magnet question

YouTube

At about 4:30 to 4:38

I don't understand why the magnet didn't grab the bottom (steel) penny in the first place.Well, it did, enough to make it stand on edge. But why did the magnet not snatch it up, instead waiting until enough steel got in the way, and then grab it all?

Originally posted by @apathist
[youtube]V8-JfSXPDp0[/youtube]

At about 4:30 to 4:38

I don't understand why the magnet didn't grab the bottom (steel) penny in the first place.Well, it did, enough to make it stand on edge. But why did the magnet not snatch it up, instead waiting until enough steel got in the way, and then grab it all?

I cant speak specifically about the force relationship at work here ( they are undoubtedly complex), but generally the force of magnetic attraction ( objects of opposite polarity) increases with decreasing distance between magnetic materials. The two forces acting (in opposite directions - effectively) on the penny are its weight and the magnetic force. So in general, if the magnet isn't "snatching the penny up" its because these forces are balanced, equal and opposite. There is a point at some distance away from the magnet the penny will "levitate". Displace it further from equilibrium it will fall, and closer it will rise.

In the video the single penny isn't levitating. Its weight is only partially supported by the magnetic force, the remainder is supported by the box or the guys finger. When he adds the second penny the center of mass of the system moves upward ( to the top of the first penny), and the systems mass is increased by one penny. Repeat for penny 3,4,5... Using a strong enough magnet the pennies may be far enough away that the magnetic force can be approximated to act of the system of pennies center of mass ( this probably doesn't hold exactly in this scenario but it illustrates the point). So as the center of mass approaches the magnet the magnetic force becomes increasingly stronger. At some point will overtake and accelerate the system of pennies upward ( ripping them apart from each other when the "system approximation" breaks down via strong force gradients across the distances of a penny).

Originally posted by @joe-shmo
... So as the center of mass approaches the magnet the magnetic force becomes increasingly stronger. At some point will overtake and accelerate the system of pennies upward ( ripping them apart from each other when the "system approximation" breaks down via strong force gradients across the distances of a penny).

Forgive my ignorance, please. Why wasn't this force present for a single penny. The first one, that didn't snap onto the magnet until it in my words became convinced.

Originally posted by @apathist
Forgive my ignorance, please. Why wasn't this force present for a single penny. The first one, that didn't snap onto the magnet until it in my words became convinced.

No problem. I put some extra info in the response, I'll try to trim it, and take it piece by piece.

The single penny is beyond the distance of "levitating" equilibrium where the force from the magnet exactly balances its force of weight. So as a thought experiment lets take the bottom of the box in the video out and replace it with a precise scale that rests on a very precise floor jack. The penny has some weight "W", however it is magnetic an immersed in a magnetic field. Based on observation ( the penny resting on the bottom of the box in the video doesn't accelerate) what will be on the scale readout "R"?

a) R > W
b) R = W
c) 0 < R < W

Hint: Picture yourself standing on a scale and me trying to lift you up. How will the scale record your weight as I begin to hoist you up?

Originally posted by @apathist
Forgive my ignorance, please. Why wasn't this force present for a single penny. The first one, that didn't snap onto the magnet until it in my words became convinced.

The pennies are magnetiseable, so for the first penny a smaller magnet was in play. Once the first penny became attached it became magnetised so they effectively had a bigger, more powerful, magnet.

Originally posted by @joe-shmo
...
The single penny is beyond the distance of "levitating" equilibrium where the force from the magnet exactly balances its force of weight. So as a thought experiment lets take the bottom of the box in the video out and replace it with a precise scale that rests on a very precise floor jack. The penny has some weight "W", however it is magnetic an immers ...[text shortened]... and me trying to lift you up. How will the scale record your weight as I begin to hoist you up?[/b]

The bottom penny gets vertical because of magnetism. But it sticks to the table top because of gravity, or acceleration towards the ground. R should be W.

Same with the other pennies stacking up. Until suddenly magnetism wins and gravity becomes negligible.I don't know how to e-shrug.

Originally posted by @apathist
The bottom penny gets vertical because of magnetism. But it sticks to the table top because of gravity, or acceleration towards the ground. R should be W.

Same with the other pennies stacking up. Until suddenly magnetism wins and gravity becomes negligible.I don't know how to e-shrug.

"R should be W"

Actually, R will be less than W but greater than 0. or option c) 0 < R < W.

"R = W" is what will register on the scale in the absence of a magnetic field.

The next step is to jack the penny up ( decrease the distance between the magnet and the penny) until a critical point of unstable equilibrium is reached. What will the scale readout be at that point?

You should be arriving at the conclusion "R = 0".

At that point you can remove the scale/jack and the penny will appear to levitate. Note: This position is above the point where the penny is resting on the box, and above the point where it is resting (elevated) on his fingertip. It would most likely be extraordinarily difficult to find in practice. However, its no different in believing in going from 0 to 2 on a continuum 1 is passed.

So the reason a single penny is not "snatched up" is because it has not passed closer to the magnet beyond that point of equilibrium.

"Same with the other pennies stacking up. Until suddenly magnetism wins and gravity becomes negligible.I don't know how to e-shrug."

Its only "sudden" because the penny is an extended body ( it has size, volume, etc... ).

Its kind of like this: pretend I am the magnetic force and you are the pennies. I'm 50 ft above you trying to lift you with a rope. You are standing on a scale. I cant lift you, but I can appear to make you weigh less. A copy of you jumps on to of your shoulders. The copy grabs the rope and you grab his legs. How the magnetic force behaves is he is 5 ft closer and I can grab the rope with 2 of my copies. So there is me tugging on you and two of my copies tugging on your copy and you tugging on him. The process repeats, you get one more copy on the shoulders of your other copy, and I get lets say 4 more copies of me pulling on the rope. At some point, "I" ( and all my copies) will be able to hoist "you" ( and all your copies) with ease because my copies are increasing at a greater rate. All your copies have to do is be able to hold on to each other. It should also be said that your copies are gaining in strength as they climb ( due to increased magnetic interaction between you copies). That is the top copy is strong enough to lift the entire chain, the next is strong enough to lift the remaining, etc...you being the weakest ( you only have to withstand lifting your body weight and the inertial forces of acceleration.

If none of this is helping you get a better picture...let me know, Ill stop. If you have specific questions I'll try and elaborate. If you're satisfied with Deepthought's response, by all means be satisfied!

Also, imagine the rope made of woven flexible iron. You are underneath the magnet and you play out the rope vertically. What do you think happens? You and gravity are holding it down from whacking into the bottom of the magnet. But the more rope you let out it gets closer to the magnet and at some point you AND gravity will be overcome because it is a very strong magnet, say 1 Tesla or so. The rope will stay vertical till you can no longer hold it back. BTW, if you didn't know, 1 Tesla = 10,000 gauss.

In my job I deal with magnets 1/3 of that.

Originally posted by @joe-shmo
...
Its kind of like this: pretend I am the magnetic force and you are the pennies. I'm 50 ft above you trying to lift you with a rope. You are standing on a scale. I cant lift you, but I can appear to make you weigh less.



If none of this is helping you get a better picture...let me know, Ill stop. If you have specific questions I'll try and elaborate. If you're satisfied with Deepthought's response, by all means be satisfied![/b]

About weight: if the first penny weighs less, then the magnet must weigh more. Weight is mass under acceleration - in this case the acceleration is due to the gravity of earth. Here neither the gravity delivered by earth nor the mass of the coin has changed, The penny must weigh as much as it ever did. This doesn't contradict your point, of course.

A copy of you jumps on to of your shoulders. The copy grabs the rope and you grab his legs. How the magnetic force behaves is he is 5 ft closer and I can grab the rope with 2 of my copies. So there is me tugging on you and two of my copies tugging on your copy and you tugging on him. The process repeats, you get one more copy on the shoulders of your other copy, and I get lets say 4 more copies of me pulling on the rope. At some point, "I" ( and all my copies) will be able to hoist "you" ( and all your copies) with ease because my copies are increasing at a greater rate. All your copies have to do is be able to hold on to each other. It should also be said that your copies are gaining in strength as they climb ( due to increased magnetic interaction between you copies). That is the top copy is strong enough to lift the entire chain, the next is strong enough to lift the remaining, etc...you being the weakest ( you only have to withstand lifting your body weight and the inertial forces of acceleration.

I almost see it. I've read your visualization several times. Is this true: while the first penny responded to the magnetic force and so stood on edge without being snatched up, a larger mass of a single steel disc may have been snatched up right away?

Originally posted by @sonhouse
Also, imagine the rope made of woven flexible iron. You are underneath the magnet and you play out the rope vertically. What do you think happens? You and gravity are holding it down from whacking into the bottom of the magnet. But the more rope you let out it gets closer to the magnet and at some point you AND gravity will be overcome because it is a very st ...[text shortened]... ack. BTW, if you didn't know, 1 Tesla = 10,000 gauss.

In my job I deal with magnets 1/3 of that.

So the more the magnet grabs this metal strand (or the more of the metal strand has been grabbed by the magnet), the more upward force is felt by the next part of strand? Even though that next part, by itself, wouldn't have been snatched up at all.

The stacking pennies are sort of like a wick in a candle.

Originally posted by @apathist
So the more the magnet grabs this metal strand (or the more of the metal strand has been grabbed by the magnet), the more upward force is felt by [b]the next part of strand? Even though that next part, by itself, wouldn't have been snatched up at all.

The stacking pennies are sort of like a wick in a candle.[/b]

The longer the rope is played out, the closer to the magnet it gets so the top of the rope experiences a higher force than the lower part, eventually getting close enough it will be very difficult to keep the top of the iron rope from banging into the magnet, especially if it is upwards of 1 Tesla.

There was a case of a child put into an MRI machine, which has multi-Tesla strength magnets. There is a hard rule, no magnetic material, like iron, in the MRI room. But someone left a fire extinguisher in the room and when they turned on the machine, the extinguisher flew right into the machine, ramming into the child and killing him instantly.

It was a sad day for all.

Originally posted by @apathist
...
I almost see it. I've read your visualization several times. Is this true: while the first penny responded to the magnetic force and so stood on edge [b]without being snatched up, a larger mass of a single steel disc may have been snatched up right away?[/b]

We have to be careful as to not confuse the issue with the side arguments. If I were to add another steel penny to the to the one already there beside it, than all else the same, No. If the force provided (at that distance) by the magnet was not able to lift a single steel penny, then double the force provided will not lift double the weight. I say we must be careful because the magnetic force is the manifestation of a field acting through a surface. So if you change how the surface is presented to the field you may change the magnitude of the force. For instance if you turn the penny horizontal (increasing the surface area perpendicular to the field) at that distance it will increase the magnetic force and it may rise.

Originally posted by @joe-shmo
We have to be careful as to not confuse the issue with the side arguments. If I were to add another steel penny to the to the one already there beside it, than all else the same, No. If the force provided (at that distance) by the magnet was not able to lift a single steel penny, then double the force provided will not lift double the weight. I say we m ...[text shortened]... rpendicular to the field) at that distance it will increase the magnetic force and it may rise.

And of course that effect would depend 100% on the shape of the magnetic field lines where the penny resides. If the lines were horizontal at the penny the opposite would be true. Which could be true if the magnet was a horseshoe shape instead of just a big block.