Pressure
Why a sharp knife cuts
- Press a blunt stick into your hand — nothing happens. A sharp pin at the same push hurts.
- The force is the same; what changed is the area it acts on.
- That idea is pressure — and it explains knives, snowshoes, and the deep sea.
What is pressure?
- Pressure is the force pressing on each unit of area:
- The unit is the pascal (Pa); $1\ \text{Pa} = 1\ \text{N/m}^2$.
- Same force, smaller area → bigger pressure.
A box pushes down with a force of $200\ \text{N}$ over an area of $0.50\ \text{m}^2$. What is the pressure, in Pa?
$p = \dfrac{F}{A} = \dfrac{200}{0.50} = 400\ \text{Pa}$.
Why area matters
- A sharp knife or a drawing pin has a tiny area, so it makes a huge pressure and cuts or pierces easily.
- Snowshoes and tractor tyres have a large area, so they make a small pressure and do not sink in.
- Camels' wide feet work the same way on soft sand.
Why does a sharp knife cut better than a blunt one (with the same push)?
Same force on a tiny area means a very large pressure ($p = F/A$), so it cuts easily.
Snowshoes stop you sinking into snow because they:
A larger area means a smaller pressure for the same weight, so you do not sink in.
Pressure in a liquid
- In a liquid, pressure increases with depth and with the liquid's density:
- It acts in all directions, not just downward.
- This is why a dam is built thicker at the bottom, where the water pressure is greatest, and why your ears hurt deep underwater.
Pressure in a liquid acts in all directions, not just downward.
A liquid pushes equally in all directions at a given depth — that is why it presses on the sides of a container too.
Find the extra pressure $2.0\ \text{m}$ deep in water ($\rho = 1000\ \text{kg/m}^3$, $g = 9.8\ \text{N/kg}$), in Pa.
$\Delta p = \rho g\,\Delta h = 1000 \times 9.8 \times 2.0 = 19\,600\ \text{Pa}$.
You've got it
- pressure $p = \dfrac{F}{A}$, unit the pascal ($1\ \text{Pa} = 1\ \text{N/m}^2$)
- small area → big pressure (knife); large area → small pressure (snowshoes)
- in a liquid, pressure rises with depth and density: $\Delta p = \rho g\,\Delta h$, acting in all directions