VCE Physics/Printable version : Analysis of experimental data

VCE Physics

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/VCE_Physics

Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-ShareAlike 3.0 License.

Foreword

[Note: this section is now starting to take shape more... but it still needs a lot more thought to ensure the ideas are expressed clearly and people take what is said as intended.]

Introduction

This book was started by Theo Hughes, currently Education Manager for the School of Physics and Astronomy at Monash University in Australia. However, any work by Theo on this book has been done in a personal capacity, in Theo's personal time. Any opinions expressed are the opinion of Theo alone, and/or other authors, and are not endorsed by Monash University.

While this book was started by an individual, the contents will be overseen by a range of VCE physics teachers and physicists and kept up to date and corrected by anyone who uses it. It's expected any users (from expert to novice) will feel free to raise any mistakes they find, and offer suggestions for improving the book. Unlike a textbook in print, corrections and improvements will be able to be made straight away.

The following uses "we" rather than I, as it is intended to represent the views of all the lead authors. It will be modified to ensure it represents the views of other lead authors (who'll be listed) as they become contributors.

Structure of the book

This is an online book

Current VCE Physics textbooks are print oriented. While they may have a digital version and online components (multimedia resources) their use and layout is designed around the print version of the textbook. In contrast, this book is the other way around. We have designed and written it as an online resource first. While you will be able to print it out and it may still be of some use to you in printed format, a printed version will loose many of the advantages of the online version e.g. you will not be able to immediately jump to a resource or reference via a link, you will not be able to access the multimedia content such as audio, video, or interactive apps, and you will not be able to provide immediate feedback on the content.

Lay out

This textbook is laid out in the same sections ("Units" and "Areas of Study") as the VCE Study Design – with information from the Study Design, as well as links to the relevant sections of the Study Design and the VCAA website, embedded at appropriate points in the text. This should make it easier for you to be sure you are covering the required course and carrying out the required assessment.

However, once you get down to the contents in an area of study (e.g. Unit 1/AoS1/ Temperature and how we measure it) the contents are arranged in a way that we hope helps you to learn. While the text covers what is specified in the dotpoints it does not blindly follow their order, and it includes any additional information that we believe is esential for a coherent understanding of the material at this level.

Style

The style of this book is different from the "traditional" textbook style that we would characterise as bland and overly authoritative.

The style of this book is intended to be conversational and casual. While we'll need to use technical terms (understanding the "language of physics" is part of learning physics!) we'll avoid floowery language or overly complicated words or expressions, in order to make learning the physics as easy possible for everyone, but particularly non-native English speakers. We do not want unecessarily complicated language, that does nothing more than try to show how clever we are, to get in the way of learning. However, as with anything, it requires commitment and hard work to learn physics and so, to paraphrase Einstein "We'll make it as simple as possible, without making it so simple you don't learn what you need to learn!"

We'll write in the [wikipedia:Active voice|active voice] and talk to you (the reader) while we navigate the difficult concepts together. We'll guide you on a journey of learning in which we can learn too (via feedback from users). We'll seek to welcome you into the community of physicists rather than exclude you. We'll not just list facts and theorems but help you to understand them in as deep a way as possible, we'll discuss how they were developed, how physics develops historically, and we will not shy away from, for example, pointing out where we are "lying" (approximating a more complex truth to aid in learning) and we will provide commentary on how, overall, the physics community works.

Where we have not followed this style, please let us know and we can try and correct it, as we would any other mistake.

Motivation for the Book

This book was born out of an initial frustration around interactions with publishers of existing VCE textbooks, and other "open source" offerings. There has also been some frustration in relation to interactions with the VCAA.

Approaches made to all these organisations, in the spirit of simply having a passion to improve existing resources, are too often met with obfuscation and layers of administrivia and beauracracy. Experts want to chat to experts, the nerds and geeks who are passionate about physics and excellence in education in physics simply want to hang out, chat, have a coffee (or other favourite beverage), exchange stories, and hammer out the best way forward in a fun and friendly environment. They do not want to have to wade through layers of people who are not so invested, and do not have the direct knowledge or expertise to be able to discuss the issues in detail... ending up with a game of Chinese whispers where the message from one end to other is passed through layers of beauracracy that both confuse the message, and increase the amount of time and effort required to enact meaningful change to such a point. It is understood that there are natural barriers to achieving this. For example, the physical cycle of the print process is complex and expensive. However, that is why this book is doing away with that. If that is a barrier to improved resources, then we should remove that barrier... and modern technology provides a way to do that. Similarly, it is understood that there are issues of probity - for example, direct access to someone who writes a VCE examination leaves open the possibility of impropriety. However, these things can be managed in a more subtle way than is done. 99% of the desired interactions are nothing more than a passion to make things the best we can. To raise barriers to ridiculous levels and have but that is one of the problems of often having middle-people who do not understand this - again, technology can cut out the middle people. This book provides a relatively simple way for teachers, students and all those who are passionate about. The VCAA can then also use this as a resource to get detailed feedback about aspects of the course, because comments about aspects of the to come together and have direct access to communicate among themselves, in detail, without the need to reveal they write exams or break proriety in any other way.

It needs to be emphasised there is no ill-will towards any individual who works for any of the organisations and institutions mentioned (or the organisations and institutions themselves), and there is an appreciation of good work that is done by individuals and the organisations and instituations as a whole. Creating suitable processes and artifacts is complex, for example, the VCAA has an incredibly difficult job to do, it is constrained by requirements (legal and otherwise) and in the face of these constraints does many things well &endash;  but that should not stop people pushing for further improvements, as well as changes that keep up with ever evolving societal and technological contexts. In addition to providing an alternative option for use by students, teachers, parents etc. it is hoped this book may stimulate such improvements and changes.

Appendices

A lot of the information in these appendices is also distributed throughout the book. However, it is brought together in these appendices so you have a handy reference. The appendices also include additional, more detailed information that would disrupt the flow of the book / bloat the contents if included in the main text.

International Bureau of Weights and Measures (BIPM)

A lot of this reference material is a summary of information from the website of the Bureau International des Poids et Mesures (BIPM) – in English, the "International Bureau of Weights and Measures". While the BIPM is an international organisation, the name of the organisation and the titles of related standards – such as the Système International d'Unités (SI) – are in French, because the organisation's headquarters are in France.

Why is the BIPM, and their work, important to you?

The BIPM is the international organisation that oversees international agreements on metrology and associated standards. Metrology is the science of measurement, and because measurement (through observation and experiment) is at the foundation of science, then for you to understand and communicate physics it is important that you understand the work of the BIPM. It is also useful, more generally, for you to be aware of the work of the BIPM and how it impacts the world you live in.

For example, if you buy a kg of sugar, you want to be sure it is a kg of sugar so you are not ripped off!... and then when you bake your cake, if your "cup measure" is not definitely "a cup" you could get the amount of sugar wrong and your cake will not come out right!... grrrr.

Can you think of other examples of the impact of the work of the BIPM on your life? In answering this question, it might help to think of areas of particular interest to you, for example: transport, sport, medicine.

International connections and Australian involvement

The work of the BIPM is endorsed by nearly every country in the world as either a Member State or Associate State. Countries participate in the work of the BIPM through their national metrological bodies. In Australia this is the National Measurement Institute and related organisations. Also, Australian scientists work for, or with, the BIPM.

The BIPM is also responsible for bringing together many international organisations. Of particular interest to you, in studying physics, the BIPM works with the International Union of Pure and Applied Physics (IUPAP) and the International Astronomical Union (IAU).

Of more general interest to you, the BIPM works with organisations such as the International Organization of Legal Metrology (OIML) – important in relation to that kg of sugar you wanted to buy!

The BIPM and your studies in physics

To clearly communicate the results of any measurements you make, while carrying out experiments in physics, you need to use international standards such as those maintained by the BIPM. Similarly, any theoretical work you do should use such standards. So, for example, when you make measurements of length, or work out problems involving length, it is often best to use metres (m).

In many instances, this does not impact the fundamental concepts you are conveying (a length does not change whether you measure, and report it, in metres or chains) but using conventional language and symbols means it is relatively simple and quick for others to understand what you are communicating.

However, the definition of quantities such as the metre, second and kilogram, have become more and more closely tied to the fundamental ways our universe works. So how we define, and use them, are of particular importance in physics, because it deals with how the universe works at the most fundamental level. Therefore, as part of your studies in physics, starting to understand these connections, is important.

A computer-generated image of the international prototype kilogram (the inch ruler is for scale).

For example, the kilogram was only recently redefined (along with the ampere, kelvin and mole, as of 20 May 2019) from being based on a physical reference object (a platinum-iridium cylinder, see image to the right) to being based on fundamental measurements of the universe – for more information see Appendix A - SI Units.

Appendices/Appendix A

Introduction

If you make a measurement, and then communicate this measurement to others, it's essential you include the correct unit.

So, imagine you're buying a bookshelf from Linda. You tell Linda the space on your wall where you want to put the bookshelf is 2.7 wide. She says, "No problem, the shelves will easily fit there." You get the bookshelf home and it does not fit!... you meant 2.7 ft and she thought you meant 2.7 m.

You might think this would rarely happen. But there are many examples of such errors in real life, including some infamous ones with significant consequences, like the case of the Mars Climate Orbiter which was a much more expensive mistake than buying the wrong bookshelf – and you'd probably be able to take the bookshelf back!

SI units

To communicate a measurement we need to agree on a unit. So, for example, we might agree on a unit to measure length based on the length of your forearm. We'll call the unit simply the "forearm" and use the symbol "F". So a length of 2F is a length that is twice the length of your forearam.

There are several issues with this definition of length for use by the wider public (further discussion to come).

The system of SI units is endorsed by overwhelming international agreement (see the introduction to the appendices) and is even endorsed by the US which still also extensively uses non-SI units. For example, the National Institute of Standards (NIST) – the leading organisation in the US for measurement standards – maintains a list of the most up to date values for many physical constants, and they list the values in SI units, for example, they express the value for the speed of light in m s^-1 (NOT ft s^-1 or mph, both of which are commonly used in the US).

Naming convention

it is interesting to note that SI follows the convention that units named after a scientist (e.g. the kelvin, named after Lord Kelvin) are written in lower case, but the symbol is in upper case. So you should write "kelvin" and NOT "Kelvin" but the symbol is "K" not "k". This does not change the physics or the maths, but it can help in remembering correct use for the name and symbol of many units.

SI units in VCE Physics

The SI system includes many units. So while you can, and should, look at the section of the BIPM website on SI units, for your convenience, we have also listed here all the SI units that are used in VCE physics:

Note: this list does not include units that are only relevant to one of the many particular options in Unit 2, Area of Study 2.

Quantity	Unit name	Unit Symbol	Named After
Length / Distance / Displacement	metre	m
Time	second	s	from the Latin "secunda pars minuta"
Mass	kilogram†	kg
Weight	newton	N	Isaac Newton
Temperature	kelvin	K	Lord Kelvin
Temperature	degree Celsius‡	°C	Anders Celsius
Current	ampere	A	André-Marie Ampère
Potential difference	volt	V	Alessandro Volta

† Usually the SI prefix "k" (short for kilo) would only be used in front of a base unit to indicate 1000 times that base unit. For example, 1 km = 1000 m, or 1 kN = 1000 N. It is correct that 1 kg = 1000 grams, and this would seem to imply that the gram is the base unit of mass, however, this is NOT correct. That the kilogram is the base unit is an historical quirk.

‡ degree Celsius is not strictly an SI unit. The SI unit for temperature is the kelvin. However, degrees Celsius and kelvin have been defined so that in terms of a difference in temperature 1°C = 1K, so the translation between the two is a simple addition or subtraction. Also, because it has been common practice to use °C, and people are usually familiar with temperatures in °C, often °C is used in science to provide a more immediate sense of the temperatures involved. This common use is acknowledged by the BIPM and is why they were defined to have a simple relationship between them.

Appendices/Appendix B

The Study Design provides limited advice in relation to the analysis of experimental data. There is supplementary material that provides more detailed information. It includes, for example, a section on Measurement in Science. However, there are some issues with both the VCAA approach as indicated by this supplementary material, and past exam questions. This section seeks to outline a consistent, coherent and pedagogically motivated approach to measurement in physics / analysis of experimental data, and it will point out where this differs from the VCAA approach. As experimental investigations are School based and school assessed, the suggested variations from the VCAA advice are generally not a problem. However, as there are also examination questions related to experimental analysis, advice will also be provided in relation to those questions.

Validity and Reliability

The Study Design uses the terms "validity" and "reliability". However, these terms are NOT commonly / widely used in relation to physics, except in a casual sense. Neither do they have specific definitions in relation to physics. They are terms that originate from statistics and while we use statistical analusis in relation to measurmeents in physics, the terms "validity" and "reliability" are more commonly used in the social and / or biological sciences. In physics, in terms of well defined concepts (just as terms such as "energy" and "work" are defined) you should be using the terms "precision" and "accuracy". Approximately, "precision" = "reliability" and "accuracy" = "validity". This equivalance can only be approximate because "validity" and "reliability" do not have such well-defined, internationally agreed meanings. The terms "precision" and "accuracy" (and the associated terms "uncertainty" and "error") will be explained in this appendix at a level suitable for VCE physics - as well as including some comments, and references, for teachers (or interested students) to provide a deeper understanding.

Precision (and Uncertainty)

"Precision" and "accuracy" are two different concepts. Do not use the terms interchangeably. If you are discussing "precision", the related numerical quantity is "uncertainty". Precision is a relative term similar to the term "tall". You might say that someone who is 6ft in height is tall. If they are in a room with others who are all over 6ft, you might change your mind! Say you make a measurement that has an uncertainty of 1%, you might ask "Is this a precise measurement?"... the answer is "It depends". If the quantity you are measuring has only previously been measured with a 5% uncertainty then you might call your measurement precise. If in later years, the quantity you are measuring is commonly measured with an uncertainty of 0.1% then your measurement still might be considered precise for when it was done, but relative to current measruments, it might not be considered precise. Explain what uncertainty is, why it is important and how it is "used", in reference to some concrete examples. Explain +/- notation. Wny it is recommended you take R / sqrt(n) as a measure of uncertainty (the number after the +/-). Ways to propagate uncertainties in calculations.

Accuracy (and Error)

"Accuracy" and "precision" are two different concepts. Do not use the terms interchangeably. If you are discussion "accuracy", the related numerical quantity is "error". Accuracy is a relative term, similar to precision - see the initial discussion under the heading "Precision and Uncertainty". Do not use "human error"!

Graphing

Advice for graphing, including

• Dependent and independent variables.
• Proportionality and linear data.
• The importance of the intercept and any uncertainty in the intercept.
• Drawing a line of best fit (linear case)... and "linearising" non-linear data.
• Displaying uncertainties (error bars - unfortunate name!).
• Determining the gradient of a line of best fit and the related uncertainty in that gradient.

References

The standard reference for information relating to the analysis of measurement data, as with the conventions around units of measurement (SI Units), comes from the BIPM. See the introduction to the Appendices for why you should consider the BIPM as the root source for this information. In relation to the analysis of measurement data the most relevant BIPM documents are the Guide to Uncertinaty in Measurement (GUM) and the International Vocabulary of Metrology (VIM).