Pressure Calculations

Pressure is the force per unit area acting on a surface.

The equation

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

Symbol	Quantity	Unit
$p$	Pressure	Pa (pascals)
$F$	Force (perpendicular to surface)	N
$A$	Area	m$^2$

1 pascal = 1 N/m$^2$.

Effect of changing force or area

Change	Effect on pressure
Increase force, same area	Pressure increases
Same force, increase area	Pressure decreases
Same force, decrease area	Pressure increases

This explains why:

• A sharp knife cuts easily (small area, high pressure).
• Snowshoes stop you sinking (large area, low pressure on snow).
• Heavy vehicles have wide tyres (large area, lower ground pressure).

Worked example

A box weighing 200 N rests on the floor. The base of the box has an area of 0.40 m$^2$. Calculate the pressure on the floor.

$p = \frac{200}{0.40} = 500\text{ Pa}$

Worked example: converting area

A stiletto heel has an area of 1.0 cm$^2$. A person weighing 600 N stands on one heel. Calculate the pressure.

Convert area: $1.0\text{ cm}^2 = 1.0 \times 10^{-4}\text{ m}^2$

$p = \frac{600}{1.0 \times 10^{-4}} = 6\,000\,000\text{ Pa} = 6.0 \times 10^6\text{ Pa}$

Common errors and how to correct them

Using area in cm$^2$ instead of m$^2$. The unit of pressure (Pa) requires force in N and area in m$^2$. Convert: $1\text{ cm}^2 = 10^{-4}\text{ m}^2$.

Using the total surface area instead of the contact area. Pressure uses the area in contact with the surface, not the total surface area of the object.

How to apply this in an exam

State the equation, convert area to m$^2$, substitute, calculate, and give the answer in Pa. For explanation questions, state how force and area affect pressure.