I am leaving HPSC and moving to a new school closer to my home; with a new baby in the family, I need more time for my family and travelling to and from HPSC each day was taking too much time.

I have won a role at Croydon Secondary College as Head of Mathematics & Science and I’m looking forward to the challenge and opportunities of this new role.

To all the students and staff at HPSC, I hope that you have an enjoyable 2012 and a great future – I hope to keep in contact with many of you – look me up on facebook and say hi, or keep watching this blog.

Physics students are particularly invited to stay active on this blog – I’m teaching both Year 11 & Year 12 in 2012 so there should be something of interest. Please feel free to keep asking questions and contributing in the comments – you are most welcome, and the extra input will be helpful.

Mathematics students – there will be less for you in 2012 (I’m not teaching mathematics this year), but keep me in your blogfeeds – who knows when I may post something mathematically interesting/ insane…

I have been lucky to have worked with you, and I hope to hear what you are up to in the rest of your studies and lives.

Farewell to All,

Andrew Grichting.

So how do you do it? Well, the most obvious stuff first: Year 12 Physics is actually Units 3 & 4 of VCE Physics. This means it is a continuation of your studies from 2011 (Year 11 Physics, Units 1 & 2), and you need to have *mastered* that information first. You will be needing the skills and knowledge you developed this year to ensure you are successful next year. This means that you must have organised all of your study notes from last year, particularly from the linear motion, light and electricity core units. Get them sorted out and organised. Identify your strengths and weaknesses – things that you are confident with, and what you know you need to improve on. We will be starting the year with a quick review of prior topics, and you will be expected to identify your areas of weakness.

Second, it’s all about the material. Make sure that you have read the curriculum documents – you have access to the same information as any teacher. Read it – know what you will have to learn, what the assessment will be, and how it is organised. Read the VCAA Physics study design documents here.  Make connections – many others are studying Physics this year (in other schools and even other states) – share resources with them, but start getting involved now – if you are in early, you will have the best chance to get the best materials. One student sharing site is here. Read what other materials I have provided for you on this site:

On Measurement: Practicals, Significant Figures, Using Technology, Extended Practical Investigations, Error & Accuracy.

On Light & Waves: Colour, Wave basics , Diffraction, Refraction, Wave interactions, Wave definitions

On Electricity: Fields, Resistance, Static charges

On Motion: XUVAT equations, Centre of mass, Energy transformations, Basic Kinematics

Finally, get some rest. You are “GO”ing to need it. Be prepared, but be “ready” to work, or you are “set” for trouble!

See you in class!

Ethan was born by C-section at 1:48 pm on the 28th of October. His birth weight was 3.545 kg (7lb13oz), and he is 47cm long. Mother & baby are both doing well.

We use three main models – Rays, Waves & Particles. This year, we focus on Rays & Waves, next year will be particles. There are a few posts on this blog about light – they have a *lot* of useful resources. Here are the links (1, 2, 3, 4, 5).

We have spent some time looking at the concept of ray tracing – the idea that you see objects where they are because that is where individual light rays intersect. This is easy when it is simple, but gets a little more difficult when dealing with reflections, and even more difficult with curved lens or mirrors. Fortunately, the internet can be very helpful with this – here is a link to six different videos working out how to find where an image will be given different lens types and different object positions.

If you haven’t finished your own ray tracing task yet, here is an applet (online program) that will help you figure it out.

The next major task you have to do is your log book practicals; remember that for the next outcome, the only thing you will be allowed to take into the next outcome is your logbook. Questions on the outcome will require you to share and use your data that you collected, and explain what it demonstrates.

So remember that what you must include in your logbook is both examples of the data you collected as well as how it links to the theory. You do not have to do full practical write ups; but you must remember that your logbook is part of your assessment, so make sure it is easy to read and well organised.

Here are the different pracs you must do (there are some missing): Experiment 1, Experiment 2, Experiment 3, Experiment 4, Experiment 7, Experiment 14, Experiment 15, Experiment 17, Experiment 18, Experiment 20.

You will be given three lessons in total; we will be conducting these pracs in the C9 darkroom. See you tomorrow.

If there are things you do not understand – particular topics, specific questions or exact concepts, you *must* comment to this post listing what it is that you do not understand.

If you are perfectly confident with the unit, then you must write your bound reference section on probability. This is due Monday of next week (the 17th).

Good luck, but if you have studied probability – you know that luck is an illusion!

Ya done wrong and ya gotta pay the price. It’s the chain gang for you. The Markov Chain gang.

You’re here until yu’ve done your time, and we are gonna make ya work.

Hard labour, kid. Work ’til ya brain burns, ya fingers cramp and ya think ya can’t do no more.

We’re gonna turn ya into a… Mathematician.

OK, enough of the high drama; Markov chains are the last bit of the course content you have to master. Despite my complaining about it, they’re not as bad as I’ve made them out to be. If you remember tree diagrams from year 9, markov chains are just one more step along that path. In short Markov Chain are about semi-independent repeated events. Independent events are probabilistic outcomes that are not affected by prior events; Markov style events are events that are only affected by the immediately prior event – i.e what happened two stages before doesn’t effect the next probability directly. In basic terms, only the last event that occured effects this event – this is not about “winning/losing streaks”.

What does that mean? Well, imagine going on a trip into the city to see a concert at the music bowl; you would probably have to take a train and a tram. Given that the two are both part of the public transport network, there is some relationship between the probabilities of them running on time. It may be that the entire public transport network is under stress (repairs needed, lots of commuters, bad weather – whatever); and thus if one part of your travel (e.g. the train to the city) is running late, the other may be running late as well. In other words, there is a probability that if the train is late, the tram will be late as well. We can express these conditional probabilities in a matrix – and working with these matrices is what the entire Markov Chain process is about.

We call the matrices of conditional probabilites Transition matrices – and the reason they are more useful than using tree diagrams is that we can apply them again and again – until we get as deep as we want. There is a good example here – unlike a tree diagram which become unwieldy after the third or fourth set of branches, a markov chain transition matrix can be used as many times as you want.

Here is a good video that shows how a Markov chain works – this is the first of a set of three, please watch them all the way through:

The most interesting thing that you should have noticed through that video was that it seems that two-state markov diagrams have an interesting outcome – stability. That after a certain number of iterations, they stabilise and further applications of the transition matrix result in no change to the probabilities of subsequent events. You can read more about this in your textbook.

You can investigate some aspects of this phenomenon at Wolfram, here.

Markov chains have some interesting applications, and as such they have appeared in mainstream media. Some of you may have seen the TV program, “Numb3rs” – they have used markov chains as a device to analyse patterns and solve crime previously, like in the episode “Harvest” (season 2, episode 14). Here is a snippet of what they showed:

While that doesn’t go a great deal into the maths, here is a site that explains exactly what he is talking about, and a simplified way you can do the same. Have some fun with it – the initial applications are remarkably simple.

See you in class – we’re nearly there now!

To Be, or Not to Be?

The name “Hamlet Happens” comes from the old idea that if an army of monkeys were to hit the keys of a typewriter (or word processor) randomly, eventually the whole of Shakespeare’s play Hamlet would be typed. Of course the length of time that we would expect to have to wait for such an extremely unlikely event to happen is billions of times the age of the universe. In this manipulative, letters are drawn at random from the beginning of Hamlet’s soliloquy, “To be, or not to be.” Any word made from those letters (such as TOE), of length five or less, can be entered in the box. When Start is pressed, letters are drawn and recorded. The process continues until your word (in the right order) appears (in blue).

Goal of Instructional Unit

The purpose of this manipulative is to help students recognize that (1) unusual
events do happen, and (2) it may take a long time for some of them to happen.

Materials

Hamlet Happens Applet

Instructions:

1. Enter your word    
2. Simulate random typing
3. After you have entered your word, click Start to begin the random drawing of letters from the draw box.
4. You can pause (click Pause) to stop the simulation, and then restart when you wish (click Start).
5. Clear the current simulation
6. Click Clear to stop the simulation. Your word will be cleared, and the list of draws will be removed.
7. Explore with words of different lengths

References

Bruner, J. S. (1961). “The act of discovery”. Harvard Educational
Review 31 (1): 21–32.

Doetsch, Carolyn; Peter Flanagan-Hyde; Mary Harrison; Josh Tabor; Chuck Tiberi,
NCSSM Statistics Leadeship Institute “An Exercise in Sampling: Rolling
Down the River” July, 2000

Year 10H Students:

For your probability test REVISION, please download and do the practice problems.

Hampton Park SC – Probability Revision

It is HIGHLY recommended that you do these problems so that you are prepared for the upcoming Probability Test on Thursday (22/09/2011).

Good Luck?

Spend some time – recall what you had to do – the skills you had to use. Think about the assessment you completed; what was it like – how do you wish you had prepared for it?

Well now you have a second chance – it’s time for the EPI again. You know what the topic is (Determination of acceleration due to gravity by means of a pendulum), so you should be making plans *right now* as to how you are going to use your time.

You only have 3 periods, and you will be using the third to write your report. Here is a file that gives you some more specifics about the project, and here is the marking guide. You should be planning exactly how you will go about using your time. Here is a video that shows a similar experiment to the one you will do:

The student in the above video does some things right, but there are many improvements needed. Think about the following questions (the answers are not simply yes or no!)

1. Is the mass of the pendulum bob relevant? If yes, why? If no, why should you use one at all?
2. Is the pendulum string important? Why? What measurements of it should be made? How should it be strung to support the bob? How long should it be/ What length(s) will you use?
3. How should the pendulum be supported? Does the support matter?
4. How should the pendulum swing? Straight back and forward or otherwise? How wide should the arc of the pendulum be?
5. How will you measure the period of the oscillation? From which point to which point? Why?
6. Have you tried running this experiment at home and seeing what can go wrong with it?
7. Have you planned your time budget, and who will do what it your group?

Those are some starting questions, and if you don’t feel stressed, YOU SHOULD!

See you in class!

You might be surprised, then, to discover that what you have learnt is only the very basics of the “Kinematics Equations”. There is much more for you to learn as you go through physics and Mathematical Methods. Let’s review some of the basics.

First and most important these equations are the “Constant (or uniform) Acceleration Equations”. This means that they only work if the acceleration of the body is constant. This means that you cannot use them if the object is increasing or decreasing it’s acceleration, i.e. it has non-zero jerk.

Secondly, you have to be careful to use the scalar version when dealing with scalars, and vector version when working with vectors – but remember that adding and subtracting vectors has special rules.

Finally, remember to use your DATA BLOCKS. Data blocks are essential to make sure you don’t make simple mistakes – and they help you earn marks in assessment (tests, exams and assignments). Speaking of which, here is the test for redoing – make sure you show a data block every time you have to use one of the XUVAT equations.

We know where some of the equations come from, and I’ve shown you one of the more complex ones. Here is a video that explains the rest:

So where to from here? You need to understand the relationship between each of the kinematics graphs (x against t, v against t and a against t), and also how they relate to the XUVAT equations. In order to do this, I want you to work completely through these two sites (this is not a work requirement, but if you are thinking that doesn’t mean you have to do it, you are absolutely wrong – and I will be able to tell.) (Yes, that is a threat… or a hint) (Hey what was that? Behind you! Something captured my attention!)

Link 1: Kinematics Equations at the Physics Classroom

Link 2: Kinematics Equations at the PhysicsLAB site

And here are two links to java applets that will allow you to investtigate some of the interactions between speed-time and distance-time graphs (1,2)

And last of all, some music to help you relax:

See you in class!

P(samecolor) = P(RR or GG or WW)

We use the tree diagram to the left to help us identify the possible combinations of outcomes. Here we see that there are nine possible outcomes, listed to the right of the tree diagram. This number is the size of the sample space for this two state experiment, and will be in the denominator of each of our probabilities.

Each of these possible nine outcomes has a probability of 1/9, which we can find using the multiplication rule P(RR or GG or WW) = 3/9.

All students in 10H,

Please download and print off a copy of the power point slide (below), and bring it into class on Tuesday.

Probability (Tree Diagrams)