Perpetual motion machines can't exist (Feynman's lectures)

[Jazzyrohan]

I have been reading Feyman Lectures Volume 1 and I am stuck on the example or proof given in the book about how no machine can be more efficient than a reversible machine.

http://www.feynmanlectures.caltech.edu/I_04.html
Section 4-2

A very simple weight-lifting 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, almostreversible: 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.

We imagine that there are two classes of machines, those that are notreversible, which includes all real machines, and those that are reversible, which of course are actually not attainable no matter how careful we may be in our design of bearings, levers, etc. We suppose, however, that there is such a thing—a reversible machine—which lowers one unit of weight (a pound or any other unit) by one unit of distance, and at the same time lifts a three-unit weight. Call this reversible machine, Machine A. Suppose this particular reversible machine lifts the three-unit weight a distance X. Then suppose we have another machine, Machine B, which is not necessarily reversible, which also lowers a unit weight a unit distance, but which lifts three units a distance Y We can now prove that Yis not higher than X, that is, it is impossible to build a machine that will lift a weight any higher than it will be lifted by a reversible machine. Let us see why. Let us suppose that Y were higher than X. We take a one-unit weight and lower it one unit height with Machine B, and that lifts the three-unit weight up a distance Y. Then we could lower the weight from Y to X obtaining free power, and use the reversible Machine A, running backwards, to lower the three-unit weight a distance X and lift the one-unit weight by one unit height. This will put the one-unit weight back where it was before, and leave both machines ready to be used again! We would therefore have perpetual motion if Y were higher than X, which we assumed was impossible. With those assumptions, we thus deduce that Y is not higher than X so that of all machines that can be designed, the reversible machine is the best.

 

[willem2]

I have been reading Feyman Lectures Volume 1 and I am stuck on the example or proof given in the book about how perpetual motion is not possible:

http://www.feynmanlectures.caltech.edu/I_04.html
Section 4-2

Section 4-2 is quite a lot of text. Exactly what are you stuck on?

 

[Jazzyrohan]

Section 4-2 is quite a lot of text. Exactly what are you stuck on?

The example of the weightlifting machine to prove that no machine can have perpetual motion

 

[CWatters]

Which bit of that example. Please copy and paste the bit you don't understand.

 

[Merlin3189]

"Let us also make a hypothesis: that there is no such thing as perpetual motion with these weight-lifting machines."
This precedes the text you quote. Also your text contains, "We would therefore have perpetual motion if Y were higher than X, which we assumed was impossible."

The argument is not intended to prove the impossibility of perpetual motion.

 

[Jazzyrohan]

"Let us also make a hypothesis: that there is no such thing as perpetual motion with these weight-lifting machines."
This precedes the text you quote. Also your text contains, "We would therefore have perpetual motion if Y were higher than X, which we assumed was impossible."

The argument is not intended to prove the impossibility of perpetual motion.

I mistakenly asked the wrong question.I have updated it since.Please do take a look.

 

[Nugatory]

I mistakenly asked the wrong question.I have updated it since.Please do take a look.

So exactly where are you getting stuck?

 

[Jazzyrohan]

So exactly where are you getting stuck?

I am unable to understand the example itself,how the machines have been used.Can you provide a detailed explanation of things from the start?It would be a great help.

 

[CWatters]

Do you understand how a lever or pry bar works?

 

[Jazzyrohan]

In the preceding text , "if,when we have lifted and lowered a lot of weights and restored the machine to its original condition ,we find that the net result is to have lifted a weight,then we have a perpetual motion machine..."
From this we can derive that to analyse a machine,we must first return it to its original condition, right?

 

[CWatters]

In the preceding text , "if,when we have lifted and lowered a lot of weights and restored the machine to its original condition ,we find that the net result is to have lifted a weight,then we have a perpetual motion machine..."
From this we can derive that to analyse a machine,we must first return it to its original condition, right?

No. That just makes the net gain in energy more obvious. It makes it obvious that the energy needed to lift the weight hasn't come from some change to the machine - because that's back in exactly the condition it started in. If the machine doesn't return to the starting condition you have to check that any difference isn't the source of the energy that lift the extra weight.

It might be worth looking at the properties of conservative forces...

https://en.wikipedia.org/wiki/Conservative_force

.. if a particle travels in a closed loop, the net work done (the sum of the force acting along the path multiplied by the displacement) by a conservative force is zero.

In other words if a particle (subject to a conservative force) moves around a path and returns to it's exact starting point the net work done by the conservative force acting on it is zero. This is regardless of the path taken.

The most familiar conservative forces are gravity...

You will be familiar with the equation PE = mgh. Note that h doesn't depend on the path taken between two points, just the difference in height.

This suggests its futile trying to make a "gravity powered" perpetual motion machine because (no matter what complicated path its parts take) if it ever returns to the exact starting condition gravity will have done no work on it. Many attempts at such a machine rotate. So they may well appear to return to their starting position once per revolution.

 

[bob012345]

No. That just makes the net gain in energy more obvious. It makes it obvious that the energy needed to lift the weight hasn't come from some change to the machine - because that's back in exactly the condition it started in. If the machine doesn't return to the starting condition you have to check that any difference isn't the source of the energy that lift the extra weight.

It might be worth looking at the properties of conservative forces...

https://en.wikipedia.org/wiki/Conservative_force
In other words if a particle (subject to a conservative force) moves around a path and returns to it's exact starting point the net work done by the conservative force acting on it is zero. This is regardless of the path taken.
You will be familiar with the equation PE = mgh. Note that h doesn't depend on the path taken between two points, just the difference in height.

This suggests its futile trying to make a "gravity powered" perpetual motion machine because (no matter what complicated path its parts take) if it ever returns to the exact starting condition gravity will have done no work on it. Many attempts at such a machine rotate. So they may well appear to return to their starting position once per revolution.

Yes, being in perpetual motion itself isn't the issue as long as there are no losses or power generated. Newton's First Law states that.