Topic One (1.1): Base and Derived Units, Estimation

Introduction

Measurements only have meaning if they are based on a coherent system of units. So proper units underpin all the rest of Physics, and it is vital to keep a good understanding and awareness of our internationally agreed system of base and derived units (SI Units).

The SI units began with the metre in 1793, defined as one ten millionth of the distance between the north pole and the equator. Nearly two centuries of work followed until the SI unit system became official in 1960. It includes the units you will be familiar with from (I)GCSE Physics, such as metres, seconds, Amperes, Newtons, etc. You will need to know each quantity symbol and its unit, for example “mass (m) measured in kilograms (kg)”. Seven of the SI units are base units. You will need to be able to express the other units in terms of the base units. For example, force can be expressed as $LaTeX: kg\ m\ s^{-2}$ $kg\ m\ s^{-2}$ . This is because LaTeX: F=ma $F=ma$ , so Newtons = kilograms x metres per second squared.

Enrico Fermi was an Italian Physicist who created the world’s first nuclear reactor. He would amaze his colleagues by making very accurate estimations of experiments without knowing the exact measurements. He made calculations using only the power of ten for each quantity. For example, imagine someone asked you “How many ants would it take to make a line which is 10 metres long?”. We can start by finding the nearest power of ten for the length of an ant, would it be $LaTeX: {10}^{-1}m,\ {10}^{-2}m$ ${10}^{-1}m,\ {10}^{-2}m$ or $LaTeX: {10}^{-3}m$ ${10}^{-3}m$ ? Well ants are certainly shorter than 10 cm and longer than 1 mm, so we can say 1 cm ( $LaTeX: {10}^{-2}m$ ${10}^{-2}m$ ). Now divide $LaTeX: {10}^1m$ ${10}^1m$ (10m) by $LaTeX: {10}^{-2}m$ ${10}^{-2}m$ (0.01m) and we get an answer of 1,000 ants. This works for pretty much anything that equations can be used to calculate and has led to the famous Drake Equation which is used to estimate the amount of Intelligent alien civilisations in the Milky Way Galaxy.

Skills of estimation are invaluable for being aware whether results are reasonable for a situation. Use this skill throughout the course, and it will rescue you from a lot of errors!

Reading

Edexcel International AS/A Level Physics Student Book 1 pages 4 to 7

Tasks

Complete the following:

Read pages 4 to 7 of the textbook.
Go carefully through the worked example on page 7.

WATCH – The Fermi Paradox – Where Are All The Aliens? Links to an external site.

WATCH – SI Units and Derived Units (YouTube) Links to an external site.

WATCH – SI Base Units and Derived Units (Cowan Physics) (YouTube) Links to an external site.

WATCH – Units of Measurement in Physics (YouTube) Links to an external site.

WATCH – Making Measurements in Science (YouTube) Links to an external site.

WATCH – The kg is Dead, Long Live the kg (YouTube) Links to an external site.

WATCH – World’s Roundest Object (YouTube) Links to an external site.

COMPLETE – Gameboard: ‘A2 Derived and Base SI Units’ (Isaac Physics) Links to an external site.

WATCH – A Clever Way to Estimate Enormous Numbers – Michael Mitchell – TED Ed (YouTube) Links to an external site.

Complete the questions on page 5 and page 7. You will find the answers in General Resources under the heading Textbook Answers. Download Textbook Answers.

Extend

WATCH – What Is The Drake Equation? (YouTube) Links to an external site.

Top Tips

Make sure that you understand the following key points:

Thoroughly memorise Tables A, B, C on pages 4 and 5. You will not be asked about candela in the exam.
Learn all the quantity symbols and their units from the textbook.
Learn all the prefixes (e.g. kilo, mega, milli, etc.) and their matching power of ten (e.g. kilo is 10³ , mega is 10⁶ , milli is 10^-3).
Use your list of Physics equations to practice deriving these quantities: force, energy, power, frequency, charge, potential difference, resistance.
Pick simple equations to derive force, frequency and charge, such as $F=ma f=1/T$ and $Q=It$ .
Several of the derived quantities (energy, power, potential difference and resistance) need combined equations to eliminate derived units. For example, energy is (work = force x distance), but force is a derived unit from . So put these together and you get (work = mass x acceleration x distance). Change these quantities to base units and you get $LaTeX: E\ =\ kg\ {ms}^{-2}\ m$ $E\ =\ kg\ {ms}^{-2}\ m$ . Which simplifies down to $LaTeX: E=kg\ m^2\ s^{-2}$ $E=kg\ m^2\ s^{-2}$ .
Always check you give appropriate units with every answer!
We don’t need the first part of the standard form number to make estimations. For example, the height of an average human is $LaTeX: 1.7\ \times{10}^0$ $1.7\ \times{10}^0$ metres, but we can just say $LaTeX: {10}^0m$ ${10}^0m$ .
By eliminating the first part of the standard form number we are rounding up or down. But when we use the rounded powers to calculate an estimation all of the ‘roundings’ cancel out and we get a surprisingly accurate result.
Use estimation to always stay aware whether values are reasonable in context. If not, do a careful check for errors!

Key Terms

Add the following key terms with definitions to your glossary:

Base units
Derived units
SI prefixes
Standard form
Power of ten