remove air from the straw and atmospheric pressure pushes the juice up.
- When you press a rubber suction cup onto glass, the air under it is pushed out and atmospheric pressure holds it against the glass.
Key points
- Pressure = force / area: p = F / S, measured in pascals (1 Pa = 1 N/m²).
- A smaller area means a greater pressure; a larger area means a smaller pressure.
- Pressure in a liquid increases with depth: p = ρ · g · h.
- Pascal's law: pressure is transmitted equally in all directions in liquids and gases — hydraulic machines rely on it.
- Normal atmospheric pressure ≈ 760 mmHg ≈ 101 300 Pa, and it drops with height.
Check yourself
10 questions. Every correct answer earns XP.