Love it, as with just about anything with Sixty Symbols.

I'd like to know why two balls broke off, rather than one, which is what happens in Newton's Cradle, no matter how hard to smack them. The row of particles has no way of knowing that the incoming particle was accelerated before it struck, so there must be something else at work here. I wonder if it's the incoming particle shifting the whole mass in the negative direction as it pulls on the magnet, and if the magnet were fixed in place if just one ball would move off.

Try splitting the beads in a Newton's cradle so there are more than one swinging in at the end, like this:


It's not that the balls know anything in particular, it's that the momentum generated by a single ball is enough to dislodge an equal ball from the other end. In the case of the three balls, there is the right amount of momentum to dislodge three balls.

Now, when we have a magnet involved the single bead is accelerated towards the magnet at a great rate of knots imparting extra momentum so it's now equivalent to many balls (with just gravity) and the only thing stopping all the balls on the other side of the magnet flying off is that the same magnetic force is stopping the closer ones from moving.
>> ^messenger:

Love it, as with just about anything with Sixty Symbols.
I'd like to know why two balls broke off, rather than one, which is what happens in Newton's Cradle, no matter how hard to smack them. The row of particles has no way of knowing that the incoming particle was accelerated before it struck, so there must be something else at work here. I wonder if it's the incoming particle shifting the whole mass in the negative direction as it pulls on the magnet, and if the magnet were fixed in place if just one ball would move off.

that was brilliant, quite unexpected (for me at least)

I know that multiple balls hitting one side will cause multiple balls to be released from the other side, but momentum isn't measured by counting the incoming particles; it's measured by mass*velocity, and that's all. One ball hitting with great speed usually releases one ball at great speed out the other side. Two balls with very low speed, even with less total momentum than the single fast-moving ball, will release two balls from the other side at the same low speed. It's something about the number of particles, not their momentum, that determines how many are ejected.>> ^oritteropo:

Try splitting the beads in a Newton's cradle so there are more than one swinging in at the end, like this:
[embed removed]
It's not that the balls know anything in particular, it's that the momentum generated by a single ball is enough to dislodge an equal ball from the other end. In the case of the three balls, there is the right amount of momentum to dislodge three balls.
Now, when we have a magnet involved the single bead is accelerated towards the magnet at a great rate of knots imparting extra momentum so it's now equivalent to many balls (with just gravity) and the only thing stopping all the balls on the other side of the magnet flying off is that the same magnetic force is stopping the closer ones from moving.
>> ^messenger:
Love it, as with just about anything with Sixty Symbols.
I'd like to know why two balls broke off, rather than one, which is what happens in Newton's Cradle, no matter how hard to smack them. The row of particles has no way of knowing that the incoming particle was accelerated before it struck, so there must be something else at work here. I wonder if it's the incoming particle shifting the whole mass in the negative direction as it pulls on the magnet, and if the magnet were fixed in place if just one ball would move off.

My own prediction was that one particle would come out the other side, be unable to escape the magnet, the magnet would pull it back, and the original particle would be sent back the way it came with equal speed, initially fast, then slow down and almost get back where it started. Oh well. That's why we have science.>> ^ghark:

that was brilliant, quite unexpected (for me at least)

>> ^messenger:

I know that multiple balls hitting one side will cause multiple balls to be released from the other side, but momentum isn't measured by counting the incoming particles; it's measured by mass velocity, and that's all. One ball hitting with great speed usually releases one ball at great speed out the other side. Two balls with very low speed, even with less total momentum than the single fast-moving ball, will release two balls from the other side at the same low speed. It's something about the number of particles, not their momentum, that determines how many are ejected.

As you said momentum is mass*velocity, and force is mass*acceleration.

It's the mass of the particles entering that determines the mass of the particles leaving.
As the balls in a Newton's cradle all have equal mass it's tempting to restate that as the number of particles rather than the mass of the particles.
However if you designed a cradle to have four 1kg balls and one 2kg ball then swinging the 2kg ball would cause two 1kg balls to be displaced. (The same effect as taping or gluing two 1kg balls together.)

In a normal Newton's Cradle the acceleration, due to gravity, is constant.
The constant mass and constant acceleration cause the predictability, as the only energy lost is to air resistance and other negligibles such as sound or minimal compression of the balls on impact.

The forces introduced by the magnet scale inversely with distance, making the outcome a lot more unpredictable.

This thread has gotten me very curious to try all these things out for myself.

As far as equally weighted particles go, what you describe is not what we observe. We always see the same number of particles leave as came in, no matter their total momentum. A single particle going 1m/s ejects one particle also going 1m/s (I'm talking in ideal terms). A single particle going 2m/s doesn't release two particles going 1m/s, just one going 2m/s. The same particle going 100m/s likewise doesn't release 100 particles going 1m/s, nor 50 going 2m/s nor any other combination. As the force passes through the stationary particles, there's nothing to say what the mass or velocity of the striking particle was, just what the product of those two things was.

As for different sized particles, not having seen this done, if a solid (I mean a single piece, or welded together) 2kg particle came in at 1m/s, I predict a single 1kg particle would be ejected at 2m/s. My reason is the same as above: that when one ball strikes, the only information transmitted through the stationary particles is the total amount of force, not the velocity or mass of the striking object. Thus, the force transmitted through the stationary particles would be identical whether a 1kg ball struck at 2m/s or a 2kg ball struck at 1m/s. All this force is transmitted into the last ball which leaves with the same amount of force in the form of velocity as a factor of its mass, whatever that may be.

I think fusing the two balls together would fundamentally change their behaviour. I think when two loose balls hit together, the first one hits the stationary ones, bounces back towards the second ball which then stops, sending a second shock wave through the stationary particles, thus sending two signals very close together, and releasing two particles out the other side.

To continue the thought experiment, what if it were a 1.2kg particle striking a row of 1kg balls? I think it would be one particle going out at 1.2m/s, rather than 1 particle at 1m/s and a second at 0.2m/s or two of them together at 0.6m/s.>> ^heathen:

As you said momentum is mass velocity, and force is mass acceleration.
It's the mass of the particles entering that determines the mass of the particles leaving.
As the balls in a Newton's cradle all have equal mass it's tempting to restate that as the number of particles rather than the mass of the particles.
However if you designed a cradle to have four 1kg balls and one 2kg ball then swinging the 2kg ball would cause two 1kg balls to be displaced. (The same effect as taping or gluing two 1kg balls together.)
In a normal Newton's Cradle the acceleration, due to gravity, is constant.
The constant mass and constant acceleration cause the predictability, as the only energy lost is to air resistance and other negligibles such as sound or minimal compression of the balls on impact.
The forces introduced by the magnet scale inversely with distance, making the outcome a lot more unpredictable.

That shoulda been @oritteropo too.

Thanks

I was actually going to suggest that the first part of the experiment should be fairly easy to replicate, with a track and marbles or ball bearings or similar. Unless you have a constant grade the velocity (and therefore momentum) calculations will be a bit tedious, and it occurs to me that angular momentum may have some effect too, so perhaps a video camera and some marks on the track (or sensors and a microcontroller) to directly measure the velocity just prior to impact would be easier. To confirm or disprove my assertion you want to keep increasing the momentum of impact until it's more than the momentum of a two balls, and see what happens.

There are videos of a Newton's cradle type setup only with different sized balls, I might go looking tonight.

p.s. Didn't find that one, but did find a good explanation of the one vs two ball collision issue in Newton's cradle:



Based on that, I wonder if a slowmo of the ball in the original video might've shown that it bounced slightly before coming to rest?
>> ^messenger:

That shoulda been @oritteropo too.

The cradle is better than the track because it allows for larger weights, where the track would require a denser material or hollow particles; but the track is easier for measuring incoming and outgoing force because on a steady grade, it’s simply a measure of distance, which is easy to capture roughly, even without a camera.

If momentum = velocity*mass, then doubling the velocity will double the momentum. Using the cradle, if you drop a ball from very very close to the first stationary ball, a single ball will move from the other side and move a very very short distance. If you then drop the ball from perpendicular, a single ball will move from the other side, and rise to (nearly) perpendicular. I have seen this much in my own observations. I don't think we need to do any calculations to understand that the impact velocity in the first essay is way less than half the impact velocity in the second essay (we don’t need exact numbers; we just need to know that the impact velocity is more than double). That means we have met your criteria for increasing the momentum to more than that of two balls at the first velocity, yet one ball still comes out.

A mental model to demonstrate my theory of “two particles in = two impacts = two particles out” is to imagine a bit of sponge between the last two balls in a Newton’s cradle. Pull the second ball out (which will push the first ball ahead of it) to a great enough height that the momentum of the outside ball’s impact is enough to completely squeeze the sponge and cause a second impact wave. The second ball would impact measurably later than the first, and before the ejected particle came back. Pretty clearly, two balls will emerge from the other side. This is what I think is happening on a micro scale when two independent balls are dropped together.>> ^oritteropo:

Thanks <img class="smiley" src="http://cdn.videosift.com/cdm/emoticon/smile.gif">
I was actually going to suggest that the first part of the experiment should be fairly easy to replicate, with a track and marbles or ball bearings or similar. Unless you have a constant grade the velocity (and therefore momentum) calculations will be a bit tedious, and it occurs to me that angular momentum may have some effect too, so perhaps a video camera and some marks on the track (or sensors and a microcontroller) to directly measure the velocity just prior to impact would be easier. To confirm or disprove my assertion you want to keep increasing the momentum of impact until it's more than the momentum of a two balls, and see what happens.
There are videos of a Newton's cradle type setup only with different sized balls, I might go looking tonight.
>> ^messenger:
That shoulda been @oritteropo too.

Yes I found a reasonably clear explanation, and added it as a postscript to my earlier comment after you'd quoted it, but before I got the e-mail notification.
>> ^messenger:

[...]
If momentum = velocity mass, then doubling the velocity will double the momentum. Using the cradle, if you drop a ball from very very close to the first stationary ball, a single ball will move from the other side and move a very very short distance. If you then drop the ball from perpendicular, a single ball will move from the other side, and rise to (nearly) perpendicular. I have seen this much in my own observations. I don't think we need to do any calculations to understand that the impact velocity in the first essay is way less than half the impact velocity in the second essay (we don’t need exact numbers; we just need to know that the impact velocity is more than double). That means we have met your criteria for increasing the momentum to more than that of two balls at the first velocity, yet one ball still comes out.
A mental model to demonstrate my theory of “two particles in = two impacts = two particles out” is to imagine a bit of sponge between the last two balls in a Newton’s cradle. Pull the second ball out (which will push the first ball ahead of it) to a great enough height that the momentum of the outside ball’s impact is enough to completely squeeze the sponge and cause a second impact wave. The second ball would impact measurably later than the first, and before the ejected particle came back. Pretty clearly, two balls will emerge from the other side. This is what I think is happening on a micro scale when two independent balls are dropped together.

I think that's what we would see. It also follows that the first ejected ball would leave with a much greater velocity than the second ejected ball as the second collision from the incoming ball would have been much smaller. Now I want to know what would happen if there was only one ball after the magnet. What do you think?>> ^oritteropo:
Based on that, I wonder if a slowmo of the ball in the original video might've shown that it bounced slightly before coming to rest?

Well it's only a guess, since I'm too lazy to do the calculations , but I don't think the kinetic energy from the impact would be sufficient to overcome the very large magnetic force, so click and no ball ejected.
>> ^messenger:
[...] Now I want to know what would happen if there was only one ball after the magnet. What do you think?

I think ideally, as momentum must be conserved, that the ball would come in, the other ball would be ejected, and decelerated until it escaped the magnetic pull going the same speed as the incoming ball was before it started accelerating.

On a real physical track like this with friction and sound energy loss, I think the ball would be ejected, not overcome the pull of the magnet, and get sucked back pretty quick. It may strike hard enough to send the other ball out a bit, but after very few iterations, they would be all stuck together.

I haven't thought yet about the effect of the magnet moving towards the first ball as it approaches. Maybe this has no net effect at all.>> ^oritteropo:

Well it's only a guess, since I'm too lazy to do the calculations , but I don't think the kinetic energy from the impact would be sufficient to overcome the very large magnetic force, so click and no ball ejected.
>> ^messenger:
[...] Now I want to know what would happen if there was only one ball after the magnet. What do you think?

Momentum can be conserved in a number of ways, and my thought was that if the ball is really stuck to that magnet then rather than ejecting the ball on the other side, the whole lot might just move along the track together. If you've ever played with neodymium magnets you'll know why I think that, the amount of effort required to unstick something from them is surprisingly large.
>> ^messenger:

I think ideally, as momentum must be conserved, that the ball would come in, the other ball would be ejected, and decelerated until it escaped the magnetic pull going the same speed as the incoming ball was before it started accelerating.
On a real physical track like this with friction and sound energy loss, I think the ball would be ejected, not overcome the pull of the magnet, and get sucked back pretty quick. It may strike hard enough to send the other ball out a bit, but after very few iterations, they would be all stuck together.
I haven't thought yet about the effect of the magnet moving towards the first ball as it approaches. Maybe this has no net effect at all.

Yep, I think you're right. My prediction above could only happen with initial speeds massive enough for the outgoing particle to overcome the magnetic pull, or with the magnet fixed to a spot on the track.

My next question is about why in this video the incoming ball hits twice. In a cradle, it only hits once, and all force is transmitted through the chain of balls in a single pulse, ejecting just one ball. Why should it be different with a magnet? Arguably, it should stick even stronger if there's a force holding it there. Maybe the difference is that in this video the ball is accelerating as it strikes, whereas in the cradle, as the ball's direction approaches level, it's acceleration goes down to zero, so that the moment of impact, there's zero acceleration happening.

An experiment to test this: get a track with a steady slope, and several balls. Hold a group of balls around the middle of the track, and a single ball well above them. Release the single ball towards the group, and before it strikes the group, release the group. The single ball will be accelerating relative to the group and eventually strike it. We can see how many balls are ejected out the front of the group. If more than one, then it's confirmed. If only one, then it's disconfirmed, and probably has something to do with magnetic attraction specifically.>> ^oritteropo:

Momentum can be conserved in a number of ways, and my thought was that if the ball is really stuck to that magnet then rather than ejecting the ball on the other side, the whole lot might just move along the track together. If you've ever played with neodymium magnets you'll know why I think that, the amount of effort required to unstick something from them is surprisingly large. [minor edit]

*learn

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