Gravitational Potential Energy discussion

[physio]

I have attached a discussion by R.Feynman where he derives the formula for gravitational potential energy using pure reasoning. I don't quite follow the reasoning and I have read the discussion many times yet can't get a grasp of things he says. With the discussion I have my doubts in red.

Please help if anyone can understand and follow such reasoning...

 

[haruspex]

//I didn’t understand this paragraph! What weight is being lowered from
Y to X?

The three unit that was just raised to Y using machine A.

How do you run the Machine A backwards?

Forwards it lowers a one unit weight one unit distance and raises a three unit weight distance X. Backwards it raises a one unit weight one unit distance and lowers a three unit weight distance X. It is defined to be able to do this.

Which one unit weight is being lifted??

There is only one one unit weight and one three unit weight. Both machines operate on both.

What do you mean by “This will put the one-unit weight back where it was before, and leave both machines ready to be used again!”?

At the end of the sequence, both weights are back where they started, despite having extracted some energy when the three unit weight was lowered from Y to X (not using A or B).

why is it weight TIMES height?

He has shown that a one unit weight descending distance 1 can raise a 3-unit weight distance 1/3. The same reasoning shows it would lift n units distance 1/n. Clearly what's constant is weight * distance.

 

[physio]

thanks a lot haruspex for reading my attachment and helping me out. I yet have some doubts..

1) In your first answer you say that the three unit that was just raised to Y was machine A shouldn't it be machine B??

2) How do I visualize the machines? Are they see-saws??

3) How many sets of 1 unit weights and 3 unit weights are there?

4) What do you mean by "we could lower the weight from Y to X, obtaining free power"??

Thanks a lot!

 

[haruspex]

thanks a lot haruspex for reading my attachment and helping me out. I yet have some doubts..

1) In your first answer you say that the three unit that was just raised to Y was machine A shouldn't it be machine B??

Yes, sorry, B.

2) How do I visualize the machines? Are they see-saws??

I don't think Prof Feynman intended they be visualised; they're just abstract mechanisms capable of the functions stated. If it helps you to visualise them, feel free.

3) How many sets of 1 unit weights and 3 unit weights are there?

One of each only.

4) What do you mean by "we could lower the weight from Y to X, obtaining free power"??

B raised the 3-unit weight to Y; A, running backwards, lowers it from X; X is below Y. So to operate B forwards followed by A backwards the 3-unit weight has to be lowered from Y to X in between. This is where Feynman points out that step could be used to obtain free energy.
You might find it clearer to think about this scenario. Suppose you had lots of sets of 3-unit weights at X and one 1-unit weight at ground level. You could run the machines like this:
A backwards raises 1-unit weight up 3 units distance, lowers one 3-unit weight distance X.
B forwards lowers the 1-unit weight back to its starting point while raising the 3-unit weight A lowered up height Y.
Repeat for the other 3-unit weights.
At the end, you've raised all the 3-unit weights from X to Y, everything else being where it started.

 

[physio]

This is what I understood from your explanation given above...

1) We place a 1 unit weight on the rack of machine B and it lifts a 3 unit weight a distance Y.

2) We somehow lower the weight from Y to X of the 3 unit weight of machine B (How??), to obtain free energy.

3) We remove this 3 unit-weight (because we only have one 3-unit weight) and let the rack hang in air (since it is an abstract machine).

4) We place this 3 unit weight on Machine A (running backwards) and this will lift the one unit weight up a unit distance.

5) Thus, we have restored machine A to it's original condition but machine B has it's one rack hanging in mid air (at a distance X from it's starting position). The end result is that we have LIFTED a weight! (Perpetual motion).

Am I right? How does it prove Y should never be higher than X? What would it be like if we used both the machines that lifted the same distance X and lowered the 3 unit weight of machine B a little less than X (not fully) i.e n units less than X, won't we obtain the same line of reasoning as before?? How does the above case prove Y should never be higher than X?
Lastly how did he get energy=mgh from the above discussion.

Thanks again haruspex..!

 

[physio]

Also are the machines in cascade i.e. machine B first then machine A??

This explains the fact that when the 3 unit weight is lowered from Y to X then machine A connected to machine B can use the 3 unit weight to lower it by a distance X and lift the one unit weight up a distance of 1 unit. Thus, the lifted weight of Machine B can then in turn do something useful (free power) but yet I don't understand why should Y be greater than X? How does the description explain conservation of energy??

I am very close to understanding this. Please help!