Centrifugal Force Question

[blamski]

i've been thinking for a while about how to reproduce or somehow replicate the lesser gravity of smaller planets for some of my experiments and projects. it'll be no news to anyone here that micro gravity is a very hard thing to replicate for anything more than a few fleeting seconds through parabolic flights or on a tiny scale via magnetic levitation.

 

another facet of my space obsession was making me think about ideas such as the stanford torus and other artificial gravity solutions that rely on centrifugal force to push an object or body outwards against another surface. then i began to wonder what would happen if instead of using this same rotation to push something against the inside of the 'wheel', what would be the effect on something on the outside of the wheel. this would be a similar effect as we see in the centrifugal governer, or the clutch, wouldn't it? is this what is known as reactive centrifugal force?

 

if one was an ant, for example, sitting on the tire of a bicycle rotating at 30rpm, for example, would one sense a lessening of gravity similar to a passenger on a parabolic flight or a car going over a humpback bridge?

 

i was wondering if any of the many physics or maths experts would be able to explain this a little... :)

[Buffy]

The magnetic levitation and the centrifugal force cases are a bit different but similar insofar as the state of the "ant" and the outside of the system relative to any existing sources of gravity are what are important.

 

For magnetic levitation: Say you built a clear hollow ball with magnets placed at strategic places around it to allow you to levitate it with an external structure with magnets built into it. Obviously you have counteracted gravity because the ball is floating. But now imagine that you've put a wooden ball inside the clear one. If your whole structure is sitting on Earth, do you think the wood ball will levitate?

 

Answer: no, because it is unaffected by the magnets and is subject to Earth's gravity, so it will sit at the bottom of the clear ball.

 

Centrifugal force (okay for purists, it's NOT a "force" and in fact what I'm describing here actually shows it, so PPbbbbttt!) is a bit different. The way it works is that the object inside the centrifuge has to be moving along with the centrifuge: an object sitting on the curved outside wall "stays there" in spite of gravity because friction with the wall is actually pushing it constantly in a line tangent to the circular wall, and the wall being there keeps it from going straight, and that causes the "force" that counteracts gravity.

 

Imagine that your centrifuge is spinning vertically on Earth (ferris wheel orientation). If you take a ball and hold it a little bit under the axis and drop it. it falls directly down due to gravity. If you hold it *above* the axis and drop it, it will also fall directly down: the fact that the centrifuge is spinning around it has no effect on it.

 

Now imagine you're in the Int'l Space Station with the same set up. What happens when you drop the ball? Nothing: it just floats there while the centrifuge spins around it. That's because the ball is falling around the Earth along with the rest of the ISS and it's going to act just like it's Frame of Reference.

 

So the point here is that in either case, unless the "ant" is physically connected to the apparatus, the mechanism that mimics microgravity is going to have no effect on him.

 

Now to take your specific question, if the ant is on the *outside* of the centrifuge and holding on for dear life, it'll feel kinda like falling, but the G-Forces will be identical to what he'd experience on the inside, it's just that his arms would be a lot less tired if he was inside. If he let go, he'd experience the same trajectory as if he was shot from a slingshot aimed tangent to the centrifuge outer wall, subject to either the presence or absence of gravity, that course being either parabolic (on the earth) or straight (on the ISS, and only "mostly straight" because you've still got "microgravity" in that case).

 

So, the point here is that while hanging on (and this by the way goes for magnetic levitation too), that ant is still going to be subject to g-forces dominated either by the surrounding gravitational effects of being on earth or in orbit, or the centrifugal "force" created by movement while "hanging on", and thus does not actually produce microgravity *until* you let go, and then you've got the good ol' Vomit Comet effect, which is indeed microgravity (but only in your reference frame!)

 

I keep the subject of my inquiry constantly before me, and wait till the first dawning opens gradually, by little and little, into a full and clear light, :phones:

Buffy

[blamski]

thanks for putting my thoughts in order, buffy. if only amelius was about he could even draw me a diagram...

 

but what about if the ant was contained in a vertical tube, made of an almost frictionless material, fixed perpendicular to the wheel? at varying rotational speeds the ant would be subject to a force (that isn't really a force) that would case it to move against its will towards the outer end of the tube? or would it...?

 

if i'm trying, for the sake of an example, to centrifuge out some fruit jiuce from its pulp and i don't have a centrifuge, i might try tieing a container of the pulp and juice mix to the end of a string and swinging it rapidly around my head. the heavier pulp moves towards the end of the container. unfortunately my hands are a bit slippy with fruit and i ket go of the string. its flies of in and outward direction from the point at which it was realeased.

 

does this have anything at all to do with what i'm trying to think about...?

 

 

the magnetic levitation i was thinking about was diamagnetic levitation - using superconductors to magnetically repel water. also a bit tricky for the home enthusiast...

 

Edited May 31, 2013 by blamski

[CraigD]

i've been thinking for a while about how to reproduce or somehow replicate the lesser gravity of smaller planets for some of my experiments and projects.

You can’t, other than by some weirdly impractical means (a couple of which I’ll mention below) replicate continuous lesser gravity like you’re describing any way short of flying it in a spacecraft orbiting the Earth, but depending on what your experiment is, you may not need to. For example, folk have shown that you can produce the effect of lesser gravity on plants in simple table-top devices known as clinostats, not by reducing the force of gravity on a plant, but by constantly changing its direction so that there is not preferred “down” direction, or the force in a preferred direction averages to a desired amount (eg: 1/6th to simulate how the plant would grow on the Moon’s surface).

 

In a lab such as one on an orbiting spacecraft, it’s easy to simulate the surface gravity on any moon or planet’s surface: just spin your lab in a centrifuge to produce the matching centrifugal pseudo-force. On Earth’s surface, you can only produce forces greater than 1 g (about 9.8 m/s/s). “Upside down” centrifuges with their “floors” on the outside of them are simply impossible – the orientation of the floor of a centrifuge, and the acceleration it produces on its sample, depends entirely on the speed and radius of the centrifuge and the acceleration of gravity where it’s set.

 

Here are a couple of the weirdly impractical ways to replicate lesser gravity:

1. Drill a straight tube through the Earth to connect any 2 point same-altitude point on its surface, and travel through it in some sort of vehicle. You’ll almost certainly have to seal and remove the air from the tube, to allow the vehicle to move freely. If you drill it vertically, directly through the center, you can simulate any lesser gravity, from zero to whatever acceleration the vehicle can produce. Drill it at angles other than vertical, and the minimum gravity that can be simulated increases.
   
2. Suffuse every material in the sample you wish to simulate lesser gravity for with a magnetic material, and place it in a nearly “flat” magnetic field.
   

There are I expect other weirdly impractical schemes, but, being weird and impractical, if you need to simulate lesser gravity for long periods, practically, you either need a spacecraft, or a clinostat.

[Guest Aemilius]

Hey blamski.... Did those responses answer your question?

[blamski]

hi all

 

 

yeah, i'd been looking at clinostats but they come with their own issues. however, without getting hold of a superconducting magnet they're about the best one could hope for.

 

aemilius - yes, pretty much thanks. basically my understanding of gravity and its relationship to centrifugal 'force' is woefully inadequate. and however much you might desire it, basic physics cannot be overcome.

 

<_<

[Guest Aemilius]

I know you said you're done with it, but I might just play around with it for another minute. So let me see if I have this straight....

 

Centrifugal force.... To satisfy the conditions required for the production of a lasting microgravity environment using reactive centrifugal force, said reactive centrifugal force must continuously act in equal and direct opposition to the force of gravity, a scenario that's only sustainable when the center of gravity and the center point around which the object is revolving are the same, as in the case of an object (like the International Space Station) in uniform circular motion around the Earth. Any other scenario will only produce a cyclic effect, genuinely reproducing the microgravity environment, but only for a very brief period of time (like the NASA training aircraft, the ant on the revolving vertically oriented bicycle wheel, the car going over the hill, etc., etc.).

 

The clinostat.... I suppose the clinostat would work, but like you said, it has issues. It really just approximates the microgravity environment rather than genuinely reproducing it (open to correction). It may be useful for observing the complete life cycle of very small plants, like moss for instance, but for larger plants, it would only be useful during germination and perhaps the initial early stages of growth, since as the plant grew past a certain critical size, it would begin to flop about, destroying the effect.

 

Diamagnetic levitation.... As in the case of the frog, diamagnetic levitation can genuinely reproduce the microgravity environment but the cost is prohibitive. That could change with advances in permanent magnet field strength. The field strength used for the diamagnetic levitation of the frog was 16 Teslas. The strongest permanent magnets currently available are 1 Tesla. Barring some sudden breakthrough.... no help there for the foreseeable future.

 

So far it's a bust. A couple of other possibilities....

 

Neutral buoyancy.... In order for that to work one would have to employ some kind of inert carbon dioxide gas carrying fluid. Perfluorocarbon maybe? The delivery of nutrients would have to be worked out. You'd also have to find a way to adjust or "tune" the specific gravity of the fluid so that the plants tendency to float equaled its tendency to sink.

 

Air pressure.... Restrain the seed/plant in the center of a vertical transparent tube with some sort of adjustable "halo" arrangement that would allow for growth and pass air under pressure (humidified to prevent drying) up the tube. The delivery of nutrient laden water to the plant could be accomplished by installing a spray nozel within the tube beneath the plant.

 

Cool problem.... even if there's currently no solution.

 

Unrelated, but I was just thinking.... I have to rotate my house plants periodically to keep them proportioned because they naturally grow towards the light coming through the window (I actually had a tall one in too small a pot fall over once). Wouldn't it be interesting to see how a germinating seed or plant floating free in the microgravity environment and nourished with nutrient laden water mist responds to diffuse light coming from all directions instead of the conventional single light source?

Edited June 22, 2013 by Aemilius

[CraigD]

Ooh! ooh! I just thought of another weirdly (or perhaps better, audaciously) impractical way to simulate lower gravity with a (very big) centrifuge on Earth!

 

Build high speed track (really high speed – enclosed, with all air removes, likely using maglev train support and propulsion techniques) around the equator. Then just put your lab on a vehicle (let’s just call it a train) traveling east on that track, and pick a speed that gives you the desired lower gravity.

 

For zero-G, you’d need to go a bit over 7441.5 m/s (the orbit speed at the Earth’s surface, about 7905.3, minus the speed due to its eastward rotation, about 463.8 m/s). That would have you circumnavigate the globe about every 5385 seconds (a bit less than 90 minutes) – pretty convenient, as you could stop and get off from the station where you started. If the scheme included parallel tracks and docking tunnels to let you change trains in motion, you could “commute” to a lab in permanent zero-G without the ease of taking a train, vs. the hassle of taking space shuttle (or whatever you want to call a vehicle used to fly into the usual kind of Earth orbit).

 

This is really just a variation on the orbiting spacecraft proposal I mentioned in post #4, because at zero-G, the train is actually an orbiting spacecraft in very, very low Earth orbit (I believe the jargon for this is “NOE” for “nap of the Earth”).

 

It’s also support for the maxim that what the world needs is really good trains. :)

[Guest Aemilius]

Hey CraigD.... that reminds me of something I wondered about some years ago. If I recall correctly, NASA launches rockets from near the equator in the same direction as the Earth is rotating to take advantage of the fact that an object at the equator is already moving at about 2,000 miles per hour.

 

So I have a little thought experiment that maybe you (as the acknowledged master number cruncher here) could help me with. Let's set two identically calibrated postal scales on the ground.... one at the north pole and one at the equator. Then let's place a container on the scale at the north pole and fill it with sand until it weighs exactly 1 lb. and seal it closed. Now let's take it to the equator where we have the other postal scale (at the same elevation/distance from the Earths center of gravity) on the ground and weigh it there.

 

The question is.... Would the scale at the equator still indicate that the sealed container of sand weighs exactly 1 lb. or will it indicate a lesser weight due to the centrifugal force?

 

And.... If the container of sand that weighed exactly 1 lb. at the north pole is lighter at the equator, what would the difference be between the two readings?

Edited June 21, 2013 by Aemilius

[Doctordick]

This is really just a variation on the orbiting spacecraft proposal I mentioned in post #4, because at zero-G, the train is actually an orbiting spacecraft in very, very low Earth orbit (I believe the jargon for this is “NOE” for “nap of the Earth”).

That is nice but orbit effects still fail if you get down to subtle effects. Both gravity and centrifugal force have another subtle characteristic. The gravitational force grows smaller as the distance from the source increases and centrifugal force (for a specific rotation rate)increases as the distance from the center increases. Therefore, unless the object of interest has dimensions of zero, one is left with tidal effects: i.e., the orbital speed changes with radius and that has consequences.

 

Oh, tidal effects are really quite small but I was just making comments. There are other subtle effects also. Normally, electromagnetic effects are totally ignored; however, photon quantization is an issue which can produce some rather surprising effects. One is the fact that gravity itself can be shown to be a direct consequence of the subtle failure of positive and negative charges to yield the exact distribution of virtual photons necessary to cancel out all consequences of the existence of those charges.

 

Have fun -- Dick

[blamski]

 

So I have a little thought experiment that maybe you (as the acknowledged master number cruncher here) could help me with. Let's set two identically calibrated postal scales on the ground.... one at the north pole and one at the equator. Then let's place a container on the scale at the north pole and fill it with sand until it weighs exactly 1 lb. and seal it closed. Now let's take it to the equator where we have the other postal scale (at the same elevation/distance from the Earths center of gravity) on the ground and weigh it there.

 

 

wouldn't this experiment be further complicated by the uneven distribution of the Earth's gravitational field?

 

i guess it would be interesting to make a calculation based on even distribution all the same...

[Guest Aemilius]

blamski "wouldn't this experiment be further complicated by the uneven distribution of the Earth's gravitational field?"

 

 

Not sure, but I would think that the variations depicted in this image are very small in magnitude and distributed over vast areas, which would render their effects on an object of finite size (like a human being for instance) on the surface negligible.... probably exagerated for illustrative purposes. I'll try and find something on that.

 

blamski "i guess it would be interesting to make a calculation based on even distribution all the same..."

 

Right.... I see my recollection of about 2,000 miles per hour was wrong, it's actually approximately 1,037.5 miles per hour.

 

The (now revised) approximate rate of 1,037.5 miles per hour the Earth is moving at or near the equator is a significant percentage (approximately 6.2 percent) of the approximately 16,646.1 miles per hour (converted from the 7,441.5 meters per second CraigD calculated) needed to achieve weightlessness.

 

If that's true, it would naturally follow that an object of a given mass, at a given elevation/distance from the center of gravity at or near the equator would be approximately 6.2 percent lighter than an identical object of equal mass at the same elevation/distance from the center of gravity located at or near the north pole. That means that if one took a 100 pound weight from a location at or near the north pole and transported it to a location at or near the equator.... It should lose about 6 pounds!

 

I must be in error. I'd be very interested/appreciative to have someone verify this one way or the other.

Edited June 22, 2013 by Aemilius

[CraigD]

So I have a little thought experiment that maybe you (as the acknowledged master number cruncher here) could help me with. Let's set two identically calibrated postal scales on the ground.... one at the north pole and one at the equator. Then let's place a container on the scale at the north pole and fill it with sand until it weighs exactly 1 lb. and seal it closed. Now let's take it to the equator where we have the other postal scale (at the same elevation/distance from the Earths center of gravity) on the ground and weigh it there.

 

The question is.... Would the scale at the equator still indicate that the sealed container of sand weighs exactly 1 lb. or will it indicate a lesser weight due to the centrifugal force?

 

And.... If the container of sand that weighed exactly 1 lb. at the north pole is lighter at the equator, what would the difference be between the two readings?

Assuming the Earth’s mass were evenly distributed and it were a perfect sphere or radius r=6378137 m (the conventional value for its actual equatorial radius) that rotates once every t=86400 s (24 hours), the speed of its surface at the equator is

[math]v = \frac{2 \pi r}{t} \, \dot= \,463.83 \,\mbox{m/s}[/math]

So its centripetal acceleration there is

[math]a = \frac{v^2}{r} \,\dot=\, 0.03373 \,\mbox{m/s/s} \,\dot=\, 0.0034 \,\mbox{g}[/math]

So that container of sand that weights 1 lb at the pole would weigh something like 0.9967 lb at the equator.

 

You’d need to be sure the scale you used was the force-measuring kind – something with springs, electronic strain gauges, etc – rather than the mass-comparing kind, like swinging, sliding, or set-stuff-in-trays balances. The balance kind wouldn’t give a different reading, no matter where on Earth or any other planet you used it, ‘cause it actually measures mass, not weight.

 

wouldn't this experiment be further complicated by the uneven distribution of the Earth's gravitational field?

Yes. But according to references like this wikipedia article, the Earth’s gravitational anomalies are on the order of 0.001 m/s/s (0.0001 g), smaller than the 0.3374 due to centripetal acceleration at the equator, so they doesn’t complicate things too much.

[Guest Aemilius]

CraigD "You’d need to be sure the scale you used was the force-measuring kind – something with springs, electronic strain gauges, etc – rather than the mass-comparing kind, like swinging, sliding, or set-stuff-in-trays balances. The balance kind wouldn’t give a different reading, no matter where on Earth or any other planet you used it, ‘cause it actually measures mass, not weight."

 

Granted.

 

CraigD "But according to references like this wikipedia article, the Earth’s gravitational anomalies are on the order of 0.001 m/s/s (0.0001 g), smaller than the 0.3374 due to centripetal acceleration at the equator, so they doesn’t complicate things too much."

 

So my hunch that the variations were exagerated for the sake of illustration in the image was correct.... negligible.

 

Your calculated result for the approximate rate of speed of the Earth's surface at or near the equator confirms the 1,037.5 mile per hour approximation.... But aren't you confusing the causative centripetal force with the reactive centrifugal force? My understanding is that the centripetal force is associated more with the cause of rotation and that centrifugal force is associated more with the reaction to rotation. Aren't we talking here about the reaction to rotation on an object here.... centrifugal force? For example.... the reaction (centrifugal) of the ant on the wheel under a variety of conditions resulting from the action (centripetal) of the wheel. At the very top of the wikipedia page you linked to (centripetal acceleration) it says "Not to be confused with Centrifugal force." What am I missing?

Edited June 22, 2013 by Aemilius

[Guest Aemilius]

No need to waste time explaining further CraigD. I get it.... Thanks.

[CraigD]

.... But aren't you confusing the causative centripetal force with the reactive centrifugal force? My understanding is that the centripetal force is associated more with the cause of rotation and that centrifugal force is associated more with the reaction to rotation. Aren't we talking here about the reaction to rotation on an object here.... centrifugal force? For example.... the reaction (centrifugal) of the ant on the wheel under a variety of conditions resulting from the action (centripetal) of the wheel. At the very top of the wikipedia page you linked to (centripetal acceleration) it says "Not to be confused with Centrifugal force." What am I missing?

No need to waste time explaining further CraigD. I get it.... Thanks.

Aw Aemilius - just as I was getting wound up to deliver a diatribe on the centripetal vs, centrifugal affair! :(

 

;) I’m self-important-feeling enough at the moment not to want to waste a heartfelt diatribe just because it’s unwanted, so here’s what I wrote between after reading your first but before your second post. Hopefully, all my fellow hypographers will sympathize and understand, and pardon the neologism, strange markup, and science folk history revisionism:

I think language like this are largely a Gordian knoted mess of natural language brushing against mathematical physics, words like “centripetal” and “centrifugal” being common in it. So I’ll take a swipe at cutting this particular knot, one of many in the whole mess.

 

First, a couple of the very fundimentalmost definitions, corresponding closely to

Newton’s laws of motion

):

Change in position (of a body, which is assumed to have mass) is motion (also called

velocity

);

Change in velocity is

acceleration

.

 

Now, a special case definition:

The change in motion that results in following a

circular

(in the simple, geometric, ideal, made-with-a-compass sense that Euclid’s fellows meant) path is called

centripetal

(simply the compounding of the Latin words for “center” and “seeking” – Newton coined the phrase, and he and his peers were fond of Latin) acceleration

.

 

Now, back to fundamental definitions,

Acceleration is caused by

force

.

 

Put it all together, and we get:

Circular motion is caused by centripetal force

.

 

A fundamental concept – for this one, I’ll use a much repeated cliché phrasing:

For every force, there is an equal and opposite force

.

 

Here, a new word needed to be invented for the opposite of centripetal force, so, sensibly enough

centrifugal

(“center fleeing”) force was coined.

 

Because centripetal force is the cause of circular motion, centrifugal force its necessary opposite, there’s a tendency to call the first real, the other a “pseudo force”, but to my thinking, this unnecessarily complicates things. When it comes to language, I’m firmly in the

descriptive rather than prescriptive

camp – when words are helpful in calculating and comprehending the physics (or metaphysics), they’re useful. When they interfere, they’re not.

[Guest Aemilius]

Never said it wasn't wanted, only that it wasn't needed. Thanks for the elaboration.