Speed, Density & Pressure (Edexcel IGCSE Maths A (Modular))

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Naomi C

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Speed, Density & Pressure

What are speed, density and pressure?

Speed, density and pressure are frequently used compound measures
- Speed is equal to distance divided by time
- Density is equal to mass divided by volume
- Pressure is equal to force divided by area

Formula Triangles for Speed, Density and Pressure

What should I know about speed, distance and time?

Speed is commonly measured in metres per second (m/s) or kilometres per hour (km/h)
- The units indicate speed is distance per time
  $Speed = \frac{Distance}{Time}$
'Speed' (in this formula) means 'average speed'
In harder problems there are often two journeys or two parts to one longer journey

What should I know about density, mass and volume?

Density is usually measured in grams per centimetre cubed (g/cm³) or kilograms per metre cubed (kg/m³)
- The units indicate that density is mass per volume
  $Density = \frac{Mass}{Volume}$

You may need to use a volume formula to find the volume of an object first

What should I know about pressure, force and area?

Pressure is usually measured in Newtons per square metre (N/m²)
- The units of pressure are often called Pascals (Pa) rather than N/m²
- The units indicate that pressure is force per area
  $Pressure = \frac{Force}{Area}$
Remember that weight is a force
- It is different to mass

Exam Tip

Look out for a mixture of units
- Time can be given as minutes but common phrases like 'half an hour' (30 minutes) could also be used in the same question
- Any mixed units should be those in common use and easy to convert, e.g., g to kg or m to km etc

Worked Example

A box exerts a force of 140 newtons on a table.
The pressure on the table is 35 newtons/m².

$p = \frac{F}{A}$ $p = pressure F = force A = area$

Calculate the area of the box that is in contact with the table.

Method 1

Substitute the numbers you know into the formula

$35 = \frac{140}{A}$

Solve the equation for A
First multiply both sides by A to get A out of the denominator

$35 A = 140$

Then divide by 35 to find the value of A

$\begin{array}{rcl} A & = & \frac{140}{35} \end{array}$

The units will be m², matching the units seen in newtons/m²

4 m²

Method 2

Use the given formula to create a formula triangle for pressure, force and area

$F p A$

A is on the bottom of the triangle, so this tells us to divide F by P

$A = \frac{F}{p} = \frac{140}{35} = 4$

4 m²

Worked Example

The density of pure gold is 19.3 g/cm³.

What is the volume of a gold bar that has a mass of 0.454 kg?

Begin by checking that all of the units are consistent
Density is given in g/cm³
Convert the volume of the gold bar into grams to match the units

0.454 kg = (0.454 × 1000) g = 454 g

The units of density are g/cm³, so divide the mass (g) by the volume (cm³)

Or, write out the formula triangle

Write out the formula that you will need

$Volume = \frac{mass}{density}$

Substitute the given values for the mass and the density

$Volume = \frac{454}{19.3} = 23.5233 . . .$

Make sure you give the correct units with your final answer
The density is given in g/cm³, so the volume should be cm³

Volume = 23.5 cm³ (1 d.p.)

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Speed, Density & Pressure (Edexcel IGCSE Maths A (Modular))

Revision Note

Speed, Density & Pressure

What are speed, density and pressure?

What should I know about speed, distance and time?

What should I know about density, mass and volume?

What should I know about pressure, force and area?

Exam Tip

Worked Example

Worked Example

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Author: Naomi C