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View Full Version : A nice stupid question (rolling perfect sphere)

Jeff Root
2007-Nov-06, 07:34 PM
In another thread, as an illustration of an unstable balance, KenG
wrote: "...akin to a pencil balanced on its point."

Can a perfectly hard, perfectly smooth, spherical ball sit at rest on
a perfectly hard, perfectly smooth, level surface?

:lol:

-- Jeff, in Minneapolis

korjik
2007-Nov-06, 07:41 PM
Yes. assuming that the ball is also balanced.

If the ball is not balanced, you should end up with harmonic motion around a spot within (pi)/4 the radius of the ball's original spot.

then over time, friction will slow the ball down and it will rest at the spot it was oscillating around.

dhd40
2007-Nov-06, 08:18 PM
In another thread, as an illustration of an unstable balance, KenG
wrote: "...akin to a pencil balanced on its point."

Can a perfectly hard, perfectly smooth, spherical ball sit at rest on
a perfectly hard, perfectly smooth, level surface?

:lol:

-- Jeff, in Minneapolis

If I understand your question correctly, then "perfectly hard, perfectly smooth" would ask for a sub-sub-sub-quark-(or lower)-incompressible-structure of the surface of that spherical ball.
Now, Heisenberg´s uncertainty principle (HUP) would forbid any "sitting on rest". Therefore, no perfectly hard, perfectly smooth body can exist.

But without HUP, why shouldn´t it be possible, if all forces, field gradients, etc have been eliminated?

Noclevername
2007-Nov-06, 08:53 PM
For normal matter, it's sort of like the old "irresistable force/immovable object" idea; not really reachable in the real world.

Neverfly
2007-Nov-06, 09:27 PM
I dunno. Can you stand an egg on end in the summer time?

Noclevername
2007-Nov-06, 09:32 PM
I dunno. Can you stand an egg on end in the summer time?

Yes, and you can also apply a force to an object. But the OP premise of "perfectly hard, perfectly smooth" is an unreachable abstract. No such thing exists, or can.

Neverfly
2007-Nov-06, 09:36 PM
Yes, and you can also apply a force to an object. But the OP premise of "perfectly hard, perfectly smooth" is an unreachable abstract. No such thing exists, or can.

I still dunno.

NoCleverName, you are perfectly hard headed and perfectly smooth with the ladies.

alainprice
2007-Nov-06, 09:36 PM
Q: Can a perfectly hard, perfectly smooth, spherical ball sit at rest on
a perfectly hard, perfectly smooth, level surface?

A: Yes, assuming the sphere starts at rest and has no external forces.
Note: An external force which is 'normal' to the surface may not cause the spehere to move.

Noclevername
2007-Nov-06, 10:10 PM
I still dunno.

NoCleverName, you are perfectly hard headed and perfectly smooth with the ladies.

I can, but sometime's I'm perfectly softheaded and... um...

I'm going to go cry now. :boohoo:

Jeff Root
2007-Nov-07, 01:47 AM
While I was typing the question, I realized that being "perfectly"
hard and smooth implied no friction between the surfaces, so the
fact that it is a ball may be irrelevant. A ball can't roll without
friction. It can slide without rolling.

Atoms are small enough. The quartz spheres made for Gravity
Probe B come real close to perfectly spherical. I wonder if the
few-atoms-thick surface irregularities would make a difference
in the ball's motion if negligently set down on a level surface.

Wait a minute. What does it matter that there is no such thing
as "perfectly" hard, smooth, spherical, and level? The fact that
the materials don't exist in reality has no effect on how an
imaginary perfect ball would behave. This isn't a situation like
an irresistable force versus an immoveable object. That is a
logical contradiction. All forces in reality are irresistable, and
it is impossible for any object to be immoveable. There are no
impossibilities with the perfect ball -- just a stoopid question!

-- Jeff, in Minneapolis

Noclevername
2007-Nov-07, 01:50 AM
Okay, so we'll ignore the part about it being perfect.

Now, can anything ever really sit at rest...? ;)

astromark
2007-Nov-07, 07:29 AM
Yes it can have no relative motion. To be perfectly still.
However what and where in space can you find some thing that is motionless?
So the yes becomes a maybe not... as Neverfly said, I dunno., too.

Neverfly
2007-Nov-07, 10:48 AM
I'll throw my two bits out...

Assuming irregularities due to atmoic structure and asuming imaginary absolute perfection- The answer is that yes, it can be balanced. Possible. It may be very very difficult to do if like a pencil as you first said- but I wouldn't deem it as an impossibility. If the imaginary perfection is involved- it may be much harder yet. Even the motion of the Earth- just because it is moving - can cause the bottom point of the pencil to slide out from under the top.

What happens when the unstoppable force collides with the immovable object? ...Something's gotta give...

WaxRubiks
2007-Nov-07, 11:42 AM
if a perfect sphere sat on a perfectly level surface; then its center of mass would be as low as it could get and I think there would be no potental energy left in that system to be transformed into kinetic energy.

John Mendenhall
2007-Nov-07, 04:08 PM
The questions can only be answered if they are physically possible. Since the OP has specified atomic as the limiting dimension, than the sphere will make a tiny indentation in the surface, and it will be stable. If you propose perfect hardness, then the question becomes irrelevant, you are proposing the physically impossible.

In a more general sense, as a math exercise, it might be a legitimate question. But with thought experiments, which this is, great caution must be used with the boundary conditions. The OP hit on one already, wrt friction. Anyhow, it makes one stop and think, and that's what BAUT is about.

Cougar
2007-Nov-07, 06:29 PM
Can a perfectly hard, perfectly smooth, spherical ball sit at rest on a perfectly hard, perfectly smooth, level surface?
There's no such thing as a "perfectly smooth" surface. Surfaces are made up of atoms, and atoms are jiggling around. Brownian motion... Einstein... 1905....

trinitree88
2007-Nov-07, 06:43 PM
Such an imperfect world........sigh....:shifty: pete

Noclevername
2007-Nov-07, 07:23 PM
That's the problem inherent to thought-experiments. They're just exercises of imagination, and in imagination anything can happen however you can think of. And can't happen in ways you can't think of. That's why science has real experiments.

Jeff Root
2007-Nov-07, 07:59 PM
if a perfect sphere sat on a perfectly level surface; then its center
of mass would be as low as it could get and I think there would be
no potental energy left in that system to be transformed into kinetic
energy.
But it's center of mass would be equally low everywhere on the
surface...

There's no such thing as a "perfectly smooth" surface. Surfaces are
made up of atoms, and atoms are jiggling around. Brownian motion...
Einstein... 1905....
So, will Brownian motion provide the necessary kinetic energy to
produce horizontal motion of the ball?

-- Jeff, in Minneapolis

kzb
2007-Nov-08, 01:24 PM
<<So, will Brownian motion provide the necessary kinetic energy to
produce horizontal motion of the ball?>>

It ought to in my opinion. Atoms or molecules that make up the ball are each oscillating around a mean position. If you assume the motion of each is random, that means at any one time, just based on probability, there will be more atoms or molecules going +x than -x. Or vice versa of course.

That should result in your frictionless ball wandering round on a random walk around the perfectly flat surface.

korjik
2007-Nov-08, 05:17 PM
Why are you all making this problem harder and different than the one stated?

This is a macroscopic ball made up of perfectly smooth matter on a perfectly smooth perfectly level surface with some coefficent of friction between them to make the problem non trivial. The end result is that the ball will sit on the surface perfectly fine. This is a classical problem not a quantum one.

kzb, you are talking about randomly oscillating atoms. Yes, at any instant in time, there should be some small force vector, and yes there is a rendom walk in force space, but you are talking about atomic masses trying to random walk gram weights. Considering the very slow total movement of a random walk, you are prolly talking millenia to move microns.

John Mendenhall
2007-Nov-08, 06:36 PM
Why are you all making this problem harder and different than the one stated?

Because it's more fun that way. I was going to nitpick at the size of the ball before. If it's only a few atoms in diameter, the situation is different.

Assume makes (you know).

If the ball slides off a perfect frictionless surface and lands on the ground, is it a thunk experiment?

Noclevername
2007-Nov-08, 06:39 PM
If the ball slides off a perfect frictionless surface and lands on the ground, is it a thunk experiment?

:clap::clap::clap:

korjik
2007-Nov-08, 06:45 PM
Because it's more fun that way. I was going to nitpick at the size of the ball before. If it's only a few atoms in diameter, the situation is different.

Assume makes (you know).

If the ball slides off a perfect frictionless surface and lands on the ground, is it a thunk experiment?

:D

kzb
2007-Nov-08, 07:04 PM
Well korjik, we're talking the theoretical case of zero friction. So any small force is enough to produce SOME motion. OK we probably ARE talking millenia to move microns, but he whole point of the thread is whether there is any reason to think it would move AT ALL.

Anyway, no-one has stipulated the size of the ball, and that issue has an interesting effect:

I suspect that the weight imbalance caused by random atomic vibrations will be related to the Poisson distribution. The standard deviation of a Poisson distribution is the square root of the mean.

If we had a steel ball of mass 56g, that would have Avogadro's number of atoms, ie approximately 6E+23. Because the movement is Poisson-distributed, I estimate the order of magnitude of a typical imbalance force as SQRT(6E+23) or 8E+11 atoms. In this case, with iron atoms, that is 7E-11 gram force. That is the imbalance on a 56g weight, or just 1E-10 percent.

If we then take a ball of mass 1 femtogram (10^-15g), the standard deviation of the number of atoms is 0.03% of the total. (As the number of atoms is decreased, its RELATIVE standard deviation increases.)

In other words, at any given moment, the femtogram steel ball is likely to be imbalanced about its centre line by about 0.03%. And as we get even smaller the relative effect gets bigger.

Where does the energy come from I hear you ask. The atomic motions in a solid are largely oscillations, ie there is no net movement. I think the ball would actually just wander around a mean position also.

Having said all that, it does not seem quite right to be taking atoms into account in this fashion when we ignore the atom issue at the ball-surface boundary. The ball cannot be perfectly smooth and friction free on the atomic scale.

Neverfly
2007-Nov-08, 07:23 PM
There is also the possibility of going up a notch from atomic oscillation and considering molecular bonds...

e.g. superglue.

Noclevername
2007-Nov-08, 07:29 PM
...Is there wind blowing on the ball? Is it in an earthquake zone? Is there sneeze guard around it? ;)

Jeff Root
2007-Nov-08, 09:40 PM
If we permit the ball to made of actual atoms, then I think there
will be a big difference between it being in an atmosphere or in
vacuum. In air, currents and thermal motion of air molecules will
push the ball, while in vacuum, the ball may be vacuum welded
(Is that the same as 'cold welded'?) to the surface.

-- Jeff, in Minneapolis

Noclevername
2007-Nov-08, 09:44 PM
in vacuum, the ball may be vacuum welded
(Is that the same as 'cold welded'?)

According to Wikipedia:

http://en.wikipedia.org/wiki/Vacuum_welding
http://en.wikipedia.org/wiki/Cold_welding

Take that for what it's worth.

Neverfly
2007-Nov-08, 10:24 PM
Where is Mandlebrot when you really need him?

I learned in school, that when bored in class, I could get quite a few oddball objects to balance quite well. In spite of chaotic factors on the atomic level.

I think any argument on this thread needs to first specify the size of the ball or as the OP Originally mentioned- pencil.

An iron ball polished very very smoothly and about 1000 feet in diameter will not move much. In fact, it will just settle comfortably into it's own crater.

An iron ball polished very very smoothly and about 1 micron in diameter may wobble a bit in absolutely still air- Just... Don't... Sneeze...

Specific conditions and sizes would help in your posts.

kzb
2007-Nov-09, 01:11 PM
<<There is also the possibility of going up a notch from atomic oscillation and considering molecular bonds...>>

True, but I think it's essentially the same argument. The bonds beween atoms in a molecule are continually vibrating and the relative positions of the constituent atoms oscillate around mean positions. The centre of mass is continually shifting on a random basis. I don't think the issue of whether the ball is made out of atoms or molecules affects the argument.

I kind of assumed the ball would be in a perfect vacuum in perfect darkness to go with the perfect lack of friction and perfect sphericalness (or is that sphericity). However if we allow atmosphere into the picture, we need to consider the more usual Brownian motion, and if light is allowed, differential light pressures on either side.