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Trying to secure a wall hanging using magnets; me and a coworker came up with an interesting question:

When the hanging is hung using 1 magnet, the weight of it causes it to quickly drag the magnet down and the hanging drops. Using n magnets retards this process; causing it to fall more slowly, but does there exist a number of magnets m such that their combined strength will prevent the hanging from slipping, entirely and permanently?

Because this doesn't make for a very good question; we worked at it and arrived at a similar one; but slightly more idealized:

A weight is suspended, perfectly still, from a wire in a frictionless vacuum. If the mass of the weight is too great; it will gradually distend the cable, causing it to snap and release the weight; but will a light enough weight hang there indefinitely, or will the mass of the weight (and indeed the cable) cause the cable to snap sooner or later?

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4 Answers 4

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Your two questions are not really related, in my thoughts. The first one is about friction of some magnets clutched to a ferromagnetic wall. The second is about failiure of some "wire".

Both are strange and unnessecary mixtures of idealized classical mechanics and some real world problem.

So, first Question is really:

does friction (at rest) last forever?

and second:

does a "wires" stability against rupture last forever?

And answer(s): Yes in a surrounding of appropriate idealization, no in real world.

Georg

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The wire is always metastable to nucleation breaking or tunneling breaking. –  Ron Maimon Mar 30 '12 at 7:20
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You slightly misinterpreted your results. They don't just fall more slowly, they accelerate more slowly.

More magnets will cause the acceleration of the object to reduce. Once you have enough magnets to provide enough force to overcome the force on your object due to gravity, then it will stay up.

The same is true of your rope. Let's say atoms in a rope have some attraction to each other, much like a magnet. If the force between these atoms is high enough to overcome the force due to gravity, it will stay together.

As people have pointed out, these explanations work well in a classical world made of spheres in a vacuum, but in the real world, nothing will stay together forever.

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Ultimately, the weight will fall.

If the weight falls, it will collide with the floor and convert its gravitational potential energy into heat, resulting in an increase in entropy, so the process of the weight eventually falling is thermodynamically favored.

One possible (and somewhat ludicrous) mechanism is quantum tunneling. A bizarre result of this mechanism is that the time we expect to wait before the weight tunnels increases exponentially with the square root of the weight's mass. That means a light object will fall to the ground before a heavy object, by a long shot!

This is a somewhat silly mechanism for a macroscopic weight to fall, but it's a theoretical limit. My guess is that realistically the weight will fall because small statistical fluctuations in the wire and weight due to their thermal energies will eventually cause molecular-scale defects in crystal structure of the wire, evaporation of atoms from the wire, etc. When enough of these defects have accumulated the wire strength will be low enough that the weight falls. If you had a very light weight and you kept the box very cold and extremely-well mechanically isolated from all surroundings, it would take an incredibly long time for the weight to fall. Nonetheless, the second law of thermodynamics says fall it must, eventually.

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It's not so ludicrous if the tunneling is producing defects in the wire. These defects extend the wire's length and bring the weight down a little, until the wire breaks. –  Ron Maimon Mar 30 '12 at 7:21
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Metals normally have crystalline, ordered structure. An atom moving from one appropriate site of the crystal lattice to the next one has to overcome a high energy barrier. If the tension is too small to distort the crystal structure, atoms will stay in their places and your weight will hang forever*.

* By forever I mean long time for any practical purpose, like thousands of years. Sometimes atoms do randomly jump inside the crystal. By putting a tension we slightly favor one direction for these jumps so eventually the cable will stretch but it will rust much faster.

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