Pressure

Press on the head of a thumbtack with your finger and nothing happens; yet the tack's point slips into the wall with ease. The force you applied was exactly the same — the difference lies not in its size but in the area. The smaller the area a given force is spread over, the more it "bites". Physicists gave this biting power a name: pressure.

Pressure equals force divided by area

$p = \frac{F}{A}$

Here $F$ is the force pressing straight down on a surface, in newtons, and $A$ is the area over which it spreads, in square meters. Pressure $p$ is measured in pascals (Pa): $1\ \mathrm{Pa} = 1\ \mathrm{N/m^2}$ — one newton spread over one square meter.

One pascal is tiny — even a sheet of paper lying flat on a table exerts about 0.5 Pa — so kilopascals (kPa) are common: 1 kPa = 1000 Pa. Standard atmospheric pressure is about 100 kPa, the weight of roughly 10 tons pressing on every square meter — no wonder a suction cup takes real muscle to pull off. What forces are and how they combine is the groundwork laid in force and Newton's laws.

Pressure masters in daily life

The thumbtack: your finger's force is squeezed into a point of a tip, so tiny an area that the pressure multiplies tens of thousands of times;
Snowshoes: the same trick run backwards — spread the force over a big sole and the pressure drops to what snow can bear, so you stop sinking;
Wide backpack straps: a broad strap spreads the bag's weight out so your shoulders stay comfortable; a thin cord with the same weight digs red lines into them;
Knife edges: the thinner the edge, the easier the cutting — the same rule of small area, big pressure.

Try the math

Snowshoes or sneakers?

A 50 kg student has a weight of about $50 \times 9.8 = 490$ N (call it 500 N for easy arithmetic). Ordinary soles touch the snow over roughly $0.05\ \mathrm{m^2}$ , giving a pressure of about $500 \div 0.05 = 10000$ Pa. Swap to snowshoes with 5 times the contact area and the pressure falls to about $10000 \div 5 = 2000$ Pa — same force, spread wide, no sinking. How weight itself is computed is covered fully in gravity and free fall.

Cord or strap?

A 6 kg backpack weighs about 60 N. A thin cord 1 cm wide resting along 30 cm of shoulder has a contact area of about $0.003\ \mathrm{m^2}$ , so the pressure is $60 \div 0.003 = 20000$ Pa. A 5 cm-wide strap covers about $0.015\ \mathrm{m^2}$ , and the pressure drops to $60 \div 0.015 = 4000$ Pa. Five times wider, five times gentler — there is not one thin strap on a backpack, and this division is why.

Check yourself

Quick quiz

1. A pressure of 10000 Pa corresponds to how much force on each square meter?
2. When the same person puts on snowshoes, what happens to the pressure on the snow?
3. Why does a thumbtack's point pierce a wall so easily?