Pressure

Pressure — the force acting per unit area, at right angles to a surface:

p = F / A

with pressure in pascals (Pa), force in newtons and area in square metres. One pascal is one newton per square metre.

The same force gives a larger pressure over a smaller area. This single idea explains most of the examples:

• A drawing pin has a broad head and a sharp point. The same push gives a low pressure on your thumb and an enormous pressure at the tip, which is why it enters the board and not your finger.
• A knife is sharpened to reduce the contact area, raising the pressure for the same force.
• Skis and snowshoes do the opposite: they spread your weight over a large area, lowering the pressure so you do not sink.
• A camel's foot is broad for the same reason in sand.
• Tractor tyres are wide to reduce pressure on soft ground and avoid sinking or damaging soil.

Watch the units of area. Areas given in cm² must be converted to m² before use, and the conversion is not what people expect:

1 m² = 10 000 cm²

so divide an area in cm² by 10 000. Forgetting this gives an answer wrong by a factor of ten thousand, which is large enough to spot if you are checking whether the number is sensible.

Example: a box weighing 300 N rests on a base of 0.20 m². The pressure is p = F/A = 300 ÷ 0.20 = 1500 Pa. Stand the same box on a base of 0.020 m² and the pressure is 15 000 Pa — ten times greater for exactly the same weight.

Atmospheric pressure is about 100 000 Pa at sea level, which amounts to roughly 10 N on every square centimetre of you. It does not crush you because the pressure inside your body pushes out equally.