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Topic: Hole in a disc! (Read 743 times) |
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Rejeev
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Hole in a disc!
« on: Oct 4th, 2004, 6:31am » |
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A metallic disc with a hole at the centre of it. if you heat up the disc, whether the hole will enlarge or contract?
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towr
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Re: Hole in a disc!
« Reply #1 on: Oct 4th, 2004, 11:24pm » |
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::That depends on wether the disc as a whole contracts or expands..
Typically both will expand::
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Rejeev
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Re: Hole in a disc!
« Reply #2 on: Oct 5th, 2004, 2:10am » |
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one clarification:- whole disc expands on heating up. (is there any metal which contracts on heating?)
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towr
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Re: Hole in a disc!
« Reply #3 on: Oct 5th, 2004, 4:36am » |
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I believe there are alloys that don't do either, up to a point.
And of course you can make a memory alloy disc that changes to almost whatever shape you want the moment you heat it up..
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Barukh
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Re: Hole in a disc!
« Reply #4 on: Oct 6th, 2004, 7:15am » |
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So, is there a consensus that the hole will expand? Has anybody got a satisfactory explanation why it happens?
Rejeev, I like this puzzle! 
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Grimbal
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Re: Hole in a disc!
« Reply #5 on: Oct 6th, 2004, 8:24am » |
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I believe the whole disk will grow uniformly with heat. Including the hole.
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Barukh
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Re: Hole in a disc!
« Reply #6 on: Oct 6th, 2004, 10:14am » |
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on Oct 6th, 2004, 8:24am, Grimbal wrote:| I believe the whole disk will grow uniformly with heat. Including the hole. |
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Yes, this seems to be case. But is it intuitive for you? Compare it with heating of rectangular strip of metal, which will grow in all directions!
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Grimbal
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Re: Hole in a disc!
« Reply #7 on: Oct 6th, 2004, 10:24am » |
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To me, yes. I first thought of the correct solution and then only I saw the reasoning that would indicate the opposite, like if the disk got a layer added on the surface or getting inflated. But now that I think of it, a long time ago, I saw the trick of unblocking a nut from a rusty screw by heating it with a blowtorch. It helps intuition...
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towr
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Re: Hole in a disc!
« Reply #8 on: Oct 6th, 2004, 10:28am » |
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Consider what should happen if you take a disc without a hole, and likewise when you take the disc with the hole, and fill said hole with a smaller disc of appropriate size.
If the hole would shrink, then the smaller disc would be buckle, but then the same should happen in the whole disc, the middle should buckle. But it uniformly expands, and so the hole should as well.
Every point of the disc (with or without hole) moves from the center when heated.
It's also no different when you take a rectangular strip with a rectagular hole in it..
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| « Last Edit: Oct 6th, 2004, 10:31am by towr » |
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Aryabhatta
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Re: Hole in a disc!
« Reply #9 on: Oct 6th, 2004, 11:26am » |
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on Oct 6th, 2004, 10:28am, towr wrote:Consider what should happen if you take a disc without a hole, and likewise when you take the disc with the hole, and fill said hole with a smaller disc of appropriate size.
If the hole would shrink, then the smaller disc would be buckle, but then the same should happen in the whole disc, the middle should buckle. But it uniformly expands, and so the hole should as well.
Every point of the disc (with or without hole) moves from the center when heated.
It's also no different when you take a rectangular strip with a rectagular hole in it.. |
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I am not convinced by this argument. In the case with smaller disc, can't the smaller disc be expanding to counteract the inward expansion of the outer disc? And expand enough to actually make the inner circle of the outer disc move away from the center?
Suppose we had a metallic disc but this time alternate sectors of it are non conducting/expanding. Now we remove a smaller disc and heat the disc with the hole uniformly. What will happen?
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Rejeev
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Re: Hole in a disc!
« Reply #10 on: Oct 6th, 2004, 9:04pm » |
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on Oct 6th, 2004, 10:28am, towr wrote:Consider what should happen if you take a disc without a hole, and likewise when you take the disc with the hole, and fill said hole with a smaller disc of appropriate size.
If the hole would shrink, then the smaller disc would be buckle, but then the same should happen in the whole disc, the middle should buckle. But it uniformly expands, and so the hole should as well.
Every point of the disc (with or without hole) moves from the center when heated.
It's also no different when you take a rectangular strip with a rectagular hole in it.. |
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Correct. Looking it from another angle, thermal expansion is something like "looking through a magnifying lense"; everything will be bigger - hole, scratch, any shape engraved, everything. yet in another view:- it is something like a three dimetional diagram redrawn in larger scale.
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SWF
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Re: Hole in a disc!
« Reply #11 on: Oct 6th, 2004, 9:28pm » |
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There are some unusual conditions in which the hole could get smaller:
It is not heated uniformly. For example, if heat is applied to the inside of the hole, the hole will initially get smaller because the cooler metal further from the hole restrains the expansion of the hot inner layer.
The metal is in a condition such that heating causes a decrease in volume. This can occur in some metals due to phase changes, such a precipitation or solutioning of various compounds in the alloy. The phase change occurs over a limited temperature range, but some materials, like I think a tungsten, oxygen, zirconium compound, have negative coefficient of thermal expansion without a phase change.
Graphite fibers often have negative thermal expansion in one direction. A low strength metal (such as aluminum) made into a disk with fibers going in the circumference direction would under many condtions have a shrinking hole when heated.
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Kozo Morimoto
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Re: Hole in a disc!
« Reply #12 on: Oct 7th, 2004, 1:58am » |
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But if you get some dough and make a ring and deep fry it, you end up with a smaller hole - you also end up with a doughnut . But if you get some dough and make a flat disc and deep fry it, the center doesn't buckle - you end up with a deep fried pancake.
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towr
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Re: Hole in a disc!
« Reply #13 on: Oct 7th, 2004, 2:39am » |
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Which just goes to show dough [ne] metal 
Dough is much more plastic, and also becomes rounder when cooked/fried (unlike metal objects), it inflates rather than simply expands.
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John_Gaughan
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Re: Hole in a disc!
« Reply #14 on: Oct 7th, 2004, 6:07am » |
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on Oct 7th, 2004, 2:39am, towr wrote:Which just goes to show dough [ne] metal
Dough is much more plastic, and also becomes rounder when cooked/fried (unlike metal objects), it inflates rather than simply expands. |
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Thankfully, dough is not metal. Otherwise, elephant ears would come from mechanical elephants 
This just goes to show that different substances have vastly different properties. Metal expands when heated, dough inflates when deep fried (and tastes good with powdered sugar sprinkled on top), and plastic melts into a puddle. The last one was proved by a little boy named John, his mother's microwave, and one of his toys 
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Icarus
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Re: Hole in a disc!
« Reply #15 on: Oct 7th, 2004, 8:58pm » |
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Another way of seeing that the hole gets larger: look at it's circumference. The atoms on the circumference of the hole move farther apart when heated, just as do the atoms in the rest of the strip. So the circumference of the hole must increase in size proportionately. But C = [pi] d ...
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Hotmale.com
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Rubber is the only material that contracts when heated.
As far as the hole through metal goes (circular or otherwise), think of it as a bunch of people holding hands in a circle. When they expand by pushing away from each other, the circle gets larger.
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towr
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Re: Hole in a disc!
« Reply #17 on: Nov 24th, 2005, 7:49am » |
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on Nov 24th, 2005, 7:33am, Hotmale.com wrote:| Rubber is the only material that contracts when heated. |
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Not so. in a certain range water contract when heated
And also, rubber has a positive linear expansion coefficient (meaning it doesn't contract, but expands when heated).
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