Pressure: Force Spread Over Area
Quick answer Pressure is the force acting on unit area. The same force concentrated on a small area produces a large pressure, which is why sharp things are sharp and bag straps are broad.
Push a drawing pin into a soft board with your thumb and it slides in easily. Now turn the pin round, press the flat head against the board with exactly the same push, and nothing happens. The force from your thumb has not changed at all. What has changed is the area over which that force acts. That single observation is the whole idea of pressure.
When you push or pull on a surface, the force acting at right angles to that surface is often called the thrust. The effect of a thrust does not depend only on how large it is; it also depends on how much surface it is spread over. Pressure is defined as the thrust acting on unit area:
Pressure = Force (thrust) / Area
In the SI system, force is measured in newton (N) and area in square metre (m2), so pressure comes out in newton per square metre (N/m2). This unit is given a special name, the pascal, written Pa. So a pressure of 1 Pa is what you get when a force of 1 N is spread evenly over an area of 1 m2.
Read the relationship slowly, because everything else in this chapter follows from it. If the force stays the same and the area becomes smaller, the pressure becomes larger. If the same force is spread over a bigger area, the pressure becomes smaller. A long list of everyday objects has been designed around exactly this.
Small area on purpose, to get high pressure. The tip of a nail, the point of a pin, the edge of a knife, the tip of an injection needle and the thin blades of ice skates are all made sharp or narrow. A blunt knife and a sharp knife may be pressed on a vegetable with the same force from your hand, but the sharp one squeezes that force on to a tiny strip of area, so the pressure there is enormous and the vegetable gives way. Blunt the edge and the same push is now shared over a much wider strip, the pressure drops, and the vegetable simply gets squashed instead of cut.
Large area on purpose, to get low pressure. School bags are given broad, padded straps rather than thin strings, because the same weight spread across a wider patch of your shoulder presses far less painfully. Tractors and heavy earth-moving machines run on very wide tyres so that they do not sink into soft soil. The foundation of a building is made much wider than the wall it carries, so that the soil underneath is not crushed. A camel crosses soft sand on broad, flat feet, and an elephant of enormous weight stands on wide soles that spread its weight out.
A simple calculation. Suppose a box presses down on the floor with a force of 300 N. If it rests on a face of area 0.5 m2, the pressure is 300 / 0.5 = 600 Pa. Tip the very same box on to a face of area 0.1 m2 and the pressure becomes 300 / 0.1 = 3000 Pa, which is five times as much. Nothing about the box or its weight changed. Only the area did.
One more everyday check: stand on both feet, then lift one foot. Your weight has not changed, but it is now carried on half the area, so the pressure on the floor has doubled. On a soft mattress or wet sand you can actually see the difference in how deep the mark goes.
- Pressure is the thrust acting on unit area: Pressure = Force / Area.
- The SI unit of pressure is the pascal (Pa), and 1 Pa = 1 N/m squared.
- For a fixed force, a smaller area gives greater pressure and a larger area gives smaller pressure.
- Nails, pins, needles and knife edges are made sharp so that a small area turns an ordinary force into a very high pressure.
- Broad bag straps, wide tractor tyres, camel feet and wide building foundations do the opposite: they spread the force so the pressure stays low.
