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Magnetic levitation has been used to suspend frogs in midair. I was wondering: Does the animal still feel gravitational pull? I mean: Does the frog feel like an astronaut on the ISS, or does he feel like a trapeze artist suspended by a harness?

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Although weightlessness seems defined in physics, feeling weightless doesn't. For example, space sickness seems to be experienced by about half of the space travellers. The feeling, I think, is part your inner ear (or the frog's equivalent), and part stresses elsewhere in your body. And the parts seem to change with regards to "importance" differently for different persons and for different exposure-times (and perhaps frogs as well). Something like that. Biology might be involved. – Keep these mind Aug 7 '13 at 18:43
up vote 21 down vote accepted

You would feel weightless if every part of your body of mass $m$ would be subject to an upward force equal to $m$ times the local gravitational acceleration $g$. Such an exact part-by-part cancellation is not going to happen via diamagnetic levitation as utilized on the frog in your example. Not only does this levitation couple according to magnetic susceptibility, and not to mass, but more importantly, such levitation relies on inhomogeneous magnetic fields. This means that one or more (central) parts of the frog get pulled up more strongly than other parts.

My guess is that the frog feels less weight but strangely suspended by its stomach.

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This is sound reasoning, but I've seen the video of the frog. Its limbs levitate as well. It may be true that the force support is uneven, but to get the feeling of weightlessness, only certain key areas need to truly be weightless. The inner ear, the digestive tract, the brain, the limbs (in part or whole), and perhaps the skeleton (that would solve most of the rest of the issues). Once you have a few key systems weightless, the brain gets tricked into feeling the full effect. Things like the circulatory system have less sensory nerves, so do not need to be weightless. +1 anyway – Jim Aug 7 '13 at 17:45
This answer is helpful, and I upvoted it (although I regret that now), but, in a way, it is bad. I believe, actually, that it is wrong. First of all, logically, instead of an "only if" or "iff", you come with an "if". (You show that a precise measurement would be not exactly the same, but that wouldn't necessarily create a distinct feeling.) – Keep these mind Aug 7 '13 at 19:03
@Gugg - if I understand you correctly, you agree that a "homogeneous suspension" (suspension force on each and every body part in proportion to its mass) is required to feel weightless. You also agree that the frog is not homogeneously suspended. However, you doubt if the inhomogeneous components in the suspension are strong enough to be sensed by the frog. This is a physics site and not a biology site, and the fundamental point needs to be made that homogeneous suspension is not achieved in the example provided. Questions on tresholds for sensory perception have no place here. – Johannes Aug 8 '13 at 1:58
@Gugg - on the "only if" vs "if" issue: I stand by my wording. An "only if" or "if and only if" would by logically incorrect as next to "homogeneous suspension" weightlessness can also be achieved by "no suspension". – Johannes Aug 8 '13 at 2:01

The feeling of weight is caused by contact forces acting on only parts of your body: forces like the pavement pushing on your feet, air rushing past certain parts of your body as you fall at terminal velocity, the floor of an elevator pushing with reduced force on your feet as the elevator starts its downward trip. Basically you feel one part of your body pressing or pulling on other parts to keep them all together.

Gravity is a distributed force. It acts on each particle of mass identically (with rare exceptions: See Larry Niven's, Neutron Star) Your body does not need any internal forces to keep all the parts together, and you feel "weightless".

With regard to floating submerged, you are suspended by the difference in hydrostatic pressure at the top and bottom of each element. Buoyancy is volume-based, not mass-based. To the extent that there are variations in density in your fluid filled body, you will feel weight floating in water. Consider, for example, the crew-members in a (non-flooded) submarine.

With regard to magnetic levitation, Johannes' answer above is correct. To the extent that various masses in the frog's body experience magnetic forces not in proportion to their mass, the frog will experience "weight".

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This is the correct answer. The only way to stop feeling weight when under the influence of gravity is to stop fighting gravity with another force. This applies equally to people standing on the ground or in a magnetically levitating train. Astronauts in the ISS are weightless because they are constantly falling, as is someone who is in a falling elevator. – Bringer128 Aug 8 '13 at 0:04

The trapeze harness feeling comes because even though you are suspended, the harness is exerting a normal force on you. an easy way to think of this is that you still have gravity pulling all of your organs down. The frog, on the other hand, experiences none of that. The electromagnetic force is acting on all parts inside and outside of its body; it completely cancels gravity. Thus, it would feel weightless.

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I'm not quite convinced - after all, underwater I also feel weightless although the surrounding water is pushing me up by a normal force. On the other hand, one of those big turbines supending wanna-be skydivers does not produce weightlessness - at least I think they can still feel gravity. – yippy_yay Aug 7 '13 at 14:59
@SebastianHenckel I disagree with Jim. Even when standing on the ground, the normal force exerted by the ground perfectly cancels with gravity. But we still feel our weight. I think it's because of the pressure felt by our legs and not the net force. Unfortunately, a google search only returns how we feel on weight loss! – udiboy1209 Aug 7 '13 at 15:15
If you think about it, there actually is a net force working on astronauts in the ISS, since they are kept in an orbit, while there is no net force working on me in my chair. I'm tempted to think that feeling weightless means accelerating exactly as fast as gravity wants you to. This seems to be consistent with free fall-weightlessness, ISS-astronauts as well as hypothetical deep-space-astronauts... hmm. Anyway, that would mean that the frog doesn't feel weightless, because he's not accelerating, even though gravity wants him to. – JSQuareD Aug 7 '13 at 15:25
@JSQuareD, I think thats the correct answer to this question, that you only feel weightless when in free-fall. – udiboy1209 Aug 7 '13 at 15:27
@udiboy thanks, I'll make it an answer :) – JSQuareD Aug 7 '13 at 15:29

There are different components to feeling weightless.

You can partially simulate weightlessness with neutral bouyancy in water. This makes gross physical activity feel like it would when weightless (well: weightless and immersed in a dense, viscous medium).

Furthermore, divers have great difficulty sensing "down" even when bouyant, so in that sense also they "feel" weightless (at least, they fail to feel their weight). Any form of support that's spread as evenly over the body as the force from an external fluid would feel about as weightless as that.

However, it's possible for a diver to have a sense of "down" from e.g. the inner ear or the organs. Humans shouldn't count on that to get to the surface in the dark, I don't know whether frogs can. An accelerometer in an air bubble in a box would of course work even if the overall gadget is neutrally bouyant. I believe that training underwater is not a good predictor of how dizzy/nauseous you'll feel in freefall, so clearly the feeling is different even if not obviously so. In some sense a highboard diver has more claim to feeling weightless than a deep sea diver -- aside from air resistance anyone falling does at least have uniform forces throughout their body.

Now, diamagnetic levitation is not a force from an external fluid, it's internal. With sufficiently even diamagnetic levitation you'll feel at least as weightless as you do when neutrally bouyant in water and possibly more so. So if you're happy to call that "feeling weightless", the frog would feel weightless in a flat magnetic field.

But aside from the shape of the magnetic field, the levitation will not be perfectly even, because your body is not universally diamagnetic: some parts are wetter than others, or perhaps more formally magnetic susceptibility need not be uniform throughout the materials of the body. So the question is whether the frog can detect the unevenness of the levitation. If not then it feels weightless. Probably the answer is like water for humans -- it's distinguishable from freefall, but the direction of the weight is not immediately obvious.

Then again, if a particular frog is vomiting copiously in freefall but not in magnetic levitation it will tell you "sure, it feels very different". Vomiting feels different from not vomiting, regardless of how subtle was the effect on its ears that caused it to vomit!

What you feel in a harness is a force equal to your weight exerted on a few square inches that are not any of the usual few square inches "designed" for that purpose. So magnetic levitation would only feel like a harness if the levitation is primarily of a few small parts of the body, with much less or no force on the rest. I do not believe that this is generally the case, and those levitating frogs don't have their limbs dangling downward, but it's possible that it is.

So, you've got your theory and then you've got your messy practical details of the construction of strong magnets and of frogs. I suspect it really comes down to what the frog is trying to achieve, and what fine mechanisms frogs have that can detect "down".

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As I mentioned in my comment, it seems you will feel weightless when the net force exerted on you is equal to the force of gravity. (So basically, gravity is the only force in play)

This is consistent with the fact that astronauts in the ISS are weightless even though they do experience a net force (they are being kept in a orbit around earth, after all). It also plays very nicely with people in free fall feeling weightless (until air resistance kicks in anyway), and hypothetical astronauts in deep space feeling weightless (no gravity, no net force).

This makes sense when you consider the definition of weight. Weight is the force you are exerting on the earth (or whatever connects you to the earth), not the other way around.

In the case of the frog suspended in a magnetic field (as well as hanging in a trapeze) there is no net force, but there is gravity, therefore the frog will experience his normal weight. In this case, the force on the earth is exerted via the magnetic field.

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