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From: Mapsread on 2 Jul 2010 10:54
On Jul 2, 8:35 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
> "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> news:329ab76b-7fb4-4a1d-ac5d-b0ff93e90f1e(a)18g2000vbh.googlegroups.com...
> On Jul 2, 12:44 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
>
>
>
>
>
> > "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> >news:2e697573-962a-48f1-a8a0-2f7daef33c07(a)j4g2000yqh.googlegroups.com...
> > | Hello all,
> > |
> > | Suppose you have a metal cylinder that has a symmetrical hollow cavity
> > | in the middle. You don't know the material composing the cylinder and
> > | don't know it has a cavity. Supposing you had a fulcrum and a scale, I
> > | thought you could place the fulcrum just under one edge of the hollow
> > | cavity and place the far end on the scale and determine it was hollow..
> > | You wouldn't know the location of the cavity so you'd have to perform
> > | some trial and error, but I maintain the readings on the (very
> > | sensitive) scale would belie the hollow. At the very least, moving the
> > | fulcrum all along the cylinder and recording the forces on the scale
> > | would indicate something was wrong. My friend disagrees. (We both
> > | agree that when the fulcrum is all the way to either end or in the
> > | exact center, no information will be revealed.)
> > |
> > | Can anybody help us out?
> > |
> > | TIA
> > |
> > | P.S. By the way, we've both found other ways to reveal the hollow; the
> > | simplest being spinning. I tend to think the fulcrum and scale would
> > | work because of the exact same principles.
> > |
> >http://www.androcles01.pwp.blueyonder.co.uk/HollowCyl.jpg
> > Go on then, explain how you'd detect the cavity with fulcrum and scale
> > alone.
>
> Ha! That one defeats me. I was referring to a cavity that was shaped
> like a cylinder smaller than the metal cylinder as a whole.
> ==========================================
> In other words, a pipe with end caps, or a hollow coin. Go ahead,
> explain how to distinguish it from a solid rod with end caps using
> a fulcrum and scale alone.
>  http://www.pvcfittingsdirect.com/zoom_img/033.jpg
>  http://www.bolts-nuts-washers.com/images/tube_end_caps_short.jpg
> This is very easy to put together, y'know.
>
> How do you tell a boiled egg from a raw egg without cracking it?- Hide quoted text -
>
> - Show quoted text -

Well, actually, that's the question I was asking. I'm not certain of
the answer, hence I thought I would ask a friendly group of people who
enjoy thinking about puzzles like this. Am I to infer that you believe
it's impossible without spinning?
From: Androcles on 2 Jul 2010 11:28

"Mapsread" <cw_chw(a)yahoo.com> wrote in message
news:137ac3ac-c559-4685-a4eb-fa00a1856c3a(a)3g2000vbg.googlegroups.com...
On Jul 2, 8:35 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
> "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> news:329ab76b-7fb4-4a1d-ac5d-b0ff93e90f1e(a)18g2000vbh.googlegroups.com...
> On Jul 2, 12:44 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
>
>
>
>
>
> > "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> >news:2e697573-962a-48f1-a8a0-2f7daef33c07(a)j4g2000yqh.googlegroups.com...
> > | Hello all,
> > |
> > | Suppose you have a metal cylinder that has a symmetrical hollow cavity
> > | in the middle. You don't know the material composing the cylinder and
> > | don't know it has a cavity. Supposing you had a fulcrum and a scale, I
> > | thought you could place the fulcrum just under one edge of the hollow
> > | cavity and place the far end on the scale and determine it was hollow.
> > | You wouldn't know the location of the cavity so you'd have to perform
> > | some trial and error, but I maintain the readings on the (very
> > | sensitive) scale would belie the hollow. At the very least, moving the
> > | fulcrum all along the cylinder and recording the forces on the scale
> > | would indicate something was wrong. My friend disagrees. (We both
> > | agree that when the fulcrum is all the way to either end or in the
> > | exact center, no information will be revealed.)
> > |
> > | Can anybody help us out?
> > |
> > | TIA
> > |
> > | P.S. By the way, we've both found other ways to reveal the hollow; the
> > | simplest being spinning. I tend to think the fulcrum and scale would
> > | work because of the exact same principles.
> > |
> >http://www.androcles01.pwp.blueyonder.co.uk/HollowCyl.jpg
> > Go on then, explain how you'd detect the cavity with fulcrum and scale
> > alone.
>
> Ha! That one defeats me. I was referring to a cavity that was shaped
> like a cylinder smaller than the metal cylinder as a whole.
> ==========================================
> In other words, a pipe with end caps, or a hollow coin. Go ahead,
> explain how to distinguish it from a solid rod with end caps using
> a fulcrum and scale alone.
> http://www.pvcfittingsdirect.com/zoom_img/033.jpg
> http://www.bolts-nuts-washers.com/images/tube_end_caps_short.jpg
> This is very easy to put together, y'know.
>
> How do you tell a boiled egg from a raw egg without cracking it?- Hide
> quoted text -
>
> - Show quoted text -

Well, actually, that's the question I was asking. I'm not certain of
the answer, hence I thought I would ask a friendly group of people who
enjoy thinking about puzzles like this. Am I to infer that you believe
it's impossible without spinning?
================================
Not at all, you can spin an egg or you can candle it. Either will determine
if it is boiled.
Back to the cylinder...
You maintain the readings on the (very sensitive) scale
would belie the hollow.
Your friend does not agree, so it now your task demonstrate what you
hope to see to determine the existence or absence of the cavity.




From: rabid_fan on 2 Jul 2010 11:49
On Thu, 01 Jul 2010 19:49:46 -0700, Mapsread wrote:

>
> Suppose you have a metal cylinder that has a symmetrical hollow cavity
> in the middle. You don't know the material composing the cylinder and
> don't know it has a cavity.
>

The mass distribution of the cylinder will have a discontinuity
near either end. This mass discontinuity will be detectable using
a fulcrum and scale (if what I envision is the same scheme that
you are describing).
From: Mapsread on 2 Jul 2010 21:35
On Jul 2, 10:28 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
> "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> news:137ac3ac-c559-4685-a4eb-fa00a1856c3a(a)3g2000vbg.googlegroups.com...
> On Jul 2, 8:35 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
>
>
>
>
>
> > "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> >news:329ab76b-7fb4-4a1d-ac5d-b0ff93e90f1e(a)18g2000vbh.googlegroups.com...
> > On Jul 2, 12:44 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
>
> > > "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> > >news:2e697573-962a-48f1-a8a0-2f7daef33c07(a)j4g2000yqh.googlegroups.com....
> > > | Hello all,
> > > |
> > > | Suppose you have a metal cylinder that has a symmetrical hollow cavity
> > > | in the middle. You don't know the material composing the cylinder and
> > > | don't know it has a cavity. Supposing you had a fulcrum and a scale, I
> > > | thought you could place the fulcrum just under one edge of the hollow
> > > | cavity and place the far end on the scale and determine it was hollow.
> > > | You wouldn't know the location of the cavity so you'd have to perform
> > > | some trial and error, but I maintain the readings on the (very
> > > | sensitive) scale would belie the hollow. At the very least, moving the
> > > | fulcrum all along the cylinder and recording the forces on the scale
> > > | would indicate something was wrong. My friend disagrees. (We both
> > > | agree that when the fulcrum is all the way to either end or in the
> > > | exact center, no information will be revealed.)
> > > |
> > > | Can anybody help us out?
> > > |
> > > | TIA
> > > |
> > > | P.S. By the way, we've both found other ways to reveal the hollow; the
> > > | simplest being spinning. I tend to think the fulcrum and scale would
> > > | work because of the exact same principles.
> > > |
> > >http://www.androcles01.pwp.blueyonder.co.uk/HollowCyl.jpg
> > > Go on then, explain how you'd detect the cavity with fulcrum and scale
> > > alone.
>
> > Ha! That one defeats me. I was referring to a cavity that was shaped
> > like a cylinder smaller than the metal cylinder as a whole.
> > ==========================================
> > In other words, a pipe with end caps, or a hollow coin. Go ahead,
> > explain how to distinguish it from a solid rod with end caps using
> > a fulcrum and scale alone.
> >http://www.pvcfittingsdirect.com/zoom_img/033.jpg
> >http://www.bolts-nuts-washers.com/images/tube_end_caps_short.jpg
> > This is very easy to put together, y'know.
>
> > How do you tell a boiled egg from a raw egg without cracking it?- Hide
> > quoted text -
>
> > - Show quoted text -
>
> Well, actually, that's the question I was asking. I'm not certain of
> the answer, hence I thought I would ask a friendly group of people who
> enjoy thinking about puzzles like this. Am I to infer that you believe
> it's impossible without spinning?
> ================================
> Not at all, you can spin an egg or you can candle it. Either will determine
> if it is boiled.
> Back to the cylinder...
> You maintain the readings on the (very sensitive) scale
> would belie the hollow.
> Your friend does not agree, so it now your task demonstrate what you
> hope to see to determine the existence or absence of the cavity.- Hide quoted text -
>
> - Show quoted text -

Oh. Cool. I guess I would figure the total weight of the bar. Then I
would put the fulcrum somewhere along the length (say, 1/4) and treat
each end separately, determining the center of mass of each assuming
uniform density (which we'll find to be incorrect), and figure the
force on the scale based on the torque of both sides (which is in
equilibrium). I think the calculated force would differ from the
measured force.
From: Androcles on 2 Jul 2010 22:39

"Mapsread" <cw_chw(a)yahoo.com> wrote in message
news:2e734315-9a44-49ce-a0ab-48e2af038a84(a)z10g2000yqb.googlegroups.com...
On Jul 2, 10:28 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
> "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> news:137ac3ac-c559-4685-a4eb-fa00a1856c3a(a)3g2000vbg.googlegroups.com...
> On Jul 2, 8:35 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
>
>
>
>
>
> > "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> >news:329ab76b-7fb4-4a1d-ac5d-b0ff93e90f1e(a)18g2000vbh.googlegroups.com...
> > On Jul 2, 12:44 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
>
> > > "Mapsread" <cw_...(a)yahoo.com> wrote in message
>
> > >news:2e697573-962a-48f1-a8a0-2f7daef33c07(a)j4g2000yqh.googlegroups.com...
> > > | Hello all,
> > > |
> > > | Suppose you have a metal cylinder that has a symmetrical hollow
> > > cavity
> > > | in the middle. You don't know the material composing the cylinder
> > > and
> > > | don't know it has a cavity. Supposing you had a fulcrum and a scale,
> > > I
> > > | thought you could place the fulcrum just under one edge of the
> > > hollow
> > > | cavity and place the far end on the scale and determine it was
> > > hollow.
> > > | You wouldn't know the location of the cavity so you'd have to
> > > perform
> > > | some trial and error, but I maintain the readings on the (very
> > > | sensitive) scale would belie the hollow. At the very least, moving
> > > the
> > > | fulcrum all along the cylinder and recording the forces on the scale
> > > | would indicate something was wrong. My friend disagrees. (We both
> > > | agree that when the fulcrum is all the way to either end or in the
> > > | exact center, no information will be revealed.)
> > > |
> > > | Can anybody help us out?
> > > |
> > > | TIA
> > > |
> > > | P.S. By the way, we've both found other ways to reveal the hollow;
> > > the
> > > | simplest being spinning. I tend to think the fulcrum and scale would
> > > | work because of the exact same principles.
> > > |
> > >http://www.androcles01.pwp.blueyonder.co.uk/HollowCyl.jpg
> > > Go on then, explain how you'd detect the cavity with fulcrum and scale
> > > alone.
>
> > Ha! That one defeats me. I was referring to a cavity that was shaped
> > like a cylinder smaller than the metal cylinder as a whole.
> > ==========================================
> > In other words, a pipe with end caps, or a hollow coin. Go ahead,
> > explain how to distinguish it from a solid rod with end caps using
> > a fulcrum and scale alone.
> >http://www.pvcfittingsdirect.com/zoom_img/033.jpg
> >http://www.bolts-nuts-washers.com/images/tube_end_caps_short.jpg
> > This is very easy to put together, y'know.
>
> > How do you tell a boiled egg from a raw egg without cracking it?- Hide
> > quoted text -
>
> > - Show quoted text -
>
> Well, actually, that's the question I was asking. I'm not certain of
> the answer, hence I thought I would ask a friendly group of people who
> enjoy thinking about puzzles like this. Am I to infer that you believe
> it's impossible without spinning?
> ================================
> Not at all, you can spin an egg or you can candle it. Either will
> determine
> if it is boiled.
> Back to the cylinder...
> You maintain the readings on the (very sensitive) scale
> would belie the hollow.
> Your friend does not agree, so it now your task demonstrate what you
> hope to see to determine the existence or absence of the cavity.- Hide
> quoted text -
>
> - Show quoted text -

Oh. Cool. I guess I would figure the total weight of the bar. Then I
would put the fulcrum somewhere along the length (say, 1/4) and treat
each end separately, determining the center of mass of each assuming
uniform density (which we'll find to be incorrect), and figure the
force on the scale based on the torque of both sides (which is in
equilibrium). I think the calculated force would differ from the
measured force.
==========================================
You think the calculated force would differ from the measured
force. Your friend does not agree.

The total weight of the bar is 10 lbs.
With the fulcrum at one end and the scale in the middle the scale reads
10 lbs, the bar is balanced on the scale.

========s========
/\ <fulcrum |

With the scale at one end and the fulcrum in the middle the scale
reads 0 lbs, the bar is balanced on the fulcrum.

s=======0========
|................/\ <---fulcrum

With the scale at one end and the fulcrum at the other the scale
reads 5 lbs, the load is shared.

0===============s
/\ <---fulcrum...............|

With the scale at one end and the fulcrum at 1/4 the scale
reads (how many?) lbs, the load is partly shared.

====0===========s
........./\ <---fulcrum.......|

So it now your task demonstrate what you hope to see to
determine the existence or absence of the cavity.

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