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Compound measures involve two or more different units.

Examples of compound measures and their units include pressure (\(N/ m^2\)), density (\(g/ cm^3\)), speed (km/h) and heart rate (beats per minute).

Units for measuring such as metres, kilograms and litres are covered in the guides on metric units and are examples of single units.

The compound units covered in Module 1 - Metric Units are speed, heart rate and fuel economy, while density is covered in Units of measure.

Pressure is the force of an object per unit of area.

Calculating pressure given force and area

Pressure is calculated by dividing the force (N) of an object by the area (m²) it is acting on.

Pressure is measured in \(N/ m^2\) or in Pascals (Pa).

\(\LARGE \text{Pressure} = \frac{\LARGE {force}}{ \LARGE {area}}\)

\(\LARGE \text{P} = \frac{\LARGE {F}}{ \LARGE {A}}\)

Example

Find the pressure caused by a force of 168 N acting on an area of 40 m².

• Force = 168 N
• Area = 40 m²

using \( \text{Pressure} = \frac{force}{area}\)

\( \text{Pressure} = \frac{168}{40} = 4.2 N/m^2\)

If the pressure and area are known the formula can be rearranged to calculate force by multiplying both sides by area.

\(\Large {\mathbf{\color{orange}{Area} \color{black}\times Pressure = \frac{force}{\cancel{Area}} \times \color{orange}\cancel{Area}}}\)

\(\textbf{Force} = \textbf{Area} \times \textbf{Pressure}\)
\(\textbf{F} = \textbf{A} \times \textbf{P}\)

Example

A box of books exerts a pressure of 184 \(\text N/m^2\) on the floor. The dimensions of the bottom of the box are 0.5 m by 0.8 m.

Calculate the force due to the weight of the box of books.

Area = 0.5 x 0.8 = 0.4 m²

Pressure = 184 \(\textbf N/m^2\)

Force = Area × Pressure
Force = 0.4 x 184 = 73.6
Force = 73.6 N

\(\LARGE \text{Area} = \frac{\LARGE {Force}}{\LARGE{Pressure}}\)

\(\textbf{A} = \frac{\textbf{F}}{\textbf{P}}\)

Example

A package exerts a force of 4.8 N on a table.
The pressure on the table is 60 N/m².

Calculate the area of the package that is in contact with the table.
Force = 4.8 N
Pressure = 60 N/m²

\(\text{Area} = \frac {\text{Force}}{\text{Pressure}}\)
\(\text{A} = \frac{4.8}{60} = 0.08 m^2\)