pencils

[MathematicalPhysicist]

we have a pencil and you put the pencil with the spearhead of it downward (lets say in earth and on a table), now you release your hand from the pencil to which direction will the pencil fall?
after a few experiments will the direction be the same as the first observation?

[Chen]

If you can keep the conditions the same throughout the series of experiments, it should fall to the same direction - if it falls at all. But you can't in real life, at least not with your hand. You can't possibly keep the pencil absolutely vertical to the table, and it's even harder to release the pencil with your fingers precisely the same way, every time.

[arildno]

I think it's a chaotic phenomenon: If the parameters governing one experiment is slightly different from those governing the second experiment, the fall direction might alter appreciably.

[MathematicalPhysicist]

I think it's a chaotic phenomenon: If the parameters governing one experiment is slightly different from those governing the second experiment, the fall direction might alter appreciably.
i thought to name this thread pencils and chaos (but because lack of full understanding of chaos didnt).
btw i might be wrong but isnt a chaotic phenomon is a situation where the initial conditions are the same (more or less) but the result is different therefore you cant predict it's behaviour.

[MathematicalPhysicist]

If you can keep the conditions the same throughout the series of experiments, it should fall to the same direction - if it falls at all.
just one thing to clear, can a pencil in earth (with it's g) not fall at all?
how can this event happen without an outside force (besides the force acting on it from the centre of earth and the friction with the air) acting on it?

[arildno]

It is the "more or less" sameness both Chen and I pointed out; the behaviour of a chaotic
system is not "indeterminate".
With "indeterminate" I mean the impossibility of setting up an initial-value problem where a unique solution exists; that is, whatever choices of parameters you make, you necessarily have an ill-posed problem.

In practice, I believe chaotic systems are studied by statistical means; i.e. calculating
probabilities of various outcomes.

[Chi Meson]

just one thing to clear, can a pencil in earth (with it's g) not fall at all?
how can this event happen without an outside force (besides the force acting on it from the centre of earth and the friction with the air) acting on it?

The other force is the support force (aka "normal" force) from the table. If you can get the pencil's center of mass to be positioned perfectly above the point of contact between pencil point and table, then the two forces will balance, and there will be no torque. This is possible, and it gets easier when the point is not so sharp.

BTW, take any dozen eggs, on any day of the year (enough with this equinox BS) you should be able to balance most of them on their ends on a flat table. Most people just assume its impossible, but with enough patience, (and no air currents) you can balance anything.

[Chen]

Haha, don't you love those people that gather around in parks on the equinox day and play with eggs? :tongue: I wonder what the origin is of this tradition.

[AntiMagicMan]

Chaotic systems are ones with an incredibly sensitive dependance on initial conditions, so a small change dx in starting posistion could make a very appreciable change x in final posistion.

[MathematicalPhysicist]

The other force is the support force (aka "normal" force) from the table. If you can get the pencil's center of mass to be positioned perfectly above the point of contact between pencil point and table, then the two forces will balance, and there will be no torque. This is possible, and it gets easier when the point is not so sharp.


what's the point in the experiment if not to give the ideal conditions and one of them is that the pencil's point is as sharp as it can be.
it's easy to balance the pencil when the point isnt that sharp (because of the surface of the point) but what about a sharp pencil (as sharp as it can cut you :cool: )?

[Chi Meson]

what's the point in the experiment if not to give the ideal conditions and one of them is that the pencil's point is as sharp as it can be.
it's easy to balance the pencil when the point isnt that sharp (because of the surface of the point) but what about a sharp pencil (as sharp as it can cut you :cool: )?

As you go from a "dull" pencil to a sharper and sharper tip, you go from "real" world to "ideal" world. If you're going into "ideal" sharpness (tip is one single atom of carbon), then you have to also allow other ideal conditions. THerefore, the balancing of the pencil becomes no less possible at ideal extremes, since you would "ideally" still be able to get the canter of mass positioned directly over the single atomic point of contact. Ideally there would be no air currents, the table would be perfectly flat and perfectly smooth, and there would be no other forces acting on the pencil.

Certainly, someone will bring on the HUP, but the uncertainty of position of the center of mass would, I'm sure, be much smaller than the size of the carbon atom at the tip of the pencil. DO correct me if I am wrong.

[Chi Meson]

what's the point... ?

Ha Ha, I get it.