Magnetic Levitating Globe Weight

[tionis]

If I put one of those magnetic levitating globes on a bathroom scale, will the scale register the weight of the base only, or the suspended sphere, too?

http://www.magneticfloating.com/photo/pc1358779-magnetic_levitating_globe_8_globe_floating_and_spinning_ufo_base_floating_display.jpg

 

[Drakkith]

It will measure both the base and the sphere.

 

[tionis]

Drakkith, is it because the sphere is pushing down on the magnetic field which in turn pushes down on the base and ultimately on the scale? Is that what's happening?

 

[Drakkith]

Drakkith, is it because the sphere is pushing down on the magnetic field which in turn pushes down on the base and ultimately on the scale? Is that what's happening?

Yep.

 

[tionis]

I must say I'm somewhat dissatisfied with my own explanation :(

Anyone here care to explain why the hovering ball contributes to the weight?

What formula do you use for it?

 

[eigenperson]

What's wrong with your explanation?

Something is exerting a force upwards on the ball equal to the weight of the ball. What is it? Clearly, it's the base, because if you take the base away, the ball falls to the earth. The mechanism by which this force is exerted may be complicated, but it doesn't matter -- we know the force is there, because the ball isn't accelerating despite the force of gravity pushing on it.

Therefore, by Newton's 3rd law, the ball is exerting a force downwards on the base equal to the ball's weight. That is exactly the same as though the ball were sitting on the base. Again, the mechanism may be complicated, but it doesn't matter.

 

[tionis]

because the ball isn't accelerating despite the force of gravity pushing on it.

But isn't the ball being accelerated upwards by the normal force?

 

[SteamKing]

Not unless the normal force is somehow greater than the weight of the globe itself.

Obviously, when levitated, whether by magnets or an invisible string, the globe is stationary with respect to the base. This implies that there is no net force acting on the globe itself. Now, the globe is being attracted to the Earth by gravity, and the magnetic field is pushing back against the globe. However, the distortion in the magnetic field caused by the globe trying to fall to Earth is not confined just to the interface of the globe with the field. The distortion in the mag field also carries around to the base, because the field is trying to redistribute itself to accommodate the distortion caused by the globe. This will cause the mag field to generate a force on the base, which is equal to the weight of the globe.

 

[tionis]

Not unless the normal force is somehow greater than the weight of the globe itself.

This implies that there is no net force acting on the globe itself.

the magnetic field is pushing back against the globe.

I don't understand this. If the magnetic field is pushing back against the globe, doesn't that mean that the magnetic field is accelerating the globe away from its free-falling trajectory?

 

[ModestyKing]

Acceleration means a change in velocity.
The ball isn't moving, so there's no velocity, therefore, no acceleration (because that 0 velocity isn't changing).
What you mean to say is that the magnetic field is balancing out the force of gravity. However, the base repels the sphere at the same time as the sphere repels the base - that's the nature of a magnetic field. You don't just have proton x repel proton y, proton y is also repelling proton x. That's electricity, I know, but a fine enough analogy.

So the sphere is pushing down on the base as well. So the base is registered as heavier. :)

 

[SteamKing]

Think of it this way: when you are standing on the ground, there is a normal force created underneath your feet. Does this normal force cause you to accelerate upward away from the earth? Obviously not, otherwise the air would be filled with people, animals, and things being flung upward. You must look at ALL of the forces acting on a body before you can conclude that motion can (or should) take place.

F = ma should be rewritten so that it reads Fnet = ma.