Shoutbox

quote:

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Originally posted by Volv
I've got a practical experiment for you to try out.

1) Put a long (30cm for example) thin chain (the smaller the links the better) on a very steep ramp which it can slide down easily and watch it slide down.
2) Repeat, this time placing 5mm of the chain over the top of the ramp, observe and record results.
3) Repeat with 1cm over the top of the ramp.

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That practice example is not the same as the system above (if you always keep the same angle of the ramps)! Both the ends of the chain must be at the same horizontal plane, see picture from SonicSam.

Which means that in your step 2 the long ramp would be almost flat.
In your step 3, the long ramp would be slightly steeper than in step 2. Etc...

Doing that, at any time, the chain will not move at all.

Similar: in your step 1: the long ramp would be completely flat. Again the chain will (in this case obviously) not move. See my previous post where I explained the limits of the system.

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EDIT: a pic to make my ramblings a bit more clear (also for myself )... can't sleep anyways... note: I suck at drawing a sloped chain with just a laptop mousepad...



The first three are very obvious (limit) cases of SonicSam's picture. In those three cases it is very obvious that there is no movement:

1) Extreme limit case, planes are both flat.
2) 'Center' case, both planes are of equal length and thus equally steep
3) Other extreme limit case, planes are both at 90°
4) SonicSam's picture.

The green line is what I talked about in this post:
You simply hang a second chain of the same type as the one you had on both the ends. This does _not_ change anything in the system since the chain would pull equally hard on both sides; aka the two opposite forces (one on the left end, the other on the right end) cancel eachother out. But, it is now a lot easier to see in pic4 why there wouldn't be a movement, not even in a frictionless environment; it's just a closed chain hanging on a irregular object; it is never going to move out of itself.

Or to put it in another way: say that it does move counterclockwise by some freak thing in nature. That would mean that part of the green part of the chain is now on the right slope and part of the red left-sloped chain is now hanging from the left slope below it. In that case there hasn't actually been any change in mass or whatever in any point of the system; we would still have the same amount of chain hanging below and the same amount of chain hanging over the triangle. So why would it have moved the first time if there wasn't any change to begin with? It wouldn't.

Or, by definition and in the opposite way: if it did move by that freak thing in nature, it would keep on moving because after the initial move the system is again exactly the same as before the move. Aka if it moved a first time, it should also move a second time, and a third time, etc, untill infinity. (= what I meant to say to toddy here).