Feynman Lecture On Conservation of Energy

Question

From Feynman's lecture series - Chapter 4 Conservation of Energy

Consider weight-lifting machines—machines which have the property that they lift one weight by lowering another. Let us also make a hypothesis: that there is no such thing as perpetual motion with these weight-lifting machines. (In fact, that there is no perpetual motion at all is a general statement of the law of conservation of energy.) We must be careful to define perpetual motion. First, let us do it for weight-lifting machines. If, when we have lifted and lowered a lot of weights and restored the machine to the original condition, we find that the net result is to have lifted a weight, then we have a perpetual motion machine because we can use that lifted weight to run something else. That is, provided the machine which lifted the weight is brought back to its exact original condition, and furthermore that it is completely self-contained—that it has not received the energy to lift that weight from some external source—like Bruce’s blocks.

A very simple weight-lifting machine is shown in Fig. 4–1. This machine lifts weights 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. This we disregard, temporarily. Ideal machines, although they do not exist, do not require anything extra. 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.

What do these sentences in bold mean exactly? You take 1 of the 3 blocks on the left and lift it off the pan? (this is addressing the first bold sentence). But that can't be right though can it? Because then you're not lifting three blocks. I don't understand the second bold sentence either. I understand Feynman is working with a hypothetical example and that perpetual motion machines don't exist, but I'm still confused here. Any help or clarification would be much appreciated.

Answer 1

As drawn the system is balanced (in static equilibrium) ie will not move on its own.

To get movement one must unbalance the system.
Feynman does this by removing a very small amount of mass from a weight (he does not remove a whole weight) thus reducing its mass and hence its weight and having a system which is no longer in static equilibrium.

He could have gone from the initial position of the system to its final position by making one of the masses move by applying a (small) force on it, thus doing some work on the mass.
Then allowing the system to reach its new position and allowing the system to do the same amount of work on him when it is stopping as the work he did on the system when he got it to move.

Another way is to start looking at the system when it is already moving and which maintains that constant motion during the "lifting" thus the system always has the same amount of kinetic energy.

Feynman chooses the "least complicated" method of achieving the lifting where the mass which is removed can be made "infinitesimally" small.

PS An equivalent complication arises when you show that a force $mg$ (which is the weight of a mass $m$) acting on an initially stationary mass $m$ moves the mass a vertical height $h$ and hence the work done by the force on the mass is $mgh$.
If the mass starts at rest and finishes up at rest and the net force on the mass is zero how can the mass change its position?

@JohnRennie has another way of looking at the complication in his answer here.