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Physical Philosophy

 
 
Reply Fri 13 May, 2011 04:53 pm
How much of a sphere will touch the surface upon which it rests-when the following criterion are met: the sphere is perfectly round, the surface upon it rests is perfectly flat as well, and no other factors are involved- no blemishes whatsoever- this is the most physically serene, sound, and scrupulously designed situation- utter perfection- what do you think?
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Type: Question • Score: 3 • Views: 4,794 • Replies: 45
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Fil Albuquerque
 
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Reply Fri 13 May, 2011 05:33 pm
@Tifinden,
I think you forget what a force is about and know nothing on atoms and how they behave...obviously the sphere will never touch the table or the flat surface or whatever else !
Tifinden
 
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Reply Fri 13 May, 2011 06:00 pm
@Fil Albuquerque,
Know nothing, please do not be so hasty to denounce, for your explanation seems to be inadequate in its simplicity and lack of corroboration- why touches it nothing else?
It is touching the surface!- that is one of the key factors in the contrived circumstance! Ask a few friends and attempt to fuel and induce a conversation to uphold and factor many varying opinions regarding this matter so that we may then achieve knowledge of this predicament.
Fil Albuquerque
 
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Reply Fri 13 May, 2011 06:08 pm
@Tifinden,
What I meant is that you cannot get any practical example on what you just did proposed...no such thing as touching the surface can be demonstrated quite the opposite...

The feeling of touch is just the effect of repelling forces between atoms which actually never enter in contact...
Tifinden
 
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Reply Fri 13 May, 2011 08:16 pm
@Fil Albuquerque,
Wait, actually, I do remember hearing of this theory that opposing atoms never touch, however, whether it is true is questionable- how much force then is applied when the one area of the sphere's atoms are in contact with the atoms of the surface- if it could be determined how the force is displaced, then it might be reasonably within reason to postulate about such matters- my comrades and I have hypothesized that just one physical point touches at one time- or perhaps an infinite amount of the sphere is touching based on various theorems- the presence of the table encompassing the sphere in multiple dimensions of individual sections of the quantum fabric- and because of the uncertainty of the quantum world, this may also be true- that the area of the sphere which is touching the surface is infinite because of its consistent fluctuation.
Render
 
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Reply Fri 13 May, 2011 10:21 pm
@Tifinden,
The sphere would touch at exactly one elementary unit.
0 Replies
 
hamilton
 
  1  
Reply Mon 4 Jul, 2011 11:41 am
i asked a question kind of exactly like this. here, you can check it out.
http://able2know.org/topic/171641-1
JLNobody
 
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Reply Mon 4 Jul, 2011 03:35 pm
@Tifinden,
Tinfinden, strange title, "Physical Philosophy." I'm not saying it's invalid, only that I tend to think of philosophy as purely "Mental."
By the way, you asked Fil Albuquerque "not to be so hasty to denounce." Don't waste your energy, competition seems to be his personality's dominant drive.
hamilton
 
  0  
Reply Tue 5 Jul, 2011 11:01 am
@JLNobody,
i actually cant imagine a physical philosophy.
Tifinden
 
  0  
Reply Tue 5 Jul, 2011 07:23 pm
@hamilton,
Exactly, and this forum and the entirety of this website, entices those of an intellectual caliber- you do not belong! Leave, join the most preferable team death-match you find, and boil your head!
Thomas
 
  1  
Reply Tue 5 Jul, 2011 08:09 pm
@Tifinden,
Are you asking a mathematical or a physical question?

If you're asking a mathematical question, the answer is "one point".

If you're asking a physical question, the answer is "approximately the square of the length between two atoms in the sphere's or the tables crystal lattice. In the case of an iron sphere resting on an iron table, that would be about 250 picometers square. (250 picometers is an inch divided by 100 millions.) I'm saying approximately, because the definitions of "rest" and "touch" get a little fuzz at this microscopic level.
High Seas
 
  1  
Reply Tue 5 Jul, 2011 08:35 pm
@Thomas,
I'm not sure about your one point calculation - it sounds like the asymptotic limit but it can't be right in the sense that a larger sphere will have more points of contact with a surface than a smaller sphere. It seems to follow that your atomic lattice calculation would also have to be adjusted for sphere size.

Try this experiment: paint 2 large spheres then roll them over a perfect 2-dimensional surface before the paint dries - you'll get a wider track with the larger sphere (I think so, haven't actually tried it). I get the same result with integral calculus and 2 spheres of different sizes at limit of cylindrical approximations for volume of sphere, given by
http://demonstrations.wolfram.com/ApproximatingTheVolumeOfASphereUsingCylindricalSlices/HTMLImages/index.en/1.gif
On the other hand I can see that a circle touching a straight line in pure analytic geometry would only touch at one point independently of radius and that the sphere is a collection of an infinity of perfect circles so radius shouldn't really matter except in an experimental sense - and that's a funny result!
http://demonstrations.wolfram.com/ApproximatingTheVolumeOfASphereUsingCylindricalSlices/
wayne
 
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Reply Tue 5 Jul, 2011 09:25 pm
@Tifinden,
I'm not sure if you wish to suspend time, re the state of flux. Also assume the atoms actually touch. Stop at the atomic level, rather than follow the infinity of quantum physics.

If we stop with atoms and assume they actually touch, you can picture a sphere and plane constructed of marbles. In which case the contact could be one marble or three, depending on exactly how the contact is made.

Even pursuing this to infinity should yield the same variable.
There will always be a space between points, if the opposite point meets this space it will make multiple contact.

I don't know what you mean by physical philosophy here, what you've proposed is correctly called a thought experiment.
0 Replies
 
hamilton
 
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Reply Wed 6 Jul, 2011 06:50 am
@Tifinden,
alright, fine. describe your "physical philosophy", if your mind is so full of such intellectual caliber.
im not going to accept an insult as an answer. its not an answer, its an insult. if you refuse, then you'll only confirm that you dont know either.
Thomas
 
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Reply Wed 6 Jul, 2011 07:15 am
@High Seas,
As I said, concepts like "point" and "contact" are murky on the level of atoms and molecules, so there really is no "right" physical answer. I merely went with the geometrical picture that comes the closest to a "point" that still makes any sense on the atomic level. And that's a picture where one atom of one surface balances in a hole formed by an elementary cell of the other surface.

There are other possible answers. One could be rigorous about it and say: "Ill-specified problem: There are no ideal geometrical bodies in physics."

Or one could define "contact" in the spirit of your objection. For example, one could say that "contact" means that the distance between the surfaces is smaller than the length of a chemical bond within them. That gives you a "point" of contact that grows with the size of the sphere.

Based on trigonometry and the back of an envelope, I'm getting a radius for this "point" of contact that's sqrt(2 * r * g), where r is the radius of the sphere and g is the size of the gap. For example, if r=5cm (for a grapefruit-sized sphere) and g=250pm (which is the length of one Fe-Fe bond) the area of contact would be a circle with a radius of 5 micrometers. And as you suggest, the area grows as r grows.
High Seas
 
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Reply Wed 6 Jul, 2011 07:16 am
@hamilton,
hamilton wrote:

.... its not an answer, its an insult.

I don't speak for Tifinden, but from what (mercifully little) I've seen of your inane posts I don't even believe it's possible to insult you. You may have a place in this forum - well away from any threads requiring basic intelligence, education in any subject, or elementary English grammar. Please stay there.
High Seas
 
  1  
Reply Wed 6 Jul, 2011 07:19 am
@Thomas,
Thomas wrote:

.......... And as you suggest, the area grows as r grows.

It does mathematically as well: radius of sphere matters - it's impossible to get it out of the final solution. In solid geometry the proof that the ratio of surface of a perfect sphere to its volume varies with the radius has been known since antiquity, so I should have thought of that sooner. Thanks for the physics part!

N.B. there's a demo of the math part on this link: http://demonstrations.wolfram.com/TheRatioOfSurfaceAreaToVolumeForACubeAndASphere/
hamilton
 
  0  
Reply Wed 6 Jul, 2011 07:39 am
@High Seas,
thats mean...
0 Replies
 
wayne
 
  1  
Reply Thu 7 Jul, 2011 01:53 am
@High Seas,
Your post got me thinking about bicycle tires. In practice, a larger diameter means a reduction in rolling resistance. While the increase of the point of contact seems to contradict this.
So that leaves me with the thought that the reduction in rolling resistance comes solely from the reduced revolution of the axle. Which must be greater than the increased point of contact.
Does this sound right to you?

hamilton
 
  0  
Reply Thu 7 Jul, 2011 02:46 pm
@wayne,
no.
0 Replies
 
 

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