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Weighing with levitation and drop?
Suppose there's a piece of metal inside a closed container filled with air, and the whole set is on a scale. Let's say the scale read W kg.
(a) First we levitate the piece of metal with a magnet. How will the scale read compared with W?
(b) Then we drop it. When it's falling, how will the scale read compared with W?
My guess:
(a) less.
The weight of the piece of metal is suspended by the magnet.
(b) same.
I think of the air inside as water, guessing it doesn't make a difference. Then falling can be thought of as swimming in the water. And I can imagine that if I was swimming in a fish tank, the tank should weigh tank+water+me.
I'm not sure if they're correct, especially of (b). I'm seeking more convincing reasonings about these questions.
Hi u.n. o,
If I were sky diving, I imagine I would feel the 'lift' of the air.
Hi mornings.,
Sorry, it was vague but I implied the magnet is held by the experimenter.
I haven't grasped your reasoning that the reading partly depends on the acceleration of what are inside. Firstly, air molecules in the container are always accelerating, in this case I think the total acceleration is downward because though air molecules are very light, they are affected by gravity. If we drop the piece of metal, I have no idea if the total acceleration will point up or down, because although the piece of metal is falling, the acceleration of the air molecules will be affected.
I heard that a bottle filled with air weighs more than the same bottle filled with hydrogen. Then if we combine what are in the 2 bottles in the same bottle, it should weigh more than any of the first 2 bottles. If we suppose the above assertion is true and if we think of the piece of metal as air lumped together, then (b) sh
-ould weigh more.
Sorry, I meant the (b) should weigh the same as W.
--if we suppose that the bottle filled with hydrogen+air would weigh hydrogen+air+container.
2 Answers
- morningstarLv 71 decade agoFavorite Answer
Backwards.
(a) same
The metal exerts the same force down on the magnet as the magnet exerts up to levitate the metal. The downward force pushes on the scale and is included in the "weight".
(b) less
The magnetic force is gone, but the weight hasn't been felt yet.
Also, in general, no matter what's in your black box, if it's not accelerating, the weight you would register corresponds to the total mass in the box. It could be a box of bees, magnets, ultra-powerful lasers firing downwards, doesn't matter.
A scale doesn't directly measure weight, it measures the upward force it applies. If the box is not accelerating, net force is zero. If no other external force is applies, then the force applied by the scale must have the same magnitude as the weight. However if the box, or anything in it, is accelerating, then net force is not zero. If something in the box is dropping, the net force is down, which means the weight (a force pointing downward) is more than the force applied by the scale (upward). The reading on the scale would be less than the weight that corresponds to the mass of the box.
As to your reasoning:
(a) The magnet is supporting the metal, but what's supporting the magnet?
(b) The difference with swimming is you aren't accelerating.
- u.n. oLv 51 decade ago
(a)
Less
(b) While it's falling, the same as (a). Once it rests on the box bottom again, obviously W.
Your analogy isn't right because in water the water lifts you (Archimedes) while in the case of the magnet the magnetic force exerts an EXTERNAL force on the metal.
