- Pressure describes how concentrated a force is when it acts on a surface.
- The effect of a force depends not only on how large the force is, but also on the size of the area over which it is applied.
- A force acting on a small area produces a larger effect than the same force acting on a larger area.
- Pressure helps explain everyday experiences such as cutting, piercing, and sinking.
- Walking barefoot on sand feels easier than walking on sharp shingle.
- Your weight (force) is similar in both situations, but the contact area is much smaller on the sharp stones, so the pressure on your skin is larger.
In the simplest situations, pressure is calculated using
$$P=\frac{F}{A}$$
where $P$ is pressure, $F$ is the force acting perpendicular (normal) to the surface, and $A$ is the contact area.
- Pressure increases when a force is applied over a smaller contact area.
- Pressure decreases when the same force is spread over a larger contact area.
- Both force and area must be considered together to understand pressure.
Changing the contact area changes the pressure even if the force remains constant.
- The SI unit of pressure is the pascal (Pa): $$1\ \mathrm{Pa}=1\ \mathrm{N\ m^{-2}}$$
- In everyday contexts, you often see:
- kPa: $1\ \mathrm{kPa}=10^3\ \mathrm{Pa}$
- MPa: $1\ \mathrm{MPa}=10^6\ \mathrm{Pa}$
- hPa (hectopascal): $1\ \mathrm{hPa}=100\ \mathrm{Pa}$ (common in weather maps)
- bar: $1\ \mathrm{bar}=10^5\ \mathrm{Pa}$ (so $1\ \mathrm{mbar}=1\ \mathrm{hPa}$)
Forgetting to convert areas into $\mathrm{m^2}$ because area depends on length squared, converting cm to m changes the numerical value a lot.
- When a force is concentrated onto a tiny area, the pressure can become enormous.
- This is why sharp tools work as they create high pressure at the cutting edge.
- Whenever you see pressure questions, write the units beside each value before substituting.
- If your final unit is not $\mathrm{Pa}$ (or an equivalent like $\mathrm{N\ m^{-2}}$), you have probably used the wrong area unit.