How much does a falling magnet weigh ?

[dipsydoodle]

[jimlup]

1. Love to show this to my students when we hit Faraday's law.

Which we'll be at in about 2 weeks.

[caraher]

2. Last months AJP had a nice investigation of this

Usually I just talk about this qualitatively, but this recent paper does a nice job developing a quantitative model backed by experiments.

[Jim Lane]

3. One thing I didn't understand

Near the end the presenter shows that the magnet weighs 370 grams. But that's the result you'd expect if the magnetic force had totally offset gravity, so that the magnet was suspended within the tube. In fact, eyeballing the magnet's fall suggests that the damping force was a significant fraction of the force of gravity but was still less. If, for example, the magnet's net downward acceleration in the metal tube was half what it would have been in a cardboard tube (and, as usual, ignoring air resistance), then wouldn't the metal tube have gained half the weight of the magnet, rather than an identical amount?

[Paulie]

4. He should have been describing the mass not weight

Weight is mass relative to the gravitational field it's in.

If you watch the balance scale during the decent portion it goes up about the same rate as when he just measures he magnet alone. The mass suspended in the magnetic field pulls downward on the tube showing the increase of "weight".

[Jim Lane]

5. Sorry, I still don't understand.

Let's say, for example, that he put a dinner plate on top of the tube, noted the total mass as per the scale, and then put the magnet on top of the dinner plate. The reading on the scale would obviously increase by 370 grams. The magnet would be pushing down on the plate-and-tube combo with a force equal to its mass times the acceleration due to gravity (roughly 32 feet per second squared).

You write that, in the actual (plateless) experiment, "The mass suspended in the magnetic field pulls downward on the tube ...." But what's the force with which it pulls downward? Whatever it is, the tube (by means of its magnetic field) exerts an equal and opposite force on the falling magnet. If that force is of the same magnitude as that in my dinner-plate example, then it would exactly offset the force of gravity, and the magnet would remain suspended, not falling at all. Yet we see that it does fall. Therefore, the force exerted on the magnet by the tube must be less than the force of gravity, and the equal-and-opposite force exerted on the tube by the magnet must also be less than the force of gravity, and must therefore be less than the force exerted on the tube by the magnet when it was resting on the plate. So if putting it on a plate causes the reading on the scale to go up by 370 grams, shouldn't letting it fall slowly through the tube cause the reading on the scale to go up by some amount that's greater than zero but less than 370 grams?

[caraher]

7. You're confusing velocity and acceleration

What's happening to the magnet is just like what happens to a parachutist, except in the latter case it's air drag rather than magnetic forces doing the braking.

Someone from a very great height with a parachute initially accelerates downward, because at low speed the weight vastly exceeds air drag. But as she speeds up, drag forces increase, and the acceleration approaches zero as the drag force approaches her weight. At this point she falls at "terminal velocity" - a constant velocity motion. It is not true that when a force "would exactly offset the force of gravity" the object "would remain suspended, not falling at all."

Substitute magnetic force for drag and magnet for parachute jumper and you have exactly the same physics. Put differently, by your argument, skydivers would have the problem of getting stuck in mid-air!

Remember, Newton tells us F=ma, not F=mv!

[Jim Lane]

10. I drew that distinction correctly but I didn't understand how the force worked.

I relied on F=ma (in #5) and I was citing acceleration, which I measured in feet per second squared. Velocity, of course, would be measured in feet per second.

What I didn't know was what muriel volestrangler explained in #6, that the magnetic force, unlike the gravitational force, varied over time (see my #9).

[muriel_volestrangler]

6. Your 'eyeballing' may be at fault here

To me, it looks more like the magnet reached a terminal velocity, which would mean the magnetic force was balancing the gravitational force (note: this wouldn't be "suspended within the tube" - just moving at a constant velocity - net downward acceleration of zero). You're saying you think it was still accelerating.

Reading your 2nd post - he's not saying the force was equal to the weight right at the top of the tube the moment he let go - then it would float at the top. It builds up a bit of speed at first, but that also increases the induced magnetic field, which in turn builds up the magnetic force, until it balances the gravitational force. So by the time he looks at the weight measurement, it has reached the weight of the magnet, indicating it's also reached its terminal velocity.

[Jim Lane]

9. No, I think it's that I was assuming a force of constant strength.

You write: "It builds up a bit of speed at first, but that also increases the induced magnetic field, which in turn builds up the magnetic force, until it balances the gravitational force."

The downward force of gravity is constant (the increase as the magnet descends, because it's slightly closer to the center of the Earth, being negligible). I assumed that the upward force due to the magnetic field, whatever its value might be, was also constant. I'm not familiar with the properties of induced magnetic fields. If, as you say, the strength of the field varies according to the speed of the magnet, then that would explain my error -- an implicit assumption was wrong. The magnetic force started out being very small, but it increased until it was strong enough to precisely offset the gravitational force.

Thanks for the explanation!

[AtheistCrusader]

8. 1 minute in: prediction, the tube gets heavier.

The magnet is riding magnetic friction as it induces current in the tube, so the tube is 'carrying' the weight of the magnet, just as it would if the puck was riding mechanical friction down the center of the tube.

Edit: yup

[caraher]

11. Another fun video

[Thor_MN]

12. Would the magnet suspend in a rotating horizontal tube?