What Feynman meant in description of reversible machine and levers

Question

In chapter four of the part one of the lectures, he mentions:

(..) A machine that we actually use can be, in a sense, almost reversible: that is, if it will lift the weight of three by lowering a weight of one, then it will also lift nearly the weight of one the same amount by lowering the weight of three.

and in the picture (is the fulcrum a bit of placed w.r.t the contex ?)

However, in order to get it actually to work, we must lift a little weight off the left pan. On the other hand, we could lift a one-unit weight by lowering the three-unit weight, if we cheat a little by lifting a little weight off the other pan.

I can't make any sense out of this.

I was confused by the same paragraph and I realised that one of the issues is that Feynman uses the verb "lift" in two different ways: (1) to get the boxes in an upper position relative to the ground and (2) to remove the boxes from the balance pans . Refer to my thread Difference between “lift” and “lift off” in Feynman Lectures for more details. — Paul Razvan Berg, Nov 23 '20 at 20:53
Also not sure if this helps anyone but @user77648 quotes Feynman in the reverse order. In the lectures, the second quotation comes before the first quotation. — Paul Razvan Berg, Nov 24 '20 at 13:01

score 5 · Accepted Answer · answered Mar 29 '16 at 13:33

5

If the example Feynman gave was "perfectly reversible", then you could move the balance up and down without doing any work. In order to overcome (even tiny amounts of) friction, you actually need to do a little bit of work. This can be done by adding or removing a little bit of weight to one of the pans of the scale.

After a cycle of moving the scale first one way, and then the other, the "state" of the scale is the same as it was before. In a perfectly reversible system, the total work done would be zero. But if you had to lift a little bit of weight to the top scale in order to tip it, then move it to the other scale to tip it back, you would have done a net amount of work on the system.

That makes this system (and any other "real world" system) irreversible.

Incidentally, the fulcrum is offset because, with 3x the weight on the left of the scale, you get "balance" when the lever on the right is 3x the lever on the left. One could have done the same example with a symmetrical scale with the same weight on each side instead.

answered Mar 29 '16 at 13:33

Floris

118,905

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Thanks for the answer. Some things are still counter-intuitive to me: 1. You can move the balance up and down effortlessly (In an idealistic world, of course) ? 2.When we pull the 3W side down, and then push it up (in real world) the same height, wouldn't the 1W side stay in the same position ? Why ? 3. Which friction - air ? 4. Why the scale is not balanced (It should be balanced of the special offset position - isn't it ? ) ? 5. He meant adding or removing part of the three/one block(s) ? – Mar 29 '16 at 16:41
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Feynman is talking about the real world, so effort is needed; 2) the 1W moves up, and then back down (to the same height where it started) 3) all kinds of friction: air and the hinge / pivot, mostly; 4) Scale is balanced (or close to it), but if center of mass is at the pivot (rather than below it) then "balanced" means "no restoring torque" results when the scale is moved slightly (unlike a normal scale); 5) I think he is talking about adding a very small "helper weight" to move the scales around. It could be a "chip off the big weight" but that doesn't change the argument.

Floris

Mar 29 '16 at 17:46

It is almost clear, but 1 . If Bob and the pictured lever are in an idealistic closed box. If bob spends a bit of energy to lift one side a bit, where the energy goes ? 2. Comparing the lever to a pulley makes it more intuitive (you can see where is the friction), but still the first quotation is not clear to me. 3. Why the "chip off the big weight" doesn't change the argument ? – Mar 30 '16 at 04:12

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1- the energy goes to heating the contents of the ideal box ("heat is work and work is heat"); 2- the important point is just that any machine has some dissipation (friction etc) turning work into heat irreversibly (as opposed to ideal Carnot cycle which is fully reversible). 3- if you consider not 1 and 3 but 1 million and 3 millions grains of sand, you can't tell the difference between a "helper weight" and a chip off the nigh weight. Was it grain of sand #1,000,000 or #1,000,001? No real difference. – Floris Mar 30 '16 at 10:36

How lever is staying balanced in any position? – Mar 30 '16 at 10:55

Is stays balanced because to move to another state requires energy. Either because it raises the center of mass or because it has to overcome friction. – Floris Mar 30 '16 at 11:16

Sorry to pester you repeatedly, but I can't understand the last sentence of yours. Also, I mentioned any position. – Mar 30 '16 at 11:19

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For anything to "stay balanced" means that it requires a force to move away from the point of "balance". If there is some static friction, then "balance" can happen over a range of positions. The less friction there is, the more you rely on the shape of the gravitational potential. If you have a marble at the bottom of a round bowl it stays there. If your marble is sticky, it will stay some way up the side of the bowl as well... If that doesn't clear it up you need a face to face conversation - do you have a physics teacher? – Floris Mar 30 '16 at 11:27

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Thanks for you help. I will try to backfill the tendrils (Ctrl+F tendril here: http://math.stanford.edu/~vakil/potentialstudents.html ). I do have two teachers (one private, one at school), but I don't have any discussion with them (except to gain stupid marks for our class; I am 14), for one propagates the stupid Jeffersonian idea of natural aristrocracy and one thinks I am speaking blather . I do have some books also, but (Feynman exception - it's cool) either they are recursive and/or they are promoting stupid line of reasoning and plug-chug method. Anyway, thanks for your persistent help. – Mar 30 '16 at 11:42

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If you are reading Feynman at 14 I tip my hat at you! Curiosity beyond the material taught in class is the way to become a master of the subject - unfortunately it may also lead to friction with your teachers and class mates. Sorry to hear even your private teacher is not meeting your need. Come back here and ask more questions! – Floris Mar 30 '16 at 11:51

Can you give an accurate step by step description (where the energy is going) of a extremely real life irreversible simple machine ? [Switching between the two pictures (irreversible <-> reversible )may help understanding.] – Apr 02 '16 at 02:29

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Imagine a cylinder with frictionless piston. Push on the piston and you do work on the gas. Pressure and temperature go up. Reversible engine: gas stays hot until you release the piston - it can push the piston back to the original position, "giving back" all the work you did. Irreversible form: while the gas is compressed, some heat flows into the cylinder. Gas cools down and it can no longer push the cylinder back with the same force. Work was irreversibly converted to heat and entropy has increased. Does that help? – Floris Apr 02 '16 at 03:04

Thanks a lot. I won't bother you more, last request - can you please repeat the argument for a simple machine ? – Apr 02 '16 at 03:12

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A lever with a hinge that has no friction: use it to lift something up, and get all the energy back when it comes down. Now add friction to the hinge: you need to do MORE work to lift the object (overcome gravity plus friction), and you don't get all the work back when the object comes down again (friction is non-conservative - irreversible) – Floris Apr 02 '16 at 03:16

that was an amazing answer. But, can you clear one doubt of mine if you can? Suppose there is no air friction, no kind of friction, nothing. We just give one of the pans a tip with our hand. So, ideally, we haven't done any work, as it was just a tip. Will this again be a an irreversible machine? And how do even reversible machines start working, if there is no initial tip to get it going? – codetalker Jun 12 '17 at 15:05

@siddarth - even "just a tip" does work and adds kinetic energy - but in the perfectly reversible case you could "reclaim" that energy by slowing the beam at the end of the cycle (thus reclaiming the energy you put in) – Floris Jun 14 '17 at 13:09

Hey Floris, thanks for your answer. I think there is a typo in "lift a little bit of weight to the top scale in order to tip it". Perhaps you wanted to use off instead, as in removing a bit of weight from the top scale? – Paul Razvan Berg Nov 23 '20 at 21:50

@PaulRazvanBerg thanks for your comment. After re-reading this, I think I did mean yo write “to”. The top scale needs to become a bit heavier for it to start dropping so I have to ADD weight. Make sense? – Floris Nov 23 '20 at 21:55

Oh, I see. In this case, I think it would make the explanation more clear if you replaced "lift" with "add"? – Paul Razvan Berg Nov 23 '20 at 21:58

@PaulRazvanBerg I used “lift” because work is involved ... that is the crux of the argument. “Add” to me doesn’t imply work done. – Floris Nov 23 '20 at 21:59

How would the action of "lifting a weight to a scale" look like if it were represented visually? Is it like someone placing a weight on the scale using their hands OR someone applying a force from underneath the scale, and lifting the scale up? – Paul Razvan Berg Nov 23 '20 at 22:02

score 1 · Answer 2 · answered Mar 29 '16 at 12:38

Feynmann often liked to deal with realistic real world examples instead of idealised ones, to illustrate how physical principles applied in the real world. In this case I suspect that what he is getting at is that a real world hinge/balance isn't frictionless, located at a mathematical point and made of perfectly rigid materials. In the real world, you can actually balance a mass of 3 Kg against a mass of 1 Kg located three times further from the fulcrum over a small range of positions and have it be stable. To make the balance reliably tip, you need to have a slight imbalance in the weights (or distances) as due to friction and material deformation (the arms of the balance bending for example), the situation is not perfectly reversible.

What Feynman meant in description of reversible machine and levers

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