Physics, and a dumb teacher
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Master
Member # 5977
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written Friday, February 17 2006 23:07
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So I have this teacher, who answers to my question "will you explain me why the following formula is like that, and not otherwise?" like this: "You only have to know how yo use not, not why it is like that." So now I ask you, if you can please explain me why the formula "E(kin) = 1/2mv^2" is like that? I just don't get the "1/2" and "^2" part. Oh, and before I forget, this is the formula for kenetic energy. I hope i spelt it correctly. My book only says "because it is clever." -------------------- Play and rate my scenarios: Where the rivers meet View my upcoming scenario: The Nephil Search: Escape. Give us your drek! Posts: 3029 | Registered: Saturday, June 18 2005 07:00 |
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E Equals MC What!!!!
Member # 5491
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written Friday, February 17 2006 23:08
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quote:Sounds like a good reason to me. -------------------- SupaNik: Aran, you're not big enough to threaten Ash. Dammit, even JV had to think twice. Posts: 1861 | Registered: Friday, February 11 2005 08:00 |
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Master
Member # 5977
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written Friday, February 17 2006 23:12
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Ahem. No. Not quite if you already have difficulty understanding what the book is trying to explain to you. People tend to think, that the books should be filled with colors and pictures, but as less information as possible. The result is things like "The 1/2 was put there because that is clever," without saying what the "1/2" is actually there for, or what excalty it changes. -------------------- Play and rate my scenarios: Where the rivers meet View my upcoming scenario: The Nephil Search: Escape. Give us your drek! Posts: 3029 | Registered: Saturday, June 18 2005 07:00 |
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Law Bringer
Member # 335
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written Friday, February 17 2006 23:12
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I believe the answer is that kinetic energy is defined as the integral of force with respect to displacement. That's equal to half the product of mass and the square of the velocity (1/2*mv^2). So the simple answer for why is that it's defined that way. The slightly longer answer is that it's defined that way because that quantity has been meaningful in the experience of physicists. [Edit: Not so hot on the math. Or memory.] —Alorael, who supposes this ultimately gets to the question of why the universe has so many simple and elegant equations for how reality works. Anthropic Principle, anyone? [ Friday, February 17, 2006 23:14: Message edited by: 4.2% Popularity ] Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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Shock Trooper
Member # 3377
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written Saturday, February 18 2006 00:45
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Schools generally teach the formula before teaching how to derive that formula. The first Google link provides a decent enough explanation. The equations are only simple when they are applied within strict boundaries. Classical physics works well enough for everyday use, but break down when you look at variables where the approximations used become inaccurate. I've never found quantum physics to be particularly elegant ... but then, I'm not a big fan of working on that level. [ Saturday, February 18, 2006 00:57: Message edited by: premonition ] Posts: 356 | Registered: Saturday, August 23 2003 07:00 |
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Warrior
Member # 6689
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written Saturday, February 18 2006 07:22
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The ^2 comes from the need to keep the energy unit in Joules (or calories, but Imperial sucks). Because potential energy is equal to the product of mass, the pull of gravity (or another conservative force that you are dealing with, i.e. electric fields) and height. That gives the definition of a Joule the unit N*m. Alternatively you can unsimplify this expression to get kg*m^2/s^2. This is a fairly easy unit to come up with before simplifying the units of kinetic energy (.5mv^2, do the math :P ). -------------------- --Dachnaz Posts: 50 | Registered: Saturday, January 14 2006 08:00 |
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The Establishment
Member # 6
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written Saturday, February 18 2006 07:34
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The 1/2 and the ^2 comes from the calculus integration of a modified form of F = ma. I suspect your teacher did not answer it because you would be in a non-calculus based physics class and he/she would not want to go into the theory of integral calculus. Your teacher could have waved his/her hands and just said calculus and that would have been better. quote:What about quantum mechanics do you not find elegant? -------------------- Your flower power is no match for my glower power! Posts: 3726 | Registered: Tuesday, September 18 2001 07:00 |
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Councilor
Member # 6600
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written Saturday, February 18 2006 09:32
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That's interesting. For a moment, when I saw the title, I thought someone from my school had joined. But the class I'm in isn't up to energy yet. Dikiyoba. Posts: 4346 | Registered: Friday, December 23 2005 08:00 |
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Master
Member # 4614
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written Saturday, February 18 2006 09:53
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Possibly because the rules of quantum mechanics can be a frustration to deal with. -------------------- -ben4808 Posts: 3360 | Registered: Friday, June 25 2004 07:00 |
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Law Bringer
Member # 335
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written Saturday, February 18 2006 10:42
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Quantum mechanics are mathematically elegant but a mess to try to imagine. The classical approach is to draw a diagram. If you try to draw a diagram of quantum mechanics you're probably wrong. —Alorael, who gives himself headaches by trying to visualize wavelengths of macroscopic objects. Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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Warrior
Member # 6689
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written Saturday, February 18 2006 11:17
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My physics class occasionally jumps into calculus and integrates a few of the more algebraically challenging (or impossible) equations. We covered energy in early October. Right now we're doing electromagnetic induction. Totally worthless in my career path (canoing). -------------------- --Dachnaz Posts: 50 | Registered: Saturday, January 14 2006 08:00 |
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Law Bringer
Member # 4153
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written Saturday, February 18 2006 11:34
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quote:I envy you for your career choice. I'm stuck in a full-year intro-level pre-med-weedout chemistry class, all in order to meet some requirements for Environmental Studies. The class is unpleasant to say the least, because we started with quantum mechanics and have just now worked up to thermodynamics. I feel like it's about 80% physics, which annoys me to no end. (And the course is seriously built to thin out the huge numbers of freshman pre-med students) As for the practicality of any of this stuff, unless you're going into a seriously quantum-intensive job (of which there seem to be very few), it's nearly worthless. I, personally, will never need to figure out the wavefunction of a frog, I'll just need to be able to count them. Heck, KE=(1/2)m(v^2) is arcane enough... how often will any of us need that in real life? It's just an interestingly-compact way of supporting the bigger theories, most of which are even harder to think about. (Now I've got myself wondering... does the wavefunction of a small frog change when it croaks?) -------------------- Gamble with Gaea, and she eats your dice. I hate undead. I really, really, really, really hate undead. With a passion. Posts: 4130 | Registered: Friday, March 26 2004 08:00 |
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Master
Member # 4614
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written Saturday, February 18 2006 19:13
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I dunno if the wavefuction of a small frog is so much of a mystery. After all, using common sense can tell you both the position and the velocity. At the same instant. Weird. -------------------- -ben4808 Posts: 3360 | Registered: Friday, June 25 2004 07:00 |
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Off With Their Heads
Member # 4045
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written Saturday, February 18 2006 19:57
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Well, if you drop a ball from some height and want to know how fast it's going to be going when it hits the ground, KE=(1/2) m * v^2 is one good way to get that speed. -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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Law Bringer
Member # 4153
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written Saturday, February 18 2006 20:12
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quote:Alright!!! Small frogs disprove quantum mechanics!!! (Yes, I know it's wrong. But the idea of tossing a frog into these calculations, literally or otherwise, has a pleasant sort of certain comic ring to it.) -------------------- Gamble with Gaea, and she eats your dice. I hate undead. I really, really, really, really hate undead. With a passion. Posts: 4130 | Registered: Friday, March 26 2004 08:00 |
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Off With Their Heads
Member # 4045
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written Saturday, February 18 2006 20:43
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Well, you could always insert a cat into the calculations. And you can find the velocity and position of a frog, but only to finite precision. -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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Apprentice
Member # 4231
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written Saturday, February 18 2006 20:49
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What's very interesting is that wavefunctions behave perfectly deterministically, it's using them to predict anything at all that introduces uncertainty. Fortunately, the wavefunctions of all the little quarks and electrons in a tree frog all average out to behave very nicely on a macro scale, reducing significantly the probability of it suddenly disappearing from the jungles of South America and reappearing in your beverage of choice. Of course, I do rather like the idea of the quantum wavefunction of a tree frog. :) -------------------- Lifetime Spiderweb Gamer and Fan of Classic Style Graphics Posts: 42 | Registered: Saturday, April 10 2004 07:00 |
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Law Bringer
Member # 335
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written Saturday, February 18 2006 20:58
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Kel, you just did the same thing as the teacher. Saying that KE can be used to calculate the velocity of a falling ball (as long as you know PE ~ mgh) doesn't explain why KE is what it is. Mass and velocity are measurable quantities, but KE isn't so obvious. A quantity could be defined as the 7/5*sqrt(m)/v^8, but that's not a useful quantity like KE. Common sense doesn't work with quantum mechanics, Ben. It just doesn't. Also, while knowing position and velocity is related to wavefunction, that's more of a contradiction of the Heisenberg uncertainty principle. —Alorael, who prefers to introduce cats into his boxes with lethal but unpredictable poisons. Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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Off With Their Heads
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written Saturday, February 18 2006 21:08
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Alo: I wasn't trying to give a conceptual explanation of kinetic energy. I was trying to answer Ephesos's objection that the equation is not used much in everyday life. Now, I don't know how often you actually have to calculate how fast a thing will be moving when it hits the ground, but sometimes it might be interesting to do so. -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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Shock Trooper
Member # 3377
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written Saturday, February 18 2006 21:39
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quote:That's what chemistry is. Except with funky smells and pretty colours. quote:That's the problem I have. All the time I was learning it, I was thinking, 'Okay, I know the equations, I can apply them where I'm told to apply them. I can even parrot the textbook in my exam. But it just doesn't make sense.' I also find it more interesting looking at stuff on a somewhat larger scale. It probably didn't help that I never quite understood anything that particular lecturer ever taught me. I passed that unit by extreme short term memory cramming. [ Saturday, February 18, 2006 21:41: Message edited by: premonition ] Posts: 356 | Registered: Saturday, August 23 2003 07:00 |
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Law Bringer
Member # 335
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written Sunday, February 19 2006 00:10
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Biology is a subset of chemistry and chemistry is a subset of physics. If you understand physics you understand everything! It just takes a little work to get there from fundamental principles. —Alorael, who once actually used that equation to calculate how fast he would be moving when he hit the ground after leaping off of a roof. He was painting the roof and the wasps were displeased. Based on his (very rough and rapid) estimates of his probable collision speed, the elasticity of collision with the ground, and the anger of wasps, he elected to jump. Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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? Man, ? Amazing
Member # 5755
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written Sunday, February 19 2006 00:54
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quote:Heheh When I was a wee lad I was often presumed guilty when guests at a cocktail party would look into their glass and find a crayfish desperately trying to drink their way out. Good times. Gooood times. -------------------- quote: Posts: 4114 | Registered: Monday, April 25 2005 07:00 |
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Master
Member # 5977
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written Sunday, February 19 2006 01:14
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quote:Yes, Alo is right there. I know you just tried to give an explanation og "what to use it for," but that's not what I asked. I already knew this, the teacher had explained that. She didn't explain why the formula is like that, and that's what I'm asking. By the way, all you guys can explain much better. now I need a dictionary to look up all the difficult words. anyway, thanks. -------------------- Play and rate my scenarios: Where the rivers meet View my upcoming scenario: The Nephil Search: Escape. Give us your drek! Posts: 3029 | Registered: Saturday, June 18 2005 07:00 |
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Off With Their Heads
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written Sunday, February 19 2006 01:15
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Thralni, since you seem to need your own personal memo: I WASN'T RESPONDING TO YOU. -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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...b10010b...
Member # 869
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written Sunday, February 19 2006 01:35
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quote:See, this is why it's best to use quote tags even if you can't see how there could be any doubt as to who you're responding to. EDIT: added quote tags, for good measure [ Sunday, February 19, 2006 01:36: Message edited by: Thuryl ] -------------------- The Empire Always Loses: This Time For Sure! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |