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        riddles >> easy >> Hole in a disc!
        
(Message started by: Rejeev on Oct 4th, 2004, 6:31am)
Title: Hole in a disc!
Post by Rejeev on Oct 4th, 2004, 6:31am
A metallic disc with a hole at the centre of it. if you heat up the disc, whether the hole will enlarge or contract?
Title: Re: Hole in a disc!
Post by towr on Oct 4th, 2004, 11:24pm
::[hide]That depends on wether the disc as a whole contracts or expands..
Typically both will expand[/hide]::
Title: Re: Hole in a disc!
Post by Rejeev on Oct 5th, 2004, 2:10am
one clarification:- whole disc expands on heating up. (is there any metal which contracts on heating?)
Title: Re: Hole in a disc!
Post by towr on Oct 5th, 2004, 4:36am
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..
Title: Re: Hole in a disc!
Post by Barukh on Oct 6th, 2004, 7:15am
So, is there a consensus that [hide]the hole will expand[/hide]? Has anybody got a satisfactory explanation why it happens?

Rejeev, I like this puzzle!  :D
Title: Re: Hole in a disc!
Post by Grimbal on Oct 6th, 2004, 8:24am
I believe the whole disk will grow uniformly with heat.  Including the hole.
Title: Re: Hole in a disc!
Post by Barukh on Oct 6th, 2004, 10:14am

on 10/06/04 at 08:24:47, Grimbal wrote:
I believe the whole disk will grow uniformly with heat.  Including the hole.

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!
Title: Re: Hole in a disc!
Post by Grimbal on Oct 6th, 2004, 10:24am
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...
Title: Re: Hole in a disc!
Post by towr on Oct 6th, 2004, 10:28am
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..
Title: Re: Hole in a disc!
Post by Aryabhatta on Oct 6th, 2004, 11:26am

on 10/06/04 at 10:28:53, 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..


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?
Title: Re: Hole in a disc!
Post by Rejeev on Oct 6th, 2004, 9:04pm

on 10/06/04 at 10:28:53, 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..

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.
Title: Re: Hole in a disc!
Post by SWF on Oct 6th, 2004, 9:28pm
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.
Title: Re: Hole in a disc!
Post by Kozo Morimoto on Oct 7th, 2004, 1:58am
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.
Title: Re: Hole in a disc!
Post by towr on Oct 7th, 2004, 2:39am
Which just goes to show dough [ne] metal :P
Dough is much more plastic, and also becomes rounder when cooked/fried (unlike metal objects), it inflates rather than simply expands.
Title: Re: Hole in a disc!
Post by John_Gaughan on Oct 7th, 2004, 6:07am

on 10/07/04 at 02:39:19, towr wrote:
Which just goes to show dough [ne] metal :P
Dough is much more plastic, and also becomes rounder when cooked/fried (unlike metal objects), it inflates rather than simply expands.

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 ::)
Title: Re: Hole in a disc!
Post by Icarus on Oct 7th, 2004, 8:58pm
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 ...
Title: Re: Hole in a disc!
Post by Hotmale.com on Nov 24th, 2005, 7:33am
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.
Title: Re: Hole in a disc!
Post by towr on Nov 24th, 2005, 7:49am

on 11/24/05 at 07:33:41, Hotmale.com wrote:
Rubber is the only material that contracts when heated.
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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