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Why a non-reversible weight lifting machine cannot lift higher that a reversible one is related to my current post, but everyone in that thread seems to have understood how Feynman's simple machine works visually. I haven't.

Figure 4.1:

Figure 4.1

And the excerpt from the Feynman Lectures on Physics Chapter 4.2:

A very simple weight-lifting is shown in Fig. 4-1. This machine lifts three units "strong". We place three units on one balance pan, and one unit on the other. 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. Of course, we realize that with any actual lifting machine, we must add a little extra to get it to run.

Feynman is blending terms, which makes visualisation hard. The said machine seems to be a see-saw, that I understand. But I can't follow whether the four squares placed on the balance pans are the "units" or the "weights". Here's why:

  1. We are told that there are "three units" placed on one balance pan. From this we should conclude that one square = one unit, because there are three squares on the left-hand balance pan.
  2. But we are also told that this machine lifts "three units strong", from which we should conclude that one square = one weight, because the single square on the right-hand balance pan is the one that is lifted. If this is true, it should follow the figure is poorly designed. Squares with higher unit "strongs" should either be drawn bigger or annotated with numbers that flag their "strongness".

I tend to lean on explanation #2, since it could account for the "three units placed on one balance pan" part, that is, the single square on the right-hand balance pan is weighing three units "strong".

To make matters worse, he is using the verb "lift" with two different meanings. The first is getting the squares in an upper position relative to the ground, while the second is about getting squares off the machine (when "lift" is used in conjunction with "off").

What are the squares in the figure? Units or weights? What does he mean by "in order to get it actually to work"?

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The way this machine works is by conservation of angular momentum. The torque provided by the three boxes (aka weights, aka units) on the left hand side balances the torque provided by the box on the right hand side. Therefore, once the balance starts to rotate, it will continue to rotate in order to preserve angular momentum, until it hits the edge of its range of motion.

However, if the balance starts at rest, then it will remain at rest forever unless an external force is applied. Feynman proposes a way to do this in practice. If you remove a little weight from the left hand side, then the torque will be dominated by the right hand side, and the machine will rotate clockwise (ie the one box will move toward the earth, lifting the other three boxes). In contrast, if you remove a little weight from the right hand side, then the three boxes on the left will lift the one box on the right.


In terms of your specific questions

What are the squares in the figure? Units or weights?

Units, weights, boxes... they all mean the same thing. Call them 1 kg masses.

What does he mean by "in order to get it actually to work"?

If you start with a state where three boxes are on the ground, and you want to lift them in the air, then "get it to work" means "getting the balance to move in such a way that the three boxes are in the air."

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  • $\begingroup$ Great answer, but let me be pedantic enough to retort that "units, weight, boxes ..." aren't interchangeable terms in either Feynman's explanation or yours. If you assert that one box = one weight, you cannot say "remove a little weight from the right hand side" because there is only weight on the right balance pan. Or, you could say it, but you would ascribe two different meanings to the word "weight", one for the drawing of the box, the other for weight as in the force acting on the object due to gravity. Which makes for an unnecessarily confusing explanation. $\endgroup$ – Paul Razvan Berg Nov 22 at 11:09
  • $\begingroup$ OK I see what you mean. Having said that in my experience it's not so uncommon to hear physicists refer to "weight" in both of these ways, so unfortunately this is a level of ambiguity you might just have to get used to. Even worse, eventually you'll get the point where people use the same symbol to mean two (or more) different things, and you need to work out which meaning is meant from context. So it's a good idea to develop some "thick skin" around overloaded terminology. $\endgroup$ – Andrew Nov 22 at 11:14
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    $\begingroup$ I see, thanks for the caveat. I've just started learning physics as a hobby and this is good to know. $\endgroup$ – Paul Razvan Berg Nov 22 at 11:18
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If we are about to talk of angular momentum we could say that in a picture that you are offering momentum on the left is greater than momentum on the right. Momenta would be equal if the balance was parallel to the ground. Lifting a bit of weight means just lifting enough to get the machine started. Once it starts to rotate to either side it will continue to do so because of the change of momentum on both sides. So to remove a bit of weight means just nudge it a bit, not to totally remove weight. Three units strong means it can lift three mass units to the height of one length unit OR lift one mass unit to the height of three length units. This is my understanding. Also, just to say, formula for torque: F x l, where F is the force and x means vector product.

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