Saturday, August 25, 2007

Energy and Newton's Laws

I'm sure you are finished with Newton's Laws by now, and will be moving on to energy. The question I would like to pose here is: what is the point of learning about energy?

Think about it: Newton's three laws cover every aspect of motion, so why can't we understand all motion by the three laws alone? Why do we have to come up with an extra concept called energy? What is energy anyway?

I'm not sure if you have thought about before, but can you define what a force is? Or for that matter, can you define mass? Some of you may have heard that by definition mass is the amount of substance in an object, but that is distinctly untrue! As chemistry students, I would expect you to know that the measure of the amount of substance is the MOLE, not the kilogram.

So what is mass? Would it bug you if I told you that there is no clear way of defining it? And for that matter, there's no real way of defining force either? And energy?

So why do we bother with all these things that can't be defined? The point is, as I've pointed out many times before, physics is a way of quantifying physical behaviours and analysing them using mathematics, and it just happens the quantity of "force", "energy" and "mass" seem to obey some kind of law. A good follow up question would then be why do they bother to follow some kind of law in first place?

I guess this is one of the most fundamentally interesting things about physics and nature: that for some reason these seemingly meaningless (undefinable!) quantities appear to have some kind of logical relationship with each other. In 1918, the female mathematician Emmy Noether published a mathematical paper, showing that if we assume that the laws of physics are invariant over time (meaning that the laws of physics don't change with passing time, a reasonable assumption), then the quantity known as "energy" is conserved, meaning that the total amount of energy always remains constant. This is of course something that you've already learnt, but here is a real explanation as to why the quantity of energy is so important.

But then we return to the question, why is Newton's Laws not sufficient for us to understand everything about motion? Why must we introduce energy?

In fact, Newton's Laws are sufficient in studying motion. But the problem is, in many cases they are incredibly cumbersome. When you begin your study of energy, note that in many cases, the questions that you are solving tend to involve information only about the initial and the final state of the object. In another words, you may be solving questions in which you know what's happening at the start, and what's happening at the end, but you may not exactly know all the details of what's happening in between. In such cases, because you don't really know what goes on in the middle, Newton's Laws become very difficult to use, and sometimes even impossible.

Energy is equivalent to Newton's Laws, but they allow the physicist to make conclusions about something just by looking at the initial and final stages, without bothering about what is going on in between. This is of course a very powerful tool.

So here's a tip: if you are unsure whether a question deals with energy or Newton's Laws, the best way to tell is what kind of information do you have? If you have no information about the process of something, or if you have no information about the time taken for a process, it most probably involves energy. As simple as that.

Remember, energy is not separate from Newton's Laws: they are like two sides of the same coin, all part of a big picture.

Saturday, August 18, 2007

Flying and the Third Law

Greetings from Cornell University! Haven't really been updating recently, been too busy packing and doing my orientation stuff, but now I finally feel quite inclined to do this.

I don't know if you feel the same thing I do, but every time I take a plane, its take off is always a test of my faith in science and the triumph of human thought. Just think about it: Something like 400 people, sitting in what is effectively a fortuitously well-designed metal tube lifting off from the ground. It defies all human experience and all human logic: it is not surprising that Wilbur Wright told Orville Wright, the two great pioneers of human flight, that man would not fly in a thousand years.

So what exactly makes a plane take off? Well, there have been plenty of misconceptions and poor explanations of the real reasons for lift, and I've also realised that my understanding of it was rather poor before doing a little research for this post. Strangely, the "Bernoulli Principle" that people like to throw around when they explain how an aerofoil generates lift is not really very appropriate.

There are two reasons to explain lift, and the first is pretty straightforward. Imagine hitting a ping-pong ball in a game of table-tennis, or a tennis ball in a game of tennis: if you incline your racket downwards so that it is tilted towards the ground when you hit the ball, you are going to generate a downward force on the ball, and by Newton's 3rd Law, the ball generates an upward force on the bat. This works as well for the airplane wing. As long as it is inclined in an angle to deflect air downwards, lift will be generated!

The other reason is pretty complicated, and you'll just have to take my word for it, because I'm taking the website's word for it! As air passes across the aerofoil, it tends to "stick" to the metal of the aerofoil, and because the aerofoil is curved, the air is forced to curve around the aerofoil. Apparently, when air is forced to make a curve, it will be flung outwards, just like passengers in a car are flung to the side of the car when the car makes a turn. Thus, the air is flung outwards, and because it is stuck to the wing, it pulls the wing along with it.

Sorry for the quick post, but time's really quite tight at the moment. I'll come back with more the next time!