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kucharek
2002-Aug-27, 10:25 AM
My four year old son asked me this yesterday and, of course, I know the scientific answer - if a mountain gets too high (and the corner of a cube is something like a mountain), it get's too heavy to be supported by the ground and it sinks in and so on.
But is there some nice story or experiment which would make the subject clear for a four-year-old? I think this is pretty difficult as even the concept of a spherical Earth without people dropping off it in Australia is a difficult concept...as long
as you don't live in Oz... /phpBB/images/smiles/icon_smile.gif

Harald

nebularain
2002-Aug-27, 11:27 AM
Ever see a guy make a hand-tossed pizza crust? It doesn't matter what shape the dough was formed into as it was flattened out; when the crust is tossed and spun in the air, the shape becomes circular. I know this is an example of how it works on the 2-D scale, but the same principle can apply to a 3-D scale.

traztx
2002-Aug-27, 11:58 AM
On 2002-08-27 06:25, kucharek wrote:
My four year old son asked me this yesterday and...

That's a common question by children who had been abducted by The Borg. You should check for hidden mech implants.

kucharek
2002-Aug-27, 12:44 PM
That's a common question by children who had been abducted by The Borg. You should check for hidden mech implants.

I'd expected such a kind of remark, but not that soon... /phpBB/images/smiles/icon_biggrin.gif

Harald

kucharek
2002-Aug-27, 12:50 PM
On 2002-08-27 07:27, nebularain wrote:
Ever see a guy make a hand-tossed pizza crust? It doesn't matter what shape the dough was formed into as it was flattened out; when the crust is tossed and spun in the air, the shape becomes circular.

Question: Why does it become circular? From bare physics of centrifugal forces (please apologize this phrase) I'd expect that when some irregularity is more distant from the center of rotation and as the pizza rotates with CAV (constant angular velocity), there would be more pull on this irregularity and this would make the irregularity even larger! I mean, cohesion is pretty different from gravity.
Any PP's (Pizza-Physicists) here?

Harald

GrapesOfWrath
2002-Aug-27, 01:55 PM
On 2002-08-27 06:25, kucharek wrote:
But is there some nice story or experiment which would make the subject clear for a four-year-old?

Why don't you just wait until they are fourteen, and then they'll tell you? /phpBB/images/smiles/icon_smile.gif

The corner of a cube is exactly like a mountain. If you had a cube-world, and poured a large glass of water onto it, the surface of the water would be basically spherical (the equipotential surface--as it is on the Earth) with the corners sticking out. They'd get worn down by erosion and mass-wasting (landslides and earthquakes, for example) and subsidence.

On the Earth, such wearing-down is reversed by mountain building processes like plate tectonics and volcanoes.

TinFoilHat
2002-Aug-27, 01:59 PM
On a large scale (like the size of a planet) the rock that the earth is made from will behave more like a liquid than a solid. In fact, the earth really is mostly liquid rock with only a thin crust of solid rock coverint it. Just as water seeks the lowest level, the liquid-like material that makes up the earth will flow into the shape where the mass is as close to the center of gravity as possible. That shape is a sphere. The crust is just rigid enough to support mountains a handful of miles high.

Any large object has to be spherical shaped, because beyond a certain point the force of gravity is enough to overcome the rigidity of the material holding it together.

Silas
2002-Aug-27, 03:07 PM
Philosophically, it goes all the way back to Aristotle. He reasoned that heavy things (e.g. soil, rocks, etc.) "want" to move downward, they would do so until they arrived in a configuration where they couldn't move downward any more. He knew, from geometry, that a sphere is the shape that is most compact -- all of the parts of a sphere are as close to the center as can possibly be, and no other shape has that property -- and so he reasoned that the earth must be a sphere.

Having two other visible examples in the sky probably helped...

Silas

Bozola
2002-Aug-27, 03:19 PM
Hmmm...a four year old...what would catch their attention?

Perhaps you could attempt to build a structure out of jello. A tad messy, but it certainly would get a child's undivided attention (sets a bad precedent for playing with their food...not that I ever did anything like that../phpBB/images/smiles/icon_wink.gif...)

traztx
2002-Aug-27, 03:21 PM
There might be some other shapes of planets out there somewhere. Could the right amount of rotation create a donut-shaped planet? Or maybe a pizza-shaped one?

GrapesOfWrath
2002-Aug-27, 03:25 PM
On 2002-08-27 09:59, TinFoilHat wrote:
The crust is just rigid enough to support mountains a handful of miles high.

Not even that rigid, probably. The principle of isostasy is at play: mountains are compensated at depth--in other words, they are floating like icebergs. But the mantle is not a liquid--just as the ice of a glacier is not a liquid.

Silas
2002-Aug-27, 05:24 PM
On 2002-08-27 11:21, traztx wrote:
There might be some other shapes of planets out there somewhere. Could the right amount of rotation create a donut-shaped planet? Or maybe a pizza-shaped one?

Rotation can (does!) cause spheres to flatten, rather as if you took a basketball and sat on it... (Obligatory obesity joke here...)

Rotation could cause a sphere to elongate, sort of like a football...but MacLaurin proved that this form is not stably stable. (i.e., it is stable...but any disturbance will cause it to become more spherical.)

I don't believe that doughnut-shaped planets are stable at all. In practical terms, there isn't any material strong enough to maintain the stresses, and in mathematical terms, I don't think that the shape itself is gravitationally stable.

Silas

Paul Unwin
2002-Aug-27, 06:03 PM
On 2002-08-27 13:24, Silas wrote:
Rotation can (does!) cause spheres to flatten, rather as if you took a basketball and sat on it... (Obligatory obesity joke here...)

I'm betting Silas (or someone with the same name) has read this book, but I recommend "A Matter of Gravity," by Hal Clement, to everyone. It explores the strange environment of the planet Mesklin, a huge rocky world with such a high rate of rotation that it is quite oblate (like, say, a tab of mescaline?). Due to centrifugal force and the increased distance from the center of the planet, the effective gravity at the equator is "only" three Earth gravities, compared to three hundred at the poles. The Mesklinites who inhabit the poles have, rather understandably, a congenital and pathological fear of heights.

_________________
The space environment is not a pleasant one; it's more like a burning and freezing, radioactive, corrosive shooting gallery with no air. - Bradley Edwards

<font size=-1>[ This Message was edited by: Paul Unwin on 2002-08-27 14:03 ]</font>

<font size=-1>[ This Message was edited by: Paul Unwin on 2002-08-27 14:04 ]</font>

Wally
2002-Aug-27, 07:03 PM
As Silas already eluded to, a sphere presents the smallest surface area for a given amount of material. Therefore, it's the shape that's most stable given the inward force of gravity on planets and stars. That's the simplistic answer that finally satisfied my quest for knowledge!

David Hall
2002-Aug-27, 07:37 PM
Think about it this way. Every point on the surface wants to get as close to the center as possible. But there's an unchangable volume to the mass, so if one point moves closer to the center another point would have to be pushed farther away. This creates a "push-of-war" that continues until all points are are at the same distance from the center and balanced with each other.

Perhaps you could try to demonstrate it with a water baloon.

Russ
2002-Aug-27, 08:02 PM
With regard to the Pizza, if you watch one being made, you'll note that they spend a fair amount of time beating the dough into a sphere. They then smash it ruoghly flat and then start the spenning. The pounding into a sphere is to distribute the material uniformly through the mass. Thus, spinning it will form a uniform disk.

How to explain the spherical planets to a four year old. Get some modeling clay (or very viscous mud) a small piece will do. Place it between the plam of your hand and and a table top. Move your hand in random directions such that you keep the clay under your palm during all moves. No matter what shape the clay was when you started, in just a few minutes you will have a nearly perfect sphere. The shape with the least stress for the average of all the forces is a sphere. You can just tell your son that this is what happens to planets only on a VERY LARGE scale.

Bob
2002-Aug-27, 08:51 PM
I'm betting Silas (or someone with the same name) has read this book, but I recommend "A Matter of Gravity," by Hal Clement, to everyone. It explores the strange environment of the planet Mesklin, a huge rocky world with such a high rate of rotation that it is quite oblate (like, say, a tab of mescaline?).
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The title is "Mission of Gravity" and yes, it is an SF classic. Alas, a "tab of mescaline" is a simile I cannot relate to.

Getting back to the original post, a 4 year old might relate to having seen soap bubbles being pulled into spherical shapes. Although the physics is not the same (surface tension vs. mechanical stress), it's something they've seen.

<font size=-1>[ This Message was edited by: Bob on 2002-08-27 16:52 ]</font>

<font size=-1>[ This Message was edited by: Bob on 2002-08-27 16:59 ]</font>

traztx
2002-Aug-27, 09:03 PM
On 2002-08-27 16:51, Bob wrote:
The title is "Mission of Gravity" and yes, it is an SF classic. Alas, a "tab of mescaline" is a simile I cannot relate to.

I wonder if it's the same as this:

"Mescaline... it's the only way to fly" -- The boyfriend of the girl with the white rabbit tattoo from The Matrix.

Also... did anyone figure out the movie I eluded to about the "Space Peanut"? I'll give a clue: it was a comedy within the past 5 years. Another clue: "J. D."

If no one gets it, I'll give the answer tomottow /phpBB/images/smiles/icon_smile.gif

<font size=-1>[ This Message was edited by: traztx on 2002-08-27 17:19 ]</font>

roidspop
2002-Aug-29, 02:01 AM
As for an experiment that might be informative, mix up some "oobleck"...corn starch and water. I don't have the exact proportions, but to about a half cup of corn starch add water sparingly and mix until it forms a very stiff paste. When you have the stiffness just right, you can mold 'mountains' with it and watch them slump and flow over a period of a minute or so. The stuff is just plain fun to play with and is a natural jumping off point for lots of messy and interesting investigations.

You might also consider getting some "silly putty" and trying the same sort of experiment.

Senor Molinero
2002-Aug-29, 02:26 AM
Ever read Terry Pratchett's "Discworld" series? Yes, it's magic and fantasy but LOL.
"The Fifth Elephant" is one of the better in the series. Great title.

mallen
2002-Aug-30, 12:37 AM
On 2002-08-27 15:03, Wally wrote:
As Silas already eluded to, a sphere presents the smallest surface area for a given amount of material. Therefore, it's the shape that's most stable given the inward force of gravity on planets and stars. That's the simplistic answer that finally satisfied my quest for knowledge!

You're going in the right direction, but the surface area has nothing to do with it.

You are obviously arguing this based on the idea that nature "seeks" the configuration with the lowest potential energy.

A sphere presents the lowest potential energy because all the mass within it is as close to the center of mass as possible.

Think of it this way: If you have a sphere and you want to move some of the mass to somewhere else, you have to move it farther from the center which causes its potential to go up.

<font size=-1>[ This Message was edited by: mallen on 2002-08-29 20:40 ]</font>

ljbrs
2002-Aug-30, 01:15 AM
Gravitational force is what causes the more massive bodies to become spherical. If the massive bodies are rotating, then the sphere gets flattened out and becomes oblate.

What is misnamed *Centrifugal force* is not a *force* per se (actually being a *fictitious force*) and has nothing to do with this question.

Gravitational force is the only answer. Lighter bodies such as most asteroids are not massive enough to become spherical or oblate (when rotating).

Whatever...

ljbrs /phpBB/images/smiles/icon_rolleyes.gif /phpBB/images/smiles/icon_biggrin.gif /phpBB/images/smiles/icon_smile.gif /phpBB/images/smiles/icon_wink.gif /phpBB/images/smiles/icon_rolleyes.gif