Energy

L13 gap-filling test for 2R at KU (2012/01/26) prepared by Kow Kuroda

The script below was a transcription ofThe Feynman Lectures on Physics, Volume 1, Chapter 4created by Kow Kuroda, based on (http://www.amazon.co.jp/Feynman-Lectures-Physics-5-6/

dp/0738202835/ref=sr_1_8?ie=UTF8&qid=1326870123&sr=8-8).

Richard P. Feynman:

Conservation of Energy

Secion 4.2: Gravitional Potential Energy

Now, uh the conservation of energy can only be work— understood if we have the formula for these things. And uh I could of course 1. list the various formulas, the dif- ferent forms of energy, we call these things different forms of energy— different— hid- den ways of calculating the number of blocks.

However, I want to amuse us, today by dis- cussing the formula for 2. gravitational en- ergy and the, in around on the surface, the earth here not going very far away and I want to derive this formula in a way that has nothing to do with the history. It’s a— It’s simply uh a set of reasoing that I have in- vented for this particular lecture. And uh it’s 3. patterned after a very excellent argument by Mr. Carnot on the efficiency of the steam engine but it is applied here to calculate or to understand the law or how to calculate the en- ergy and what the conservation of energy is in the case of gravitational energy.

So, what I want to do is to consider weight lifting machines that is a machine that has

this property that if you put a weight here, it lifts another weight by lowering some other.

I want also to make a 4. hypothesis which is that there’s no such a thing as perpetual motion with these weight lifting machines In fact, that there’s no perpetual motion at all, it’s a general statement of the conservation of energy law. I must be careful to define

5. perpetual motion.

First, list— if you apply it to the weight lifting machines if you have lifted and low- ered a lot of weights, take the weights off you can 6. restore them— restore the ma- chines to the original condition, then uh and find when you’re all finished, the net result is to have lifted a weight, then you have a perpetual motion machine because you can use that lifted weight to run something else, 7. provided that the machine, which lifted the weight, was brought back to exactly the same condition as it was before furthremore, that it was completely self-contained but it hasn’t repeated the energy to lift that weight from some 8. externals , but Bruce’s blocks someone has thrown in.

Now, I have a very simple weight lifting machine here. Here’s a machine for lifting

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weights three units —stone— which I have put on this panel by placing a weight on this panel in order to get the things to work right [?to ?have ?it].

I’ll explain about this. If you have to lift this little thing. Now we just don’t worry about that that lifts this— that lifts this.

On the other hand, I could lift the one unit weight by lowering three unit weight[s]. By that, I 9. cheat a little bit, by lifting one on this side

I want you to realize that any actual lift- ing machine, I have to add a little extra to get it to run. Please disregard that temporar- ily. The ideal machines wouldn’t require that.

They don’t exist and I will come back and discuss that little business. and in order to make it work, I have to move this. The uh machine that I have here is in the sense 10. almost revsersible, that is if it’ll lift the weight of three by lowering the weight of one, then it will also lift the weight of one, the same amount, by lowering the three, the same amount: 11. nearly !

So, if we imagine that there are two classes of machines: those which are not reversible.

This is really not reversible because I have to fiddle around with these extra weights, but we have a machine— so general machine is not reversible. In fact, any real machine is not partic– uh precisely reversible, but as we improve the 12. fulcrum and levers and so on, we find that the amount of stop that has to be lifted gets weaker and weaker. And so with our imagination, we 13. idealize to the exist— possible existence of a reversible weight-lifting machine. So suppose that there

were such a thing.

Suppose now that I have a reversible ma- chine which does this: A one unit weight—

let’s say a pound or any other 14. marker for the unit— one unit weight is lowered by one foot, say, or one the other unit of dis- tance, [it] doesn’t make any difference. And when this 15. happens , the weigh– the leve–

the machine lifts a uh weight three— three units, say— and this one does and that’s all the machines I’m going to consider now, all the various devices, this is the 16. simplest possible one. I get screws and accels, inclined planes in all kinds of levers and machinery can be inside, but the net result of the ma- chine that I wanna discuss is that it takes one pount weight, lowers at one foot and in doing so, lifts a three pound weight, some distance.

Now, let’s suppose that we have a machine Aand it’s a reversible machine. And this par- ticular reversible machine 17. lifts the three pounds at distanceX.

Now, I have another machine, a machineB, which is not necessarily reversible; [it] is not reversible or is, whichever you want: is or is not is not important. Let’s say it isn’t for the sake of argument. It lifts three a distanceY.

Now what I wanted to prove is that Y is not higher than X and it is impossible to 18. build a machine that it will lift a weight any higher than will be lifted by a reversible machine. Let’s see why.

Well, let’s suppose thatY 19. were higher thanX.

You don’t have to draw pictures the way ?it

?my own. Look. You take a weight, one and you lower it at one foot with the machine B

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and that lifts the weight three up a distanceY. Now you lower that— let’s see if— if Y is greater— I’m gonna prove or let’s say I’m gonna proveY is not higher thanX.

Suppose that it 20. were and I lifted that weight higher then I need thanX, the distance Y up here and supposeXis only this high and I can lower the weight fromXtoY obtaining free energ— free power, and then use the re- versible machineA running 21. backwards , which, according to this, will lower [the] three pound weight X and lift[s] the one pound weight, one foot which you put the one pound weight back where it was before and I’m ready to use the machine B again. In other words, I 22. lower —I lift with the machine B by lowering the pound lowering the weight one pound, I lift the thing three pounds upY.

Then I lower at the distanceX and get my one pound weight back before, but sinceX is less thanY, I have a little bit lift to go. I can make the thing do something [?due ?to ?one and four] betweenY andX, therefore I have a perpetual motion. So ifY were higher thanX, I have a perpetual motion, which I assumed was impossible. So, therefore, with those as- sumptions, I 23. deduce thatY is not higher thanX.

Therefore, of all machines that can be de- signed the reversible machine is the best, no matter how you figured out with the 24. wheels and gears , you’d better try to make it reversible.

Now I’ll show you something else, or re- versible machines must lift it at exactly the same height, because suppose that B were re- ally resersible also, well, the 25. argument ,

if B is reversible, thatY cannot, is not higher thanX. Of course, this is just as good as be- fore. So, Y is not higher than X. B is not reversible, however. And I can make my ar- gument the other way around, ?let’s see, stop and think and manage you see what I mean I can— make the machine run in the opposite order. So I can just 26. interchange the B andAin the argument. And I can easily prove the other thing thatX is not higher thanY. In other words, if I had two reversible machines and one lifted higher than the other, then I can use that extra difference, and then make one run the other backwards, uh, to keep the 27. cycle going. So therefore, I have a set of rever— if I have a reversible machine, all reversible machines lift the same distance, no matter how they are constructed. If they drop one pound one foot and lift three pounds, the same distance, no matter how they are con- structed. This then is a very remarkable ob- servation because it 28. permits us [to] ana- lyze the heights in which different machines are going to lift something without looking at the interior mechanism. We know right away that if somebody’s concocted a series of levers that’s enormously 29. elaborate , that lifts this, a certain wei– [a] distance and I can compare it to a simple lever like this, which is fundamentally reversible, I know this is gonna lift it no higher— uh, no— less high. I know exactly how high it’s going to lift and I know that it is no use trying to 30. redesign the ma- chine to get greater height.

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調査

授業の方設計するために，以下の二つの点 に関して意見を述べてください．

(1) 問題の量は適切でしたか？

1. ^多過ぎた

2. ちょっと多かった 3. ちょうどよかった 4. ^{ちょっと少なかった} 5. 少な過ぎた

(2) 聴き取る箇所の難易度は適切でしたか? 1. 難しいところが多すぎた

2. 難しいところが多かった 3. ちょうどよかった 4. 簡単なところが多かった 5. 簡単なところが多すぎた

他に意見があれば書いてくれてよいです．

今後の授業に生かします(成績には影響しま せん)．

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