# How to get 100% in your Leaving Cert Physics exam. Part 2: Answering Graph Questions

Drawing the graph

• You must use graph paper and fill at least THREE QUARTERS OF THE PAGE.
• Use a scale which is easy to work with i.e. the major grid lines should correspond to natural divisions of the overall range.
• LABEL THE AXES with the quantity being plotted, including their units.
• Use a sharp pencil and mark each point with a dot, surrounded by a small circle (to indicate that the point is a data point as opposed to a smudge on the page.
• Generally all the points will not be in perfect line – this is okay and does not mean that you should cheat by putting them all on the line. Examiners will be looking to see if you can draw a best-fit line – you can usually make life easier for yourself by putting one end at the origin. The idea of the best-fit line is to imagine that there is a perfect relationship between the variables which should theoretically give a perfect straight line. Your job is to guess where this line would be based on the available points you have plotted.
• Buy a TRANSPARENT RULER to enable you to see the points underneath the ruler when drawing the best-fit line.
• DO NOT JOIN THE DOTS if a straight line graph is what is expected. Make sure that you know in advance which graphs will be curves.
• BE VERY CAREFUL drawing a line if your ruler is too short to allow it all to be drawn at once. Nothing shouts INCOMPETENCE more than two lines which don’t quite match.
• Note that examiners are obliged to check that each pint is correctly plotted, and you will lose marks if more than or two points are even slightly off.
• When calculating the slope choose two points that are far apart; usually the origin is a handy point to pick (but only if the line goes through it).
• When calculating the slope DO NOT TAKE DATA POINTS FROM THE TABLE of data supplied (no matter how tempting!) UNLESS the point also happens to be on the line. If you do this you will lose beaucoup de marks and can kiss goodbye any chance of an A grade.

What goes on what axis?

Option one

To show one variable is proportional to another, the convention is to put the independent variable on the x–axis, and the dependant variable on the y-axis, (from y = fn (x), meaning y is a function of x). The independent variable is the one which you control.

Option two

If the slope of the graph needs to be calculated then we use a difference approach, one which often contradicts option one, but which nevertheless must take precedence. In this case we compare a formula (the one which connects the two variables in question) to the basic equation for a line: y = mx.

See if you can work out what goes on what axis for each of the following examples (they get progressively trickier):

1. To Show Force is proportional to Acceleration
2. Ohm’s Law
3. Snell’s Law
4. Acceleration due to gravity by the method of free-fall
5. Acceleration due to gravity using a Pendulum

There is usually a follow-up question like the following;

“Draw a suitable graph on graph paper and explain how this verifies Snell’s Law”.

There is a standard response to this;

“The graph of Sin i against Sin r resulted in a straight line through the origin (allowing for experimental error), showing Sin i is directly proportional to Sin r, and therefore verifying Snell’s Law”.

If you are asked any questions to do with the information in the table, you are probably being asked to first find the slope of the graph, and use this to find the relevant information.

# Imagine if the key-word in the Leaving Cert Physics syllabus was ‘wonder’

This is an image, courtesy of Wordle.net, of the current Leaving Certificate Physics syllabus. Wordle is a program that gives the most common words the largest font size:

This is a similar image of the proposed new syllabus.

Notice the new focus on the words ‘learners’ and ‘learning’.

Imagine if a syllabus had as its most common words the following:

Engage

Passion

Awe

Curiousity

Inspire

Un-nerve

Emotion

Story

Creativity

Wonder

If any of this was a priority then chances are that Particle Physics wouldn’t have been removed (and with it Pair Annihilation, Anti-matter, Neutrinos, Fundamental Forces, etc.).

Chances are that Cosmology would also feature strongly in the new syllabus (Black Holes, Quasars, Pulsars, Big Bang, Neutrinos (again), Dark Matter, Alien Life, etc. etc.). It doesn’t.

Maybe it’s just me.

# Energy – the most poorly-taught concept in all of science?

It is important to realize that in physics today, we have no knowledge what energy is.

Richard Feynman

Sometimes when I’m teaching I have been known to go off on a tangent which may be only marginally related to what we’re doing in class; other times I manage to restrain myself and may just allude to the tangential concept in passing.

But then there are times when these tangents are actually necessary, and by leaving them out I am doing the students an injustice. Ususally I try to include this information in the students’ notes also but sometimes I just don’t get around to it. Energy is just such an example.

Georgina (this is where I’m supposed to say that Georgina is not her real name, but as far as I’m aware it actually is) is one of the top students in my fifth year class this year and I used to think that she was a bit of a ‘slogger’ – liked to work hard and liked to know that there was always a ‘correct’ answer. In fact I wasn’t even sure if she would adapt to my style of teaching, where I tend to ask questions and not always provide the answers. But Georgina showed what she was really make of when we were revising the chapter on Energy.

“I know this sounds like a silly question”, she said, “and I know we’re finished the topic now, and it’s not that I can’t do the problems and exam questions because I can, it’s just that I don’t seem to get what energy actually is

I realised that there was more to this student than I first thought.

You see nobody gets energy; in fact by pretending that it’s all straightforward we actually do the students a disservice. Not only are we ignoring the wonder associatied with the idea, we are also denying them the opportunity to engage with the concept at any level beyond the superficial.

Bottom line – nobody gets energy because there’s nothing ‘to get’. Energy is not tangible (alghough it is ‘an indirectly observed quantity’ if you want to sound clever), you can’t hold it in your hand, you can’t weigh it on an electronic balance, you can’t see it, touch it, smell it etc. Yet when the universe was first created there was a certain amount of this put in to the mix (actually now that I think about it the mix itself was energy (with perhaps just a little dash of time)), and it’s all still there today. Its form can change, but the energy itself can’t ever disappear – no sirree bob.

It could be argued that it is in fact merely an accountant’s trick which enables him to ensure that all actions balance.

Consider the following analogy which I like to use.

If a child asks you ‘what is money?’ you could take a few coins out of your pocket and show them to the child and say ‘this in money’. Now fast forward a couple of decades; all transactions are now done electronically/online and all coins and paper money are no longer legal tender. Now how do you explain what money is?

Well it’s a means of payment for goods and services, right? Somebody sells you an orange and you agree to transfer into their account a set amount of this ‘money’. And now that the shopkeeper has this money in his account he can use it to buy something else. So it’s a bit like a transferrable IOU.

Now energy is a bit like this, but there is only a certain amount of IOU’s in the universe and this was set when the universe first came into being (I’m not sure if we know how much energy is in the universe – presumably we do?), although to complicate matters since the early part of the last century (thank you Albert) we now know that all matter (‘stuff’) is basically energy in another form.

Anyone still with me?

Now the point of all of this  is to highlight once again that there is no reference to this concept on either the Junior Cert or Leaving Cert syllabus. It could be argued that this is because it would be too difficult, but the obvious response to this is that nobody understands Energy as it is currently presented anyway. Students merely learn off the definitions and formulae and if they think about it at all will probably just assume that it’s just another example of Physics being ‘too hard’ to understand.

So what’s the actual point in asking students to learn the definition in the first place?

In fact I’d imagine many students who can give the appropriate definition for Energy (“Energy is a form of Work”) couldn’t follow up by explaining what Work is (it’s a mathematical product of force and displacement to give the simplified version).

At Junior Cert level students are expected to be able to show how light and sound are forms of energy – again most students should be able to give the correct demonstration but if you ask them how this demonstration verifies that it is is form of energy few will be able to give a convincing answer. In fact while Energy is the single greatest unifying concept in all of science, even that idea alone is not worthy of mention in the sylllabus; as a consequence Energy is seen as just another chapter to be learned off, with (once again) no emphasis on how it ties together everything else.

Now if teaching Junior Cert Science and coming from a Biology or Chemistry background what are the chances of your students developing an appreciation of this all-encompassing concept? – were you ever told about it?

I thought I’d find something on YouTube to illustrate this, but I couldn’t find anything.

Below are some quotes from other more prominent commentators on this elusive concept:

When Feynman wrote,

“It is important to realize that in physics today, we have no knowledge of what energy is,” he was recognizing that although we

have expressions for various forms of energy from (kinetic, heat, electrical, light, sound etc) we seem to have no idea of what the all-encompassing notion

of “energy” is.

The various forms of energy (½mv2, mgh, ½kx2, qV,mcT, ½I2, ½CV2, etc.) are abstractions not directly observable.

2007 American Association of Physics Teachers

Feynman’s quote in context:

There is a fact, or if you wish, a law governing all natural phenomena that are known to date. There is no known exception to this law – it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call “energy,” that does not change in the manifold changes that nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is a strange fact that when we calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same. It is important to realize that

in physics today, we have no knowledge of what energy “is.” We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. It is an abstract thing in that it does not tell us the mechanism or the reason for the various formulas.

The Feynman Lectures on Physics Vol I, p 4-1

# The origin of the decibel scale

A standard leaving cert physics exam question is “why do we have the decibel scale”?
The standard answer is that the range of sound intensities is so large that a second, much more compact scale is required to make the numbers more manageable, and for sound this scale is based on multiples of ten and is called the decibel scale (and what it measures is called sound intensity levels).

The old syllabus included a detailed analysis of this scale so that the numbers actually meant something. For the new syllabus (2002 onwards) it must have been decided that the maths was too difficult so this part was scrapped, except for one very odd ‘fact’; the student must know that a doubling of the sound intensity results in an increase of sound intensity level of  3 dB. Now needing to know that piece of useless trivia is ridiculous and is probably only there as a sop to some university professor who was horrified that the detailed analysis was dropped:

At least that’s my best guess, which doesn’t seem too dissimilar to what the author of a recent book on Physics and Music  entitled How Music Works thinks about the decibel in general.

I think the decibel was invented in a bar, late one night, by a committee of drunken electrical engineers who wanted to take revenge on the world for their total lack of dancing partners.

Ouch!

Now what’s the betting that students will remember this explanation and forget all about the technical one?

# Leaving Cert Physics: Section A Questions and Solutions

Section A of the Leaving Cert Physics exam contains 30% of the overall marks so it’s worth studying it in detail.

I have put together a booklet which contains every Section A question which has appeared on an exam paper at higher and ordinary level together with all the solutions.

The booklet can be accessed from the revision page of thephysicsteacher.ie

Hope it’s useful.

# Leaving Cert Physics: Definitions from Past Papers

This word document has now been updated; not only does it now include all definitions from the 2009 paper but it also includes all definitions from Ordinary Level papers from 2002 – 2009.
The document can be accessed from the revision page of thephyiscsteacher.ie

The answer to each question is also included; hopefully this allows for non-physics friends/parents/brothers/sisters to ask the questions and check the answers as you go along.

It is notable that in some instances the ordinary level definitions are actually more difficult ( and at times rather obtuse) than the higher level questions. I have noticed something similar in the Junior Cert Science papers over the years. I suspect that while many of us write in to exams commission to comment on the higher level paper, few of us ever bother to analyse the ordinary level paper in the same detail and so these anomalies go unchecked.
Anyways, as always the document is on the leaving cert physics revision page.
Hope it’s useful.

# Physics, Hollywood and Rock Stars

What Hollywood actress said the following in a recent interview for GQ magazine?

I’m interested in elementary particles, any spare time I have, I bury my head in a physics textbook. The elements at the atomic and subatomic level make up everything. You, me, the buildings, our souls, our minds. I’m reading a lot about Einstein. I like theories. I want to understand string theory. I’m dying for someone to explain quarks to me!

Anne Hathaway.

What rock-star recently acknowledged that watching quantum physics videos on YouTube had affected her music?

Quantum physics has done my band a world of good.

Courtney Love

Thanks to Physics World for those.
It reminds me of the beginning of the brilliant E = mc squared; A biography of the world’s most famous equation, written by David Bodanis, where the author describes his inspiration for writing the book:

A while ago I was reading an interview with the actress Cameron Diaz in a movie magazine. At the end the interviewer asked her if there was anything she wanted to know, and she said she’d like to know what E = mc squared really means. They both laughed, then Diaz mumbled that she’d meant it, and then the interview ended.

All the material required to make Leaving Cert Physics a fascinating subject already exists – all we have to do is bring it together.

# Survey finds Physics dropped in 10% of schools

With all the media attention on NAMA these times it’s understandable that most of us missed this headline from RTE the other day (hat-tip to eagle-eyed Jude for bringing it to my attention).
The RTE article leads with the following:

Research suggests that almost 10% of second level schools have been forced to drop Physics as a subject offered to students.
The findings indicate that the decision is as a direct result of education cutbacks.

Not a happy statistic, but presumably many of these schools had less than ten students in the class, and it just wasn’t feasable to maintain this. So why don’t more students do physics? It’s a very complex issue but the problem is causing concern to authorities throughout the western world. I believe that one very important factor is the picture of physics which students get from the  Junior Cert – if we don’t get this right then it’s going to create a poor impression when they go to choose their leaving cert subjects.

So what would I change in Junior Cert Physics? – stay tuned.

btw – should we read anything into the fact that the accompanying picture in the RTE webpage is chemistry-related, not physics?

# What a family. What a teacher.

##### Photo taken from here, permission pending

Antoinette O’Connor from Cork has won a medal for achieving first place in the country in Leaving Certificate Physics, awarded by Institute of Physics.

Nothing strange so far, after all someone has to come first, don’t they?

There’s more: Her sister Martha O’Connor won the award in 2005.

Still more:  Another student from the same school, Deirdre O’Leary, won the award in 2000.

No prizes for guessing that all three were taught by the same teacher; serious respect to Diarmuid Hickey from Coachford College, Co. Cork

Read more on UCC ‘s website

# Bloody Electrostatics demonstrations

Got up at 6:30 this morning to be in school at 7:15 to have lots of time to prepare for a form 5 class on electrostatics which I wanted to film.
Now I’m not normally this dedicated, but because it was being videod (‘videoed’?) I wanted to get everything right.
Electrostatics is dodgy at the best of times, but at half eight this morning every thing was going like a dream. To such an extent that I started wondering why other teachers made such a big deal of it. Maybe they should prepare more – like I was doing.

Class began at about 12 o clock. I started the video, and spent the first ten minutes correcting homework on the board, then started into the demos.
Not one worked as well as it did in the morning.
Some didn’t work at all.
It was baffling, frustrating and funny in roughly equal measures.

I take that back.
Mostly it was frustrating, especially since I had prepared it so well.
The smug factor had felt good too.

It’s possible that atmospheric conditions had changed over a few hours, but I suspect one other variable was that the classroom had had four sets of students sit in there for forty minutes at a time, each breathing in nice clean dry air, and breathing out air which contained a higher percentage of water. As one of the students said: “Come on now sir, I know you blame us for everything else, but you can’t seriously think you can blame us for this one.”
So;
tomorrow I repeat the process first thing in the morning, then again a few hours later, and if the same thing happens I think I might use hot plates or bunsen burners to dry out the air for a spell and then repeat (what happens the water / water vapour when the air drys? Where does it go?).
Edge of the seat stuff this . . .