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Topic: A Heated Debate. (Read 1058 times) |
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rloginunix
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A Heated Debate.
« on: Jun 30th, 2014, 8:43am » |
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A Heated Debate.
A solid thin steel ring with inner and outer radii r and R is heated gradually:
How would r and R behave?
Why?
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Grimbal
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Re: A Heated Debate.
« Reply #1 on: Jun 30th, 2014, 9:32am » |
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Assuming the steel is heated uniformly, then both r and R increase in equal proportions.
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towr
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Re: A Heated Debate.
« Reply #2 on: Jun 30th, 2014, 10:17am » |
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What he said.
One way to look at it: the average volume taken up by an atom -or the average distance between atoms, if you prefer- increases as it heats up. So all points move apart in the same proportion, the disc simply scales.
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rloginunix
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Re: A Heated Debate.
« Reply #3 on: Jun 30th, 2014, 12:04pm » |
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Grimbal correctly identified the what. And, yes, of course the heating is uniform.
towr gave one explanation of the why.
1). Everyone seems to get R correctly. But some people think that r will decrease.
The high school physics justification of the opposite that I still remember was in principle touched by rmsgrey in the "Balls of Steel" discussion. This line of reasoning uses the method of contradiction ...
2). Can anyone think of a technical application of this phenomenon?
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dudiobugtron
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Re: A Heated Debate.
« Reply #4 on: Jun 30th, 2014, 5:22pm » |
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on Jun 30th, 2014, 12:04pm, rloginunix wrote:| 2). Can anyone think of a technical application of this phenomenon? |
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One application would be: to allow you to put the ring in place easily when hot, then have it contract and form a strong connection once cooled.
Another would be as a one-off thermostat; place the ring tightly around something which doesn't expand, it will then fall off once the heat rises to a set point.
Also note that perhaps the most important 'application' of this phenomenon is: the fact that you can construct something out of the same material as the ring, join it together with the ring, and have them not come apart even when heated. If such constructions (eg, bicycles) didn't behave like this, they would fall apart or jam up depending on the temperature.
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rloginunix
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Re: A Heated Debate.
« Reply #5 on: Jul 1st, 2014, 12:02pm » |
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My teacher's why r increases was based on a contradiction between the assumption and the observable reality. Not exactly the Trichotomy Law but r can only decrease, stay the same or increase. Assume it decreases or stays the same - continued heating, while R increases, will create enough internal tension as to ruin the structural integrity of the ring, not necessarily visible to the naked eye. But, since the experiment is easy enough to conduct, this is not observed.
My line of reasoning was the inserted disc idea. Its external radius, which grows, will be equal to r ...
One could also use the Division approach - divide the ring into infinitesimally thin sub rings, cut them with the lines through the center of the ring, each resulting elementary piece will be a trapezoid type shape, etc.
I'd add one more application from the horse and buggy (horse and carriage) era.
Would anyone care to take a guess?
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dudiobugtron
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Re: A Heated Debate.
« Reply #6 on: Jul 1st, 2014, 2:38pm » |
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on Jul 1st, 2014, 12:02pm, rloginunix wrote:I'd add one more application from the horse and buggy (horse and carriage) era.
Would anyone care to take a guess? |
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Is it making wagon wheels? I.e.; heating up the outside metal 'tire', then fitting it around the wooden wheel, and cooling it so it would contract into the groove.
It could also have something to do with horseshoes.
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rloginunix
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Re: A Heated Debate.
« Reply #7 on: Jul 5th, 2014, 6:46pm » |
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Yes, dudiobugtron, good observation - the carriage wheel manufacturing process of the past was my sample application.
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dudiobugtron
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Re: A Heated Debate.
« Reply #9 on: Jul 7th, 2014, 2:30pm » |
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on Jul 7th, 2014, 2:23pm, EdwardSmith wrote:| R and r will expand at the same rate |
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Proportionally, yes. But not the same absolute rate. The ratio R:r would remain constant.
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Annettagiles
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Re: A Heated Debate.
« Reply #10 on: Sep 24th, 2014, 2:03am » |
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By heating the r will gets increase in terms of size.
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