Physics/maths Question

R B Customs

R B Customs

R B Customs

Soldato
Joined
22 Sep 2005
Posts
3,267
Location
Manchester
this one has been bugging me for years and none of my teachers at school seemed to know.
here goes :)

Hyperthetically speaking: ( ideal situation)

if you had a perfectly FLAT, SMOOTH surface

and an absolutly PERFECT sphere / ball of about 10 CM in diametre

you rest the ball onto the perfect surface. how much of the ball is touchign the surface?


__ __ __ __ __ __ __ __ __ __ __ __ __ __

Part 2

if you had the same scenario as above, but this time the ball was say 100CM in diametre.
how much of the ball would be touching? would it be more than that of the smaller ball ?



inspiration:
mysterylv7.jpg
 
R B CUSTOMS said:
this one has been bugging me for years and none of my teachers at school seemed to know.
here goes :)

Hyperthetically speaking: ( ideal situation)

if you had a perfectly FLAT, SMOOTH surface

and an absolutly PERFECT sphere / ball of about 10 CM in diametre

you rest the ball onto the perfect surface. how much of the ball is touchign the surface?
Click to expand...

I assume that they are perfectly rigid too? Then I guess it would be either a single atom, or two atoms, depending on the balance. Although Heisenburg's uncertainty principle would probably claim that you could only put a probability distribution on the individual atoms.
 
Erm, it should be the same on both spheres (I think). No idea how much, but I'd assume with an absolutely perfect sphere its gonna be roughly one molecule (or maybe an atom). OR I could have no clue what I'm talking about and have just made an idiot of myself, but at least it's wasted some of my day :D
 
You could never find out, as even solids deform under their own weight to a certian point even if it is only a few microns, but that could be enought to increase the contact area.

In an ideal world where nothing like this happens (as thats the only way you seem to be working) it would be down to 1 atom or molecule iirc.

KaHn
 
Pudney@work said:
Wow, don't tell me my A-level physics has actually helped me work this out correctly :eek:
Click to expand...

No generally its common sense, but as sam pointed out, with in the sphere the molecules dont just stay in one spot, which means the one which is touching the floor might not be the same all of the time, which is where the probability comes into it.

KaHn
 
3 atoms.

The only stable support, one or two atoms and it will be unstable and "roll".

All theoritcal of course as already pointed out :)

At the atomic level objects also fit "into" each other so it's not an accurate "real world" answer without being able to know the atomic structure of the materials involved.
 
Actually, it would probably be at least 3 to create a stable tripod in both directions. However, you also have to add thermal vibrations of atoms too that would mean many of them near the contact point would be rapidly bouncing off the surface too!

EDIT: 3, as person above said.
 
You need to know the weight, dimensions and the modulus of elasticity of both the surface and the sphere. With that information one can calculate the force that the sphere imposes on the surface, the modulus of elasticity can then be used to determine the distortion in the sphere and thus the area that is forced onto the surface.

If there is no distortion of the sphere or surface then the answer is one molecule or it could even be argued only one atom. However, I think the real answer is that none of the sphere ever really touches at an atomic level because at that level it is the repulsion between the electrons of individual atoms that keeps the two objects apart. Inter atomic forces are just so much stronger than mavity.

EDIT: Not forgetting the vibration of the atoms as well, as pointed out above. That is, of course, temperature dependent so there is another variable we need to know.
 
What is the ball made from?
What is the graviational and other accerleratory forces applied?
What is the environmental temperature and that of the ball and surface?
What is the atmospheric/environmental composition and density?
 
I think it'd be impossible to begin with as you can have perfectly smooth surfaces (even if we tried to assume it) as at an atomic level they wouldn't be round, eg:

ghettock0.gif


(Excuse my ghetto image skillz I'm at work)
 
some interesting rplies here !

as i said this is entirly hyperthetical. so deformation / sagging of objects doesnt count here.

i was thinking 1 atom my self. but when you visualise a REALL big ball and a REALLY small one. its hard to think that its the same surface area touching.

interesting answer AJ

Rick
 
R B CUSTOMS said:
some interesting rplies here !

as i said this is entirly hyperthetical. so deformation / sagging of objects doesnt count here.

i was thinking 1 atom my self. but when you visualise a REALL big ball and a REALLY small one. its hard to think that its the same surface area touching.

interesting answer AJ

Rick
Click to expand...

Ignoring effects such as elasticity, thermal vibrations, quantum mechanics and anything else that would bring realism into it, then it would have to be 3 (or could be 1 or 2 if balanced carefully).
 
Samtheman1k said:
Ignoring effects such as elasticity, thermal vibrations, quantum mechanics and anything else that would bring realism into it, then it would have to be 3 (or could be 1 or 2 if balanced carefully).
Click to expand...

Wouldn't it always be balanced perfectly? Mainly because as a perfect sphere it should be completely uniform, thereby meaning any deviation from a normal "perfect" point would ensure that the mass is still evenly distributed and still perfectly balanced? I'm not sure bout this though.
 
You can't work on the assumption that the ball is made up of particles; if it is, then it's not a perfect sphere by definition. The only way it can be a perfect sphere is if it is a perfect solid (which doesn't really make a huge amount of sense). If the ball is perfectly spherical, then there'd be 0 (or infinitessimal) area of the ball in contact with the surface. Of course, this makes no sense in reality, but then, the neither does the question ;).
 
Last edited:
Samtheman1k said:
Ignoring effects such as elasticity, thermal vibrations, quantum mechanics and anything else that would bring realism into it, then it would have to be 3 (or could be 1 or 2 if balanced carefully).
Click to expand...
It couldn't possibly be 3, because there will always be something lower. It is, afterall, an arc.


*Thinking of ways to draw for an example.
 
ok, to assume its perfect, ie had no indents ect it would have to be a single object, not having any joints at all so as such would have no sub objects to select as the rest point - so an atom wouldn't be a valid answer based on the question.

i would tend to say 0 - in the sence that the contact patch on a perfect surface and a perfect sphere would tend towards 0 to such an extent that it pretty much becomes zero (having said that i guess it would effectively be 1-0.9r or near as damn it)
 
For an absolutely perfect sphere resting on an absolutely smooth plane, the answer is that the area of the sphere touching the plane is zero, no matter how big the sphere is.

It's a stupid answer, but then it's a stupid question. ;)
 
It's probably worth pointing out to half the people in this thread that an atom isn't a unit of area.

Taking the perfect hyperthetical (impossible) scenario the OP stated. From a small distance you could say: the sphere is touching less than 1cm of the surface, so you look a little closer and see it is actually touching less than 1mm of the surface, so you look a little closer and see it touching less that 1nanometre of the surface, no matter how close you keep looking is will always be touching less than a certain area, i.e. it's tending to 0. So i guess you could argue they arent touching at all!
 
You must log in or register to reply here.
Back
Top Bottom