Nilly, I got your card, but it wouldn't play.(I just got an icon wanting me to download Flash. I did, but it still didn't work.)Thanks for thinking for me, and have a good Yom Tov.

Happy birthday Nutty!

I think so, yes.

I'm all sad about the photo scavenger hunt. It was an awesome list and I had half the stuff all plotted out in my brain, and then work and Matilda ate up the entire week and now there's no way I can manage more than maybe two items on the list. I may just go ahead and do the whole list next week if things calm down and I've got breathing space, just for the awesomeness of it.

Happy Birtday Nutty and Spidra!

The photo scavenger hunt is one of the reasons I need a digital camera -- the lists are great and people have sent in such awesome pictures.

Thanks, JZ!

Um, well, you guys, if you think I could have sent you a "Good New Year" card, I probably tried, and it bounced back and I'm so sorry. If you think I might-have-sent-but-not-for-sure, I probably tried, and it bounced back and I'm so sorry. If you think that I-don't-know-you-at-all-and-what-is-this-name-posting-and-who-does-she-think-she-is-anyway, I probably never had any e-mail address for you and never tried to send you anything, but, hey, I hope you have a good year anyway, why not.

[Edited to Happy-birthday Nutty!]

Birthday Happies for Nutty!!

Hey Nilly - Last Friday I posted some physics stuff I had been thinking about. It's about some aspects of the physics of motion seeming rather unintuitive to me (especially the fact that the kinetic energy of an object in motion is proportional to the square of its velocity) so I tried to get a sense of others' intuition about this.

If you got a second, I'm curious what your thoughts are...

tommyrot "Natter 53: We could just avoid making tortured puns" Sep 7, 2007 8:03:35 am PDT

tommy, you put your finger on a touchy subject - that of energy.

I was teaching some of the basics about it this year, and I've been looking into books trying to find a good way of explaining it. You know what they did? They all went "Energy is a very complicated concept to explain. There are many kinds of energy: heat, motion, electric... ", and *none* of them explained it!

The physics way to explain energy is through the concept of work (force times distance). Work is changing the energy of a body. It seems so the-opposite-of-intuitive when explaining it this way, doesn't it?

But once you do it this way, getting to the law of conservation of energy is pretty easy and straight-forward (and for simple cases, where you don't need integrals, the math is very straight-forward, as well). And then, once you have *that*, the questions you talk about are not only easy, but intuitive, in the sense of that language.

The law of conservation of energy says (well, sort of, I'm not getting into any subtleties here):
Energy-in-initial-state + Work = Energy-in-final-state.
It doesn't matter what form the energy is.

Kinetic Energy = 1/2mv²
m = mass, v = velocity

Height Potential Energy = mgh
m = mass, g = gravity acceleration, h = height

When you put the data from your questions in the form of the energy conservation equation, it all balances out just as the answers you gave.

The thing is, there are so many steps *before* getting to the intuition part (energy, work, the forms of kinetic and potential energy, the energy conservation equation), it doesn't seem intuitive at all when you just ask the question. It's the sort of physical intuition that takes time and practice to develop. It's actually the most difficult thing to learn - and teach - when trying to approach these subjects.

We think in "force", not in "energy". I guess we could blame Newton for that, seeing as he formulated his three laws, which dealt with force, not with energy (which may be the more fundamental aspect of the problem), and got everybody used to thinking in these terms rather than in energy. But it's too late to change that now, isn't it?

Similar things happen with momentum vs. velocity. The more basic concept in the momentum (mass times velocity), that's the part that's conserved, not the velocity. But we're *used* to thinking about velocity, not its product with the mass, and therefore it seems completely counter-intuitive to start looking at the mass that's moving, as well. Again, it's an intuition that can be developed, but it takes practice and time.

Did anything of what I said help at all, or just confuse things even further?

[Edited because even when I'm talking about physics and throwing equations, I should try to remember some grammar rules.]

Impatient kitty. Video.

Happy Birthdays, Nutty and Spidra!

Did anything of what I said help at all, or just confuse things even further?

I had to read your post a few times, but yeah, it makes sense. I'll probably end up doing some more thought experiments while walking to and from train stations. (Yeah, I do stuff like that all the time.)

We think in "force", not in "energy". I guess we could blame Newton for that, seeing as he formulated his three laws, which dealt with force, not with energy (which may be the more fundamental aspect of the problem), and got everybody used to thinking in these terms rather than in energy. But it's too late to change that now, isn't it?

Sometimes I think of energy - like, the kinetic energy a car has when its moving, and how that energy gets converted into heat when you brake to a stop. Or how hybrid cars can take some of that kinetic energy and recoup it as electricity (which is then stored in a battery) so it can be used again instead of released as waste heat.

Similar things happen with momentum vs. velocity. The more basic concept in the momentum (mass times velocity), that's the part that's conserved, not the velocity. But we're *used* to thinking about velocity, not its product with the mass, and therefore it seems completely counter-intuitive to start looking at the mass that's moving, as well.

Huh. I'm not used to thinking of momentum at all. How does momentum (mass * velocity) relate to kinetic energy (1/2 mass * velocity²)?

Off to google momentum....