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.]
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....
tommy, I would love to discuss these matters further with you, but I gotta go now - could you please remind me, when we post on each other's screens again?
Abi and I are going to go get Steak -n- Shake
Damnit. I wish there were Steak n Shake here. Or Sonic. I'll bet there's neither of those in Seattle either, huh? Grr.
I know I don't earn enough now to quit the day job, but it's a "if I quit the day job and had more time for other jobs, how much would I need to do to pay for health insurance & such?" issue
Good luck, Strega! One of the options I had after being laid off was to become a contractor, but the thought was too intimidating and scary, so i didn't pursue it. Go you for having the chutzpah!
(Note to self: you suck at keeping plants alive. No chocolate tree for you!)
Well, plus it apparently wont' make chocolate for you. Useless!
oon-to-be-divorced friend who was going out on her fourth ever post-separation date (opening night at the SF Opera, including red carpet walk, so my babysitting duties included lacing her into her Dark Garden brocade corset
Dude! That's an awesome date!
My sunday paper this morning was missing the comics section. That's just not right.
I really wish I had my own washer and dryer.
How did you know that I am looking at Bugaboo strollers right now?
Psychic powers?
Nilly, I got your card - thank you so much!
I am effing stuck on the couch alone with a busted foot and no internet but this. This sucks!
