Where does the energy come from?

[barryj]

The figure shows two cases of conservation of momentum (I think).

In case A we have a magnet and a ball bearing just sitting on the table. We bring another ball bearing close to the magnet. The bearing is grabbed by the magnetic force.

In case B, we add another bearing, number 3 as shown. Now when the bearing 1 is brought to the magnet, bearing 3 will shoot away from bearing 2 with a large velocity.

My question is where does the energy come from in case B that causes the bearing 3 to shoot away so fast. Is the residual field of the magnet reduced?

 

[anorlunda]

Pretty clever. You modified the standard Newton's Cradle to put a magnet in the middle. I don't think the magnet changes the physics equations much, but it could change the amplitudes of the swings. The physics of Newton's Cradle are explained pretty well here.

https://en.wikipedia.org/wiki/Newton's_cradle

 

[Biker]

Sixty symbols made a video about this:


Might find it useful :D

 

[barryj]

I do think the magnet changes the physics but I do not know how to explain it. The video shows the same thing I have attached. Still, no matter how slowly you push bearing 1 into the magnet in case B, there is a lot more kinetic energy coming from bearing 3. One would think that in case A bearing 2 should move away from the magnet and then return very quickly. Maybe this is what happens.

 

[sophiecentaur]

It strikes me that there is significant Potential Energy in the form of the magnetic field and Ball 1 (plus any KE due to the approach velocity). Ball 1 will rapidly accelerate towards the magnet and clang! There is always some energy loss in the impact and Ball 2 will not have enough energy to escape. That energy can either be dissipated inside the magnet, balls 1 and 2.
The energy has to go somewhere and there is nowhere for it to go than 'inside'. The balls will vibrate against each other (mechanical energy) but with not enough energy to fly off. However, when you put Ball 3 against Ball 2, Ball B is at a slightly higher Potential level than Ball 2 (less attracted). The initial impulse against Ball 3 is enough to overcome the attraction and Ball 3 will escape. It's almost an analogous model for a Quantum System (Photoelectric effect, for instance); Ball 2 can't escape because its potential is too low but Ball 3 can because it's further out from the potential well.
I could imagine a suitably shaped magnet for which Ball 2 would actually escape.
I even drew a diagram:

 

[davenn]

Sixty symbols made a video about this:

Been a while since I have seen that video ... very cool

I do think the magnet changes the physics but I do not know how to explain it.

it is explained quite well in the video, maybe you missed it ? watch the video again and listen very carefully to the explanation and note the slow motion video

note the words "high acceleration", "enormous energy" and "much more momentum"

Dave

 

[Merlin3189]

In case B, we add another bearing, number 3 as shown. Now when the bearing 1 is brought to the magnet, bearing 3 will shoot away from bearing 2 with a large velocity.
View attachment 107920

I think you are being disingenuous when you say, "...bearing 1 is brought to the magnet."
If you do pecisely that - bring 1 to the magnet, under control - then I don't think 3 moves off any faster than 1 arrives. It is the transfer of kinetic energy which moves 3.
In all the demos I've seen of this, either 1 is rolled towards the magnet and is obviously free to accelerate throughout, or it is held simply and jumps out of control to the magnet over the last few mm.
The only reason 3 does move off very quickly (as it does whenever I've tried it), is that it is very difficult to prevent 1 from accelerating rapidly in the final approach to the magnet. Then 3 moves off at the contact speed of 1, but decelerates more slowly than 1 accelerated, so ends up moving faster than 1 was moving when it became out of control.
If you can indeed engineer a situation where 1 is controlled up to very near to the magnet, then I think it possible that it will acquire so little KE that 3 will stay attached, or at least, move away so slowly that it is pulled back to 2, either seeming to bounce / vibrate, or simply appearing not to move at all.

Edit: PS. I've now watched his video and, of course, one would hardly describe that as "bringing 1 to the magnet." But what it prompts me to add is, if he clamped the magnet so that it did not move so much towards 1, he would have a more spectacular result. Because they are all free to move in his setup, 3 (or in his case 5) is already moving backwards when 1 hits, reducing its final forwards speed.

 

[sophiecentaur]

obviously free to accelerate throughout,

That is the hidden magic in the demo. The ball must be allowed to accelerate in order to provide energy for the loosely attached ball 3. A crude energy level diagram is in one of my posts above.
Looking at that diagram, it strikes me that a totally mechanical version could be made, involving balls and sloping channels. But it would not be as efficient as steel bearings colliding.

 

[RonL]

Now just build a ring with the magnets secured (non-movable) three or four spaced exactly at a proper distance, as one ball is drawn into a magnet the third is moved with force to the next magnet, the movement would continue until physically stopped. Can it do anything useful ?

 

[sophiecentaur]

Now just build a ring with the magnets secured (non-movable) three or four spaced exactly at a proper distance, as one ball is drawn into a magnet the third is moved with force to the next magnet, the movement would continue until physically stopped. Can it do anything useful ?

It would not go on for ever. Once the last ball 3 in the ring reached the next magnet there will be no ball 3 to release and the ball 2 would be bound. End of process with all ball 3s stuck behind all ball 1s.

 

[RonL]

It would not go on for ever. Once the last ball 3 in the ring reached the next magnet there will be no ball 3 to release and the ball 2 would be bound. End of process with all ball 3s stuck behind all ball 1s.

Your right, my brain didn't see the front side after the action. I think David Copperfield would have it working.

ps. Just kidding

 

[sophiecentaur]

Your right, my brain didn't see the front side after the action. I think David Copperfield would have it working.

ps. Just kidding

Haha. I read what you wrote and thought "Perpetual Motion?" It just had to be wrong.

 

[RonL]

Haha. I read what you wrote and thought "Perpetual Motion?" It just had to be wrong.

I won't spend anymore time on it, but changing the permanent magnets to electromagnets can make resetting the balls a reasonable thing, if the ring is in motion.
But that takes us down the forbidden rabbit hole

 

[Stephen Tashi]

My question is where does the energy come from in case B that causes the bearing 3 to shoot away so fast. Is the residual field of the magnet reduced?

A general question is whether there are definite spatial locations "where" potential energy may come from and where it may go to.

That was discussed in https://www.physicsforums.com/threads/does-energy-have-a-position.790771/#post-4966586 (I don't claim to understand all of those answers!)

The question about whether there is a change in the magnetic field seems simple to answer. Allowing for the magnetic permeability of the ball, I'd say that after the collision the magnetic field (of the system as a whole) is stronger some places and weaker at others. But I don't know whether there is a meaningful way to claim that the field is weaker as a whole .

A conceptually simpler situation that balls on a track is the case of a magnet and an metal ball "in free space". When the ball and the magnet begin moving toward each other, they gain kinetic energy. It is natural to think of the kinetic energy as being localized "in the" magnet and "in the" ball. Is potential energy being taken from definite spatial locations in the magnetic field to create the kinetic energy?

 

[sophiecentaur]

But I don't know whether there is a meaningful way to claim that the field is weaker as a whole

The impact could could cause some degradation of the permanent field but is that relevant? It's not that degradation that drives the ball - it's just the asymmetry in the distribution of Potential.