[ExI] Thermal expansion - Ball and ring experiment

[spike]

> Yep, that's my contention also. My problem is, how to prove this to
> someone who doesn't believe me, short of actually doing the
> experiment?
> 
> Emlyn


Because of my outbox stalled for a day and a half, all my posts in that
interval went out just half an hour ago, putting me over the voluntary 5
posts a day limit, but I will answer this one if you indulge me.

The intuitive proof would come from the intermediate value theorem.  For a
thought experiment, let's imagine a ring that is heated to temperature T
expands 1 percent from its ambient temperature size.  The inside of the hot
ring has a diameter about 1% larger, ja?  

Imagine the ring with a thin cut.  The cut can be thought of as a gap with
zero length, or a C with zero gap.  As the ring is heated to T, the gap is
still zero.

Now imagine the ring cut in half.  The gap increases 1 percent when heated
to T.  If the gap is pi radians, the gap increases 1%.  If zero pi, then 0%.
I would argue that if the gap is half pi, then the size of the gap increases
about half a percent.  A tenth pi, then about a tenth of a percent.  

The actual function probably isn't linear, but close enough to illustrate
that the gap grows as heat expands the C.

spike




> -----Original Message-----
> From: extropy-chat-bounces at lists.extropy.org [mailto:extropy-chat-
> bounces at lists.extropy.org] On Behalf Of Emlyn
> Sent: Tuesday, June 12, 2007 6:54 PM
> To: ExI chat list
> Subject: Re: [ExI] Thermal expansion - Ball and ring experiment
> 
> Yep, that's my contention also. My problem is, how to prove this to
> someone who doesn't believe me, short of actually doing the
> experiment?
> 
> Emlyn
> 
> On 13/06/07, spike <spike66 at comcast.net> wrote:
> > The gap gets larger.  Imagine the arc piece that is missing from the
> ring to
> > form a C.  That piece of nothing expands the same way the piece of
> something
> > would have expanded were it present.  So the gap gets larger as the C is
> > heated.
> >
> > spike
> >
> >
> >
> > > -----Original Message-----
> > > From: extropy-chat-bounces at lists.extropy.org [mailto:extropy-chat-
> > > bounces at lists.extropy.org] On Behalf Of Emlyn
> > > Sent: Tuesday, June 12, 2007 5:42 AM
> > > To: ExI chat list
> > > Subject: [ExI] Thermal expansion - Ball and ring experiment
> > >
> > > I was just in a "heated" discussion with a friend about a twist on the
> > > classic ball and ring experiment:
> > >
> > >
> http://www.physics.usyd.edu.au/super/therm/tpteacher/demos/ballring.html
> > >
> > > When the ring is heated, it expands, and so the hole gets larger, and
> > > you can pass the ball through the ring, even though the ball doesn't
> > > fit through the ring when the ring is at room temperature.
> > >
> > > The point of contention was this: What if there was a gap in the ring
> > > (so it is now a letter "C" shape). Will the gap in the "C" close or
> > > open further on heating?
> > >
> > > My contention is that the gap will get larger, only in that the entire
> > > C shape scales up as it is heated.
> > >
> > > My friend's contention is that the gap will become smaller, (because
> > > the metal expands into the gap).
> > >
> > > I can't find anything online even close to settling this score. We
> > > tried some experiments with wire rings and the gas stove top playing
> > > the role of bunsen burner (amazingly no one ended up branded for
> > > life), but it was inconclusive.
> > >
> > > Any pointers to anything that can settle this argument?
> > >
> > > Emlyn
> > > _______________________________________________
> > > extropy-chat mailing list
> > > extropy-chat at lists.extropy.org
> > > http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
> >
> >
> > _______________________________________________
> > extropy-chat mailing list
> > extropy-chat at lists.extropy.org
> > http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
> >
> _______________________________________________
> extropy-chat mailing list
> extropy-chat at lists.extropy.org
> http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat