Ciencias
Pressure: The Same Force Spread Over a Different Area
Pressure is force divided by area, in pascals. Worked for one person in flat shoes and in stilettos: the same weight, and an answer 300 times larger.
Pressure
Pressure is the force acting at right angles to a surface divided by the area over which that force is spread, measured in pascals.
- Dónde lo encuentra el alumnado
- Grade 7 science, and again at GCSE and IGCSE, where p = F ÷ A is extended to p = h ρ g for the pressure at a depth in a liquid.
La respuesta corta
Pressure is the force acting on a surface divided by the area that force is spread over, measured in pascals, where one pascal is one newton per square metre. The same person standing on a stiletto heel exerts hundreds of times the pressure they exert in flat shoes, because only the area has changed.
Un ejemplo
p = F ÷ A = 600 N ÷ 0.0001 m² = 6 000 000 Pa
Take a person of 60 kg, whose weight is about 600 N with g at 10 N/kg. Suppose the tip of one stiletto heel is a square centimetre, which is 0.0001 m². All 600 N is now delivered through that patch, and the pressure is six million pascals. The measurements of the heel are an estimate chosen to make the arithmetic clean; the weight is not an estimate, and it never changes in this question.
One person, two pairs of shoes, two very different answers
Run the same 600 N through a flat sole and the picture changes completely. Say the two soles together touch the floor over about 300 cm², which is 0.03 m². The pressure is 600 ÷ 0.03 = 20 000 Pa, or 20 kPa. Standing on one stiletto heel gives 6 000 000 Pa. The pressure is roughly three hundred times greater, and nothing about the person is different.
This is the point of the example, and it is worth saying out loud: the force was constant throughout. Pressure questions look like they are about how heavy something is, and they are almost always about how the load is spread.
- Flat shoes, two soles: 600 N ÷ 0.03 m² = 20 000 Pa
- One stiletto heel: 600 N ÷ 0.0001 m² = 6 000 000 Pa
- Same person, same weight, area smaller by a factor of 300
Objects that are designed around this
A drawing pin is the argument in miniature. Your thumb pushes on a wide flat head, so the pressure on your thumb is low and it does not hurt. The identical force leaves through a point of almost no area, so the pressure on the wood is enormous and the pin goes in. One force, two areas, two outcomes — that is the entire design.
The same reasoning runs in both directions. Where you want a large pressure, shrink the area: a knife is sharpened, an ice skate rides on a thin blade. Where you want a small one, spread it: snowshoes, the wide tyres of a tractor, a camel's foot, and the advice to lie flat rather than stand if you find yourself on thin ice.
The conversion that costs more marks than the physics
Pascals are newtons per square metre, so the area must be in square metres before it goes into the formula. Converting square centimetres to square metres means dividing by 10 000, not by 100, because a square metre is 100 cm by 100 cm. An answer that is out by a factor of 100 is nearly always this.
One more distinction worth having straight: force is a vector and has a direction, but pressure is a scalar. In a liquid or a gas, pressure at a point acts equally in every direction, which is why a submarine hull is squeezed from all sides and why the depth formula has no direction in it at all.
Preguntas frecuentes
Is pressure the same thing as force?
No. Force is measured in newtons and pressure in pascals, and one is the other divided by an area. The same force can produce almost any pressure you like depending on how it is spread, which is why a person can walk on snow in snowshoes and sink to their knees without them.
How do I convert cm² to m²?
Divide by 10 000. A square metre measures 100 cm along each side, so it contains 100 × 100 = 10 000 square centimetres. So 50 cm² is 0.005 m². Doing this before you substitute, rather than trying to fix the answer afterwards, is the safest habit.
Why does pressure increase as you go deeper in water?
Because the weight of all the water above you is pressing down, and there is more of it the deeper you go. The pressure at a depth depends on the depth, the density of the liquid and gravitational field strength — the shape of the container does not come into it, which surprises people.
Why do my ears hurt on a plane or in the mountains?
Air has weight too, so atmospheric pressure falls as you climb. The air trapped behind your eardrum stays at the pressure it was sealed at, so there is a pressure difference across the drum and it is pushed outwards until swallowing or yawning lets the two sides equalise.
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