## Archive for August 2011

### XUVAT – it’s not just a good idea, it’s a rule!

August 28, 2011

So you have learnt your 5 equations of motions, but do you really understand them? Most of you are probably nodding your heads… and those of you who aren’t should be working towards making sure you can be nodding! (please note that sometimes these are called the SUVAT or DUVAT equations as well)

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.

### Tree Diagrams

August 27, 2011

Tree diagrams can be a helpful way of organizing outcomes in order to identify probabilities. For example, if we have a box with two red, two green and two white balls in it, and we choose two balls without looking, what is the probability of getting two balls of the same color?

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.

### Stick or Switch?

August 26, 2011

During a certain game show, contestants are shown three closed doors. One of the doors has a big prize behind it, and the other two have junk behind them. The contestants are asked to pick a door, which remains closed to them. Then the game show host, Monty, opens one of the other two doors and reveals the contents to the contestant. Monty always chooses a door with a gag gift behind it. The contestants are then given the option to stick with their original choice or to switch to the other unopened door.

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### Getting the most out of your Tests

August 24, 2011

Everyone knows that you should revise before a test – you have to prepare and write you bound reference, review all the things that might be on the test, and practice any tricky skills… That’s straight forward – any student knows that!

But who knows that you should revise after the test?

That’s silly, isn’t it? The test is over, you don’t need that material any more – the exam is a long time away! It’s all over and done with, right?

Well, to put it simply, NO!

This is the best time to revise! Your skills and understanding are at their peak – you have learned even more than before the test – you now know something you didn’t before the test – you know what you didn’t know but thought you did!

This is the best time to revise, because you are ready to finish your studies of this topic by ensuring that you have all the information you need – including fixing up those parts you thought you understood, but weren’t able to demonstrate on the test.

### Don’t Drink & Derive

August 12, 2011

Well, here we go – the last gasp of calculus for the year, and it is *neat* trick.

By now, you are (or should be!) confident and competent with differentiation, but you should be beginning to wonder about the reverse of the process – it is possible to get the gradient function from the function, but how do you go the other way? Can you get the original function from the gradient function?

The answer is yes, but it is weirder than that (this is MAAATHSA! It is always weirder than that!). Lets start from a simple example. We know the derivative of x^2 is 2x, so the reverse (called the “integral”) leads to the fact that 2x integrated is x^2 (not quite, but it’ll do for now.

Check that for a second. If you take any point, x, on the function 2x, you get a height (y value) of 2x. The line f(x) = 2x makes a triangle of base x, and height 2x, which gives it an area of…

### Tree-gonometry!

August 7, 2011

So here you are, at the end of your studies of Trigonometry. Take some time to think of all the new things you have learned – you have all covered so much, and you should be proud of what you have achieved.

Now it is time to get the reward your efforts have earned – this week is test week (both ODT & Trigonometry!). You know what skills we have practiced through our tests this year, and you need to be prepared for the same structure again – but you should be planning how you will best make use of your time, to demonstrate your knowledge. Remember what we have spoken about regarding “owning your test” – it belongs to you, and at the end it shows what you can do. Since it is all about you, it is yours to do with what you want to. Choose your own path!

### What is at the centre of gravity? V.

August 6, 2011

When an object is in motion, it can be very complicated. Just think about the way a car starts moving or stops moving – it behaves a whole group of bits and pieces – it does not behaves as a single unit.

But if we have to deal with every object and figure out what is happening with each piece, physics would be insanely complicated. It is necessary to do these complex calculations if you are an engineer, but as a student, you are trying to learn the underlying principles, not guarantee that a bridge is going to stay up!

So how do we simplify these complex problems? We use a concept called “Centre of Mass” (note that this is similar to centre of gravity – it is the same physical point in an object). The centre of mass of an object is the point at which, if all the mass of the object where concentrated there, it would behave identically when in motion.

This means that an object in motion can be treated as a single point – and that makes your work a lot easier – all the calculations can be simplified down to a single application of each needed formula, rather than having to repeat it for each part (or even particle!) of the item.