# OK Math Geeks, answer this!



## Big Don (Mar 14, 2012)

If a perfectly spherical ball is sitting on a perfectly flat surface,  what is the size of the contact area?


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## Kinghercules (Mar 14, 2012)

Big Don said:


> If a perfectly spherical ball is sitting on a perfectly flat surface,  what is the size of the contact area?



Mathematically, the contact area is zero, and so if the ball had any mass, it would apply infinite pressure to the flat surface.  The smallest possible area would be of the order of the Bohr radius squared.


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## elder999 (Mar 14, 2012)

Kinghercules said:


> Mathematically, the contact area is zero, and so if the ball had any mass, it would apply infinite pressure to the flat surface.



Contact "area" of zero, or, rather, a single point.

_Undefined_ pressure.(Says the amateur mathemtician)



Kinghercules said:


> The smallest possible area would be of the order of the Bohr radius squared.



Or, "three points of contact, each one atom." (Says the reluctant physicist)

Or, the two surfaces must deform on contact, resulting in a small but definable contact area, and a large but definable pressure (says the *engineer*)

Or, "there's no such thing as a perfctly spherical ball or a perfectly flat surface." (Says the *realist* :lol


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## Steve (Mar 14, 2012)

Very small says the English major.  




Sent using Tapatalk.  Please ignore typos.


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## Big Don (Mar 14, 2012)

elder999 said:


> Or, "three points of contact, each one atom." (Says the reluctant physicist)


 H2O I assume? What about the flat surface's make up?





> Or, "there's no such thing as a perfctly spherical ball or a perfectly flat surface." (Says the *realist* :lol



Since the very idea of trying to figure this out gives me a headache, I posted it, because the smart *** prick in me, knows it will drive someone to long hours of mathematical endeavor...
That and I figured it would be good for a smart *** response from Elder, and it was totally worthwhile.


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## Kinghercules (Mar 14, 2012)

Its weird to think about the illusion of any contact made and that  their is really just an electrostatic repulsion between adjacent atoms  of the sphere and flat surface, at the atomic level. From a quantum  perspective some percentage of the contact atoms are actually  simultaneously inside the surface. Beyond that its even stranger to  try to wrap our heads around & try to understnd what matter really is.


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## elder999 (Mar 14, 2012)

Kinghercules said:


> Its weird to think about the illusion of any contact made and that their is really just an electrostatic repulsion between adjacent atoms of the sphere and flat surface, at the atomic
> *Pancake bunny.*







Seriously?



Kinghercules said:


> From a quantum perspective some percentage of the contact atoms are actually simultaneously inside the surface. Beyond that its even stranger to try to wrap our heads around & try to understnd what matter really is.


 :lfao: 

This is unprecedented. 

_Double *pancake bunny,*_ :lfao:


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## Kinghercules (Mar 15, 2012)

Lmfao!!!!!


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## cdunn (Mar 15, 2012)

Big Don said:


> H2O I assume? What about the flat surface's make up?
> 
> Since the very idea of trying to figure this out gives me a headache, I posted it, because the smart *** prick in me, knows it will drive someone to long hours of mathematical endeavor...
> That and I figured it would be good for a smart *** response from Elder, and it was totally worthwhile.



Water has nothing to do with it. Three points makes a plane, a functional tripod for the sphere - each atom being equidistant from the surface gives you a stable balance for the sphere, engaged with their opposites on the plane, whose number will depend on the packing coordination of the surface material. Less is possible, but distinctly less likely, else we go for a roll.


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## Xue Sheng (Mar 15, 2012)

Well your all WRONG the correct answer is..... 42


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## Big Don (Mar 15, 2012)

Xue Sheng said:


> Well your all WRONG the correct answer is..... 42



No, no, no, that is the answer to life the universe and everything.


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## Xue Sheng (Mar 15, 2012)

Big Don said:


> No, no, no, that is the answer to life the universe and *everything*.



EXACTLY....it is the answer to "everything"


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## Carol (Mar 15, 2012)

elder999 said:


> _ *pancake bunny*_



*deadpan*

I can see the flat surface.  And I can get the idea of a round surface.  But those are far from perfectly flat or perfectly round.


:lfao:


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## Kinghercules (Mar 15, 2012)

cdunn said:


> Water has nothing to do with it. Three points makes a plane, a functional tripod for the sphere - each atom being equidistant from the surface gives you a stable balance for the sphere, engaged with their opposites on the plane, whose number will depend on the packing coordination of the surface material. Less is possible, but distinctly less likely, else we go for a roll.



If it were frictionless than it wouldn't roll it would glide across surface unless the initial force imparted a rolling motion.


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## Kinghercules (Mar 15, 2012)

I would say that the Physicist-Engineer case here is a bit of a false  dichotomy, physicists and engineers both sometimes do rigid body and  sometimes deformation modeling. I should point out that you can also say that, at an atomic level,  there's really no definite contact (as well as no uniform surface).  There is still space between the atoms of the spherical object and those  of the planar object.


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## elder999 (Mar 16, 2012)

Kinghercules said:
			
		

> I would say that the Physicist-Engineer case here is a bit of a false  dichotomy, physicists and engineers both sometimes do rigid body and  sometimes deformation modeling..



Well. as a nuclear and mechanical engineer with a PhD in physics, _I'd sa_y......*what I said.* :lol:


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## Jenna (Mar 16, 2012)

Big Don said:


> If a perfectly spherical ball is sitting on a perfectly flat surface,  what is the size of the contact area?


I further wonder does a perfectly spherical ball sitting on a perfectly flat surface roll around _infinitely with no resistance_ if nobody is there to witness it?


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## Sukerkin (Mar 16, 2012)

Very Zen, Jenna :lol:.


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