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MacGyver Inner circle St. Louis, MO 1419 Posts |
ARGH I lost a 2 page reply twice now because of the darn attachment requirements...> I made it 14k but The dark pixel's must have been off...
Oh well I'm late for a meeting I will reply later with why your wrong Ok. Hopefully this post won't get deleted for some unforseen reason, but just in case I'm saving every paragraph to file Anyway, to the point: Mikey: Yes I read that link, and it is fine and dandy for what they are considering. Which is a 2 dimensional object existing in a 2dimensional world where the only bit of physics that affects it is the law of Thermal Expansion. It is not a real world example, it isn't even 3d. I am not overcomplicating anything, it is the mathematics that is oversimplyfying physics. Another thing, I don't think we are thinking of the same object as mine only has 1 ring through each center and has multiple circles, see the attached image: Ok anyway, my point is that in a 3d world there are forces that act on objects, and these forces must be taken into account before you can go explaining something this complex. The reason that my way is right and the "uniform expansion" is wrong for a 3d real world object is a difficult answer, but I'll try to start from the basics: Expansion occurs outward from the individual objects center. Basically the space between each molecule of the object gets bigger and bigger, causing the whole object to increase in size. Imagine two cubes floating in space 1 foot apart. Now when heated they are each going to expand so that each face is 1 foot farther away from the center of the cube than before. Now what happens when you heat these cubes? First off they start expanding from their centers of gravity, so that the space between them(the hole) shrinks, while the outer edges move farther away so the total width increases. The Center of mass stays stationary because of inertia. But halfway through the cubes touch, and then there is a "virtual" center of mass in the center of where they touch, Now the cubes still are expanding from the center of their gravity, but their centers are moving away from eachother and away from this "virtual" center of mass. To the outside observer it looks as if the cubes are growing away from the virtual CoM(center of mass). But what happens when they shrink? Because the objects aren't connected, each cube will shrink back down on its individual CoM, causing a gap to occur. Now imagine the circles in my picture are the cubes and the donut is the rectagular formed when they join. each circle has no idea where the "hole" is, it only learns that information from the forces that act upon it by the other pieces of the puzzle. Now the reason that a donut would shrink or grow is due to the fact that each circle that makes up the object is connected, so that both compressive and expansive force acts upon them. But if you were to slice the donut either at rest or when expanded, you are able to isolate the expanding and shrinking phases. If the "uniform expansion" theory were really correct, then a donut sliced when expanded should shrink back towards the center. But it doesn't, because there is not attractive force on each circle, so it finds it's own center of mass and the whole circle shrinks back upon itself, causing gaps in the donut. Similarily, if you slice a donut into circles when its at a rest state, you will see it will expand just like normal because the compressive force is acting on each circle, but again it will stay gapped when cooled. the only reason a real donut doesn't stay gapped is because the infinite amount of circles making up the donut are connected, so they exert force on eachother making them shrink together. so while the "uniform expansion" rules do find the same result, it is not because they are right, but because they oversimplify the problem. In truth, it is the compressive and expansive forces acting upong each circle that makes up a donut shrink or grow. Each circle by itself will expand from its own center, causing the hole to shrink, but the compressive forces make the center of the expanding circle move outward away from the hole, and therefore it is due to physics and force, NOT uniform expansion that make this puzzle work. That would be like saying there is a 9.8m/s2 downward force acting everywhere on the whole universe, just because it happens on earth, which it turns out is round.... Try doing this with a super soft compressible material with "uniform expansion". The hole will shrink because the compressive force won't cause the ring to expand, it will cause the inside of the donut to compress, because it is easier for the force to buckle the insides than force it to grow. whew.... I hope this post doesn't get deleted again. |
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landmark Inner circle within a triangle 5194 Posts |
<<Try doing this with a super soft compressible material with "uniform expansion">>
Like, say, sponge balls? Jack Shalom
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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dlhoyt Regular user 176 Posts |
Maybe MacGyver can explain why, in machining, a metal ring (a torus) is heated to fit onto a rod and, upon cooling, it becomes impossible to remove. Also, as someone previously mentioned, when a metal jar lid is on too tight you can loosen it by running hot water over the lid. The metal expands and the lid can be unscrewed.
It seems clear to me that the hole expands. |
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MacGyver Inner circle St. Louis, MO 1419 Posts |
Dlhoyt, please read my post, which both did explain why those things happen.
My post were not about whether the ring expands or contracts, but WHY it expands or contracts. |
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cheesewrestler Inner circle Chicago 1157 Posts |
A "torus", from what I can find on the 'net, is hollow ... would a hollow donut react to heating differently than a solid copper donut?
I would think that in "real world" terms, heating a hollow copper donut would result in (unpredictable?) deformation, rather than even expansion or contraction ... ? |
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MacGyver Inner circle St. Louis, MO 1419 Posts |
Everything is predictable, if you can overcome the difficulties in observing quantom mechanics without disturbing them(impossible as of yet but I'm sure that the solution will present itself in the future, we just won't use light or EM waves to observe things).
Anyway, a 3d hollow donut would definatly deform different than a solid one. Depending on the solid part, such a torus would definatly have a shrinking hole, since the gas(or whatever) was filling it would expand faster than the metal.... intresting though. |
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penguinbloke New user 3 Posts |
The donut hole would not shrink as it is exerting an equal force on itself. Should the heat continue to rise however one of two things would happen
A. the metal would deform away from the centre probably cacking the donut. B: depending on the width of the donut it might melt first |
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