I set a little Fermi Problem for students yesterday – with the promise of a prize for the best written argument which answers these questions.
I’ll be judging the entries tonight and deciding on prizes in time for the last day of term. I might even publish the best entries here, but meanwhile, you can read an earlier version of this exercise (which was a slightly different problem) here and my solution to it is here (click to see it full size):
With the timetable being so tight, and all of us so busy at the moment (you wait until *after* Christmas!), thought it would be cool to have a place where we can ask questions, prompt, encourage and support each other without having to wait until we are all in the same room.
I have created Mr. Hood’s Forum for this purpose and set up a couple of places for us to get started. I hope you find it useful. Check it out!
This tutorial shows how to draw the ray diagrams for a convex lens for the three important cases: (i) an object placed further than 2x focal length from the lens, (ii) an object placed between 1x and 2x focal length from the lens and (iii) an object placed less than 1x focal length from the lens.
You will see how in each case, the image is (i) real and inverted, (ii) out of focus and (iii) virtual, upright and magnified.
Try to construct the diagrams yourself, remembering the three construction lines from the top of the object parallel to the optical axis, through the centre of the lens and through the focal point.
Our Advanced Higher students joined a hundred or more from the local area at the University of Dundee today for a day of Physics. We arrived in time for the start of the practical investigations, despite the bus not showing up (we jumped into the car and drove up). These were not mind blowing at all, but we did get a chance to do something with real equipment in a real teaching laboratory.
Dr. Paul Prentice
This was followed by a real lecture from Dr. Paul Prentice on sound waves. His lecture was pitched (his joke, not mine) at the right level for the audience and included a simple demonstration, using tuning forks, of beat frequencies and interference. Students were able to respond to questions and were not short of some good questions themselves.
We stopped for lunch and some demonstrations, both put on by the university. I especially liked the infra-red camera which gave me scientific evidence that compared to my face, I have a cool tie.
Using Optical Tweezers
The afternoon was dedicated to four very useful talks – we thought they were too short – on the practical applications of Physics and how Physics in your degree can lead you to some fascinating and rewarding career paths. The first talk from Dr. David McGloin focused on climate change and how lasers are used in tackling this and in other areas of scientific application. His reference to optical tweezers was picked up by Dr. Andrew MacKay who threw us the fastest ball of the day – that photons have no mass but they do have momentum. He went on to explain and demonstrate how light is used to move physical objects by conservation of momentum and refraction.
Dr. Jane Greaves gave us a great talk on astrophysics, brilliantly illustrated with images from Hubble and other telescopes. She talked in particular about the birth, life and death of stars as well as the formation of planets and the new discoveries of extra-solar planets, down to sizes of two Earth masses. She asked us to look up Olbers’ paradox as an example of the big puzzles that Physics helps us to solve.
The day finished with Dr. Maria-Ana Cataluna describing how Physics is at the heart of everything: the skills it gives you include:
I don’t do many book reviews here* but this is a book not to be missed. I bought it in Borders on Saturday after a student recommended it to me – well, to be honest, she was asking me about some of the interesting concepts described in the book.
You can see a short video introduction to the book by the authors over at Amazon.
The flyleaf describes the book as the most accessible, entertaining, and enlightening explanation of the best-known physics equation in the world, as rendered by two of today’s leading scientists. The equation referred to is Einstein’s famous .
The subtitle and why should we care? frames the question asked by Cox’s wife, Gia Milinovich, who describes herself as a science groupie and professional dork. You need not be either of these to appreciate the answer to her question.
The language of the book is very easy-going and the mathematics is kept to an absolute minimum – nothing harder than Pythagoras (and the authors even explain that, in case you have forgotten it). For me, the hook comes in the preface. Don’t skip the preface: it contains some of the most fundamentally important principles of the study of science, for example:
By building a model of space and time, Einstein paved the way for an understanding of how stars shine…
Notice the word model. There’s the greater truth coming:
In science, there are no universal truths, just views of the world that have yet to be shown to be false.
I refer you back to the personal task I set you – and which I have not forgotten, by the way – about the nature of knowledge. The authors of this book are perfectly clear about what knowledge is and what it is not.
Finally, to pique your interest – not just in this brilliant little book, but in the study of physics – let your mind consider this excerpt from chapter 1:
Einstein’s universe is one in which moving clocks tick slowly, moving objects shrink, and we can journey billions of years into the future. It is a universe in which a human lifetime can be stretched almost indefinitely. We could watch the sun die, the earth’s oceans boil away, and our solar system be plunged into perpetual night. We could watch the birth of stars from swirling dust clouds, the formation of planets and maybe the origins of life on new, as yet unformed worlds. Einstein’s universe allows us to journey into the far future, while keeping the doors to the past firmly locked behind us.
I hope you get the chance to read this excellent little book.
It can be tricky getting your head around the Advanced Higher Physics investigation, otherwise known as the “fourth unit” of the course. There’s a great deal of the unknown about it, as you are required to choose (or worse, have chosen for you) an investigation of suitable complexity for the assessors when they read your report, quite possibly before you have covered the physics in the course. There’s also the small matter of the mysterious day book. Let’s take a look at what you have to do for this part of the course.
Read the guidance
Start off with a look at the course guidance produced by the SQA. Here you will read that the investigation is:
a piece of individual research undertaken to prove that you can … research a physics topic … design and plan experiments … carry out experiments safely and accurately to collect data … process and present the data … evaluate … produce a written report
The report is assessed by the SQA examiners. Your school will assess your day book and the investigation itself, including your recording of the data.
There are three phases to the investigation: planning, execution and reporting. Read the course guidance first, before thinking about which investigation you want to do, then set about planning it. Don’t be one of the entries without the basics taken care of: read the guidance again and again as you progress.
Start your day book
The day book is simply a kind of running record of your activities as you conduct your investigation. Your school may give you a hard-backed lab book to use for this, but you are not constrained to this format – loose leaf is OK, for example. The photo shows part of my library shelf containing the day books I have kept, which shows you that I quite like the A4 hard-back type.
Day books
Begin writing your day book entries as soon as you start thinking about which investigation you are going to do. Write down, date and reference everything you do in relation to the project. I personally number my pages and you should too. A margin at the side of the page is also helpful for comments and provides a place for your teacher to put a date and signature every time he or she checks your day book. It is your responsibility to ensure it is regularly checked: at least once a week is reasonable until the investigation report is finished.
Some people worry about copyright when putting things into the day book – it’s perfectly OK to paste a photocopy or digital photo of a text book page describing a procedure into your day book if it’s relevant to the investigation. Don’t forget to fully reference all of your sources of information and to record even informal discussions with teachers, technical or university staff who might be offering advice and support. Referencing means stating exactly where the information came from: details of a book’s author, etc., or the address of a web page and when you accessed it. Record these details in your day book as you find the information – you’ll need them when you write up the report.
Choose an area of interest
There is almost no limit on what your investigation is about, provided that it meets the basic requirements of the course. Students sometimes just plump for something they have read about on a forum somewhere (see, for example, here, here, here or here) or really push the boat out and do something outstanding with a hook into their degree aspirations. My advice would be to generally keep it simple and make sure your report is as good as you can make it.
A few years ago, Linlithgow Academy made a list of suggestions for the investigation available. You can find a copy of that list here. There is also a relatively new site used by physics teachers in Scotland to share resources: the AH investigations pages, with suggestions for investigations, can be found here.
Things to watch out for
Firstly, don’t panic. This isn’t rocket science. OK, it might be rocket science but it’s doable rocket science and you not only are allowed to seek support and guidance, you are expected to do so.
Secondly, don’t get complacent. Start now. Read, dive into the text books and experiment books: see if there’s a copy of Tyler in your lab. Get on with it. Locate the equipment you need. Talk to people. You probably have prelims after Christmas and the exams will follow oh so quickly after that. You don’t need to be burdened with the investigation at that time (although this is often when they are done).
One other area you will need to pay close attention to is uncertainties. Read the guide downloadable from the LTS website. Your day book does not have to be exam-perfect in terms of number of decimal places and so on but keep in mind the golden rule that as a scientist, you must record what you see: fairly, accurately and without bias.
Getting help
So, what help can you get? Apart from the SQA website, there are a number of good sources of help in getting your investigation off to a good start, and in keeping you going if things get a little tricky. The Science 3-18 website, run by the Scottish Schools Equipment Research Centre (SSERC), has some resources related to the investigation here, including some specific notes on investigations using radioactive sources. SSERC also offer support to students directly – whether trouble-shooting or making equipment available or just good solid advice. I happen to live not far from SSERC, so arrangements can be easily made.
Our local universities (specifically Dundee, St. Andrews and Heriot-Watt) all offer support for the investigation. Glasgow University also offers an Advanced Higher Helpline, an e-mail advice and support service which aims to provide the following support:-
advice on possible experiments to develop or complete an investigation
advice on the treatment of uncertainties in more complex situations
a booking facility for access to investigation enhancement experiments within the department or the possible loan of equipment
help to understand “unexpected” results or systematic errors
To use the Helpline contact Peter Law, the Advanced Higher Support Coordinator, at the following address (remove the “NOSPAM” first): AH-HelpNOSPAM@NOSPAMphysics.gla.ac.uk
Finally
The SQA’s External Examiner’s report for 2008 indicates that the average mark for the investigation was just under 14/25. The “something outstanding” mentioned above got 25/25.
This tutorial addresses what you need to know for Advanced Higher Physics as far as those equations for relativistic mass and energy are concerned. Two key equations are described: with a very short explanation of what makes up the total relativistic energy of an object with mass, when travelling at speeds of a significant fraction of the speed of light.
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