Speed, density and pressure: Formulae and units
In a nutshell
Speed, density and pressure are three quantities used all the time in the real world. They each have their own formula which can be rearranged to calculate other quantities.
Definitions
| Definition | Formula triangle
| Units |
Speed
| The distance travelled per unit time. | | m/s - metres per second km/h - kilometres per hour
|
Density
| The mass per unit volume of a substance.
| | kg/m3 - kilograms per metre cubed
g/cm3 - grams per centimetre cubed
|
Pressure
| The force acting per unit area. | | N/m2 - newtons per metre squared
Pa - pascals
|
Note: Newtons are used to measure force!
Formula triangles
Formula triangles are really useful tools to help rearrange formulae. To use them, simply cover the quantity that you want to find out and write down whatever is left as the formula.
Example 1
Find the formulae for a, b and c.
Cover each letter and write down the remaining formula.
abc=cb=a×c=ab
| |
Speed, density and mass units
All three quantities are made up of two units of measure and therefore conversions between units need to be done in steps. If two conversions are needed, convert one of the two units first and then the other.
Note: It's vital that units remain consistent across each of the three measures used in the equation.
Example 2
Convert 150,000,000m/s into km/h. Give your answer to one decimal place.
Start by converting into kilometres.
1km=1000m
150,000,000÷1000=150,000
Then convert into minutes and then hours.
1 min=60 secs1 hour=60 mins150,000÷60=25002500÷60=41.6666=41.7km/h
Speed
Using the formula triangle, the formula for speed can be rearranged in three ways where: S = speed, D = distance and T = time.
Speed=TimeDistance
| Distance=Speed×Time
| Time=SpeedDistance
|
Example 3
Anna is having a race with her sister between two lamp posts which are 25 metres apart. It took Anna 6.8 seconds to run between the two - what speed was she going at? Give your answer to two decimal places.
Use the formula triangle to write down the formula for speed.
Speed=TimeDistance
Plug the values into the formula.
Speed=6.825=3.67647059=3.68 to two decimal places.
Look back to the question to find units and add these to the answer. Since metres and seconds have been used, the units are metres per second: m/s.
3.68m/s
Density
Using the formula triangle, the formula for density can also be rearranged in three ways where: D = density, M = mass and V = volume.
Density=VolumeMass
| Mass=Density×Volume
| Volume=DensityMass
|
Example 4
A solid chocolate egg has a mass of 320g. If its density is 3.4g/cm3, what is the volume of the egg? Give your answer to two decimal places.
Use the formula triangle to write down the formula for volume.
Volume=DensityMass
Plug in the values into the formula.
Volume=3.4320=94.1176471=94.12 to two decimal places.
Select units based on what is used in the question.
94.12cm3
Pressure
Using the formula triangle once more, the formula for speed can be rearranged in three ways where: P = pressure, F = force, and A = area.
Pressure=AreaForce
| Force =Pressure×Area | Area=PressureForce
|
Example 5
A 50cm×30cm book exerts a pressure of 12N/m2 onto a table top. Calculate the force exerted by the book.
Use the formula triangle to write down the formula for force.
Force =Pressure×Area
Calculate the area of the book.
50cm×30cm=1500cm2
Check the units in the question. Pressure is measure in N/m2 so cm2 must be converted to m2.
1500÷100÷100=0.15m2
Plug into the equation.
Force=12×0.15=1.8
Add units.
1.8N