Compound measures
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
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 \( \text{Pressure} = \frac{force}{area}\)
\( \text{Pressure} = \frac{168}{40} = 4.2 N/m^2\)
Question
The surface area of a pair of skis is 0.25 m².
How much pressure does a skier with a weight of 700 N exert on the snow?
Solution:
- Force = 700 N - Note: The force in this case is the weight of the skier.
- Area = 0.25 m²
\(\text{P} = \frac{F}{A}\)
\(\text{P} = \frac{700}{0.25} = 2800 N/m²\)
Answer
Pressure = 2800 N/m² or 2800 Pa (Pascals)
Calculating force given pressure and area
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 Ă— Pressure
Force = 0.4 x 184 = 73.6
Force = 73.6 N
Calculating area given pressure and force
If the pressure and force are known the formula can be rearranged to calculate the area
\(\LARGE \text{Area} = \frac{\LARGE {Force}}{\LARGE{Pressure}}\)
\(\textbf{A} = \frac{\textbf{F}}{\textbf{P}}\)
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
\(\text{Area} = \frac {\text{Force}}{\text{Pressure}}\)
\(\text{A} = \frac{4.8}{60} = 0.08 m^2\)
Question
A girl with a weight of 520 N is standing with both feet on the floor. Her shoes exert a pressure of 3.25 N/cm² on the floor.
What is the surface area of the sole of one of her shoes?
Solution:
Force = 520 NPressure = 3.25 N/cm²
\(\LARGE \text{Area} = \frac{\LARGE {Force}}{\LARGE{Pressure}}\)
\(\textbf{A} = \frac{520}{3.25}=160 cm^2\)
Answer:
Area of both shoes = 160 cm²
Area of the sole of one shoe = 80 cm²
Test yourself
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