# Some fun teaching Vectors

This week we were looking at Vectors. It can become a bit tedious so no harm to introduce the topic with a fun puzzler.
So you’re travelling in a pick-up at 30 mph and you fire your beer bottle backwards at exactly the same speed. What happens?
Well Naturally Mythbusters had to find out.

The original was Japanese:

And finally, for a few minutes fun at the end of the class, what happens when the second largest ship in the US Navy is on patrol in the Irish Sea and encounters . . .

For teaching addition of Vectors the pHet site is very useful

These links can all be accessed through the Vectors page of the website.

# 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.

What is it about this idea that we want to avoid?

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