## Gravity, Acceleration, or Centrifugal Force?

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Strangelander
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### Gravity, Acceleration, or Centrifugal Force?

You're inside a large cubical container with no way to reference the outside world. You are drawn to the "floor" of the cube by a force similar to Earth's gravity. You may have any equipment you wish in the cube, provided it does not measure or reference anything outside the cube.

How do you tell whether the force pulling you "down" is gravity, acceleration, or centrifugal force?

(Yes, centrifugal force is a pseudo-force, rotating reference frame, blah blah blah. You know what I mean.)

MSTK
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### Re: Gravity, Acceleration, or Centrifugal Force?

This is silly. One of the core principles of the Theory of Equivalence is just that -- equivalence of gravitational force and acceleration. Although I'm sure someone here will find some clever way to get around this through a loophole.

What's the nature of the centrifugal force, by the way? Is the cube rotating around its center? If so, then just throw an object high up and if, once it gets past the center, it starts flying upwards, it's probably centrifugal. Also, walking on walls would be generally easier.

Nitrodon
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### Re: Gravity, Acceleration, or Centrifugal Force?

Spoiler:
Somehow, get an extremely accurate measure of the direction of force at three noncollinear points. The forces will act as follows:

Gravity: The forces push toward a point.
Acceleration: The forces push in the same direction.
Centripetal force: The forces push away from an axis.

From the angles that the force vectors make with each other, you should be able to distinguish between the three cases.

skeptical scientist
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### Re: Gravity, Acceleration, or Centrifugal Force?

Spoiler:
The rotating reference frame is easy to check - just see if there is a Coriolis force. For example, you could jump straight "up", and the presence or absence of a force should be quite apparent (for reasonable sized distances from the axis of rotation). However, this can be made arbitrarily difficult by increasing the distance from the axis of rotation, so you need arbitrarily sensitive instruments to tell the difference in all possible cases. Also, determining the difference between a uniform gravitational field and a constant acceleration is impossible. The only way to tell a gravitational field apart from a constant acceleration is if you can detect non-uniformities in the gravitational field. Again, this can require arbitrarily sensitive instruments, depending on how far the gravitational field is from being uniform.

Nitrodon wrote:
Spoiler:
Gravity: The forces push toward a point.
Spoiler:
Not necessarily. This is true if the gravitational source is spherically symmetrical, or you have a spherically symmetrical object providing most of the gravitational force, with small perturbations. (In other words, the type of field we are used to living on Earth.) It is not true in general. In fact, according to Newton's theory of gravitation, if you had mass distributed in an infinite flat plane of constant density, the gravitational field generated would be perfectly uniform.
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fyjham
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### Re: Gravity, Acceleration, or Centrifugal Force?

skeptical scientist wrote:
Spoiler:
Not necessarily. This is true if the gravitational source is spherically symmetrical, or you have a spherically symmetrical object providing most of the gravitational force, with small perturbations. (In other words, the type of field we are used to living on Earth.) It is not true in general. In fact, according to Newton's theory of gravitation, if you had mass distributed in an infinite flat plane of constant density, the gravitational field generated would be perfectly uniform.

Spoiler:
It does say similar to earth's gravity though, not just generic gravity. As you said, the equipment would need to be arbitrarily sensitive or the box arbitrarily big, but I think the wording of the puzzle excludes an infinite flat plane as the gravity source.

thomblake
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### Re: Gravity, Acceleration, or Centrifugal Force?

Spoiler:
Gravity. A mysterious force pulling you down is properly identified as gravity. If you're in the situation, you won't even think about the alternatives.

parallax
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### Re: Gravity, Acceleration, or Centrifugal Force?

Never mind that all three of those cases are gravity.
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skeptical scientist
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### Re: Gravity, Acceleration, or Centrifugal Force?

fyjham wrote:
Spoiler:
It does say similar to earth's gravity though, not just generic gravity. As you said, the equipment would need to be arbitrarily sensitive or the box arbitrarily big, but I think the wording of the puzzle excludes an infinite flat plane as the gravity source.

It doesn't say that in the gravity case, the gravity is similar to Earth's gravity. What it says is that in all three cases, the force appears similar to Earth's gravity; clearly the gravity due to an infinite flat plane is at least as similar to the Earth's gravity as is centrifugal force.
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fyjham
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### Re: Gravity, Acceleration, or Centrifugal Force?

Ah, good point, that was the description of the force rather than the item to distinguish it as

douglas_fir
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### Re: Gravity, Acceleration, or Centrifugal Force?

Spoiler:
Gravitational force becomes stronger as you move the sensitive instrument in the direction of the force whereas a force caused by linear acceleration will not and a centrifugal force will become weaker as you approach the center of rotation. Moving the instrument around within the box, the gravitational field of the planet earth creates an arc of consistent gravitational pull around the center of the earth. If it were a centrifugal force, the arc would be around the axis of rotation, which is "up". If the instrument is not sensitive enough to detect an arc, then it is likely a planet or plane, since a centrifuge big enough to create that kind of result would be ridiculous. I recently learned that moment forces can be split into components in different directions, so I'm going to have to say a gyroscope would be completely useless.

BoomFrog
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### Re: Gravity, Acceleration, or Centrifugal Force?

Spoiler:
If it's gravity, infinite plane or not, it will be weaker at the top of the box compared to the bottom of the box, acceleration "force" would not be different. Centripetal as already stated can be found by the change in direction of the force at different points.
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skeptical scientist
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### Re: Gravity, Acceleration, or Centrifugal Force?

BoomFrog wrote:
Spoiler:
If it's gravity, infinite plane or not, it will be weaker at the top of the box compared to the bottom of the box.

Spoiler:
No, actually. At least not according to Newton's law of gravity; I have no idea how general relativity would affect things. If you have an infinite plane of constant mass density [imath]\lambda[/imath], the net force acting on a particle of mass m which is z units above the plane is obviously directly downwards (by symmetry). We can work out the total force as
$\lambda mG\int_{\mathbb{R}^2} \frac{z}{(x^2+y^2+z^2)^{3/2}} \, dx \, dy=\lambda mG\int_{\mathbb{R}^2} \frac{1}{\left (\left(\frac{x}{z}\right)^2+\left(\frac{y}{z}\right)^2+1\right )^{3/2}} \, \frac{dx}{z}\frac{dy}{z}=\lambda mG\int_{\mathbb{R}^2} \frac{1}{(u^2+v^2+1)^{3/2}} \, du \, dv.$ (The last step uses the change of variables u=x/z, v=y/z.) This shows that the force is actually a constant independent of z, and it is therefore impossible to distinguish the force of gravity due to an infinite plane of constant mass density from the (fictitious) force arising from a constant acceleration.

p.s. Why can't jsMath handle \iint?
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Cauchy
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### Re: Gravity, Acceleration, or Centrifugal Force?

On a related note to the "gravity is independent of distance from an infinite plane" comment, since luminance falls off as the square of the distance, like gravity, an infinite plane of material producing the same amount of light per unit area will look just as bright no matter how close or far away you are from it. I hear that it's very dangerous to skydive over vast snowy fields for this very reason: since the snow is roughly equally luminous everywhere, it's very difficult to judge how far you are from the ground.
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arvid96
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### Re: Gravity, Acceleration, or Centrifugal Force?

centrifugal force can be identified with the coriolis effect thingy

if the force would be caused by acceleration, the acceleration of the ship would be 9.8 m/s^2
according to Einstein, no object can move faster then 299.792.458 m/s
so, if you wait for 299.792.458 /9.8 = 30 591 067,1 seconds = approximately 1 year and the force doesn't change, it can't be acceleration

it's possible this way, you just need loads of patience

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### Re: Gravity, Acceleration, or Centrifugal Force?

arvid96 wrote:if the force would be caused by acceleration, the acceleration of the ship would be 9.8 m/s^2
according to Einstein, no object can move faster then 299.792.458 m/s
so, if you wait for 299.792.458 /9.8 = 30 591 067,1 seconds = approximately 1 year and the force doesn't change, it can't be acceleration

I'm afraid that won't work. Special Relativity has ways of taking care of accumulated acceleration that would, under classical mechanics, cause you to exceed the speed of light. There's no reason you can't accelerate constantly (in your frame) forever. To someone in the stationary frame, your acceleration would diminish over time and you'd asymptotically approach c, but this won't affect how you experience it.

MANN
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### Re: Gravity, Acceleration, or Centrifugal Force?

There are no forces or force fields in space. Force is an induced effect within mass. There must be an accelation to
produce any force. Example, electron motion within matter has centerifugal force; when a mass is exposed to an unequal electromagnetic field and or, field types the orbits of the electrons become stressed. The product of a force is produce by the unbalanced centrifugal force on the electrons, the force of Gravity, Magnetic force, and Electro static forces are produced. Space has an by-directional electric static scalar potenual that is superimposed net > zero-point. All matter is a product of this space field being closed looped hormic wave formations called particals. Large mass of particals like a planet will block the space fields from being equal thus producing a gravity well, as a massive dielectric sheld thus inducing the effect of gravity force based on the size of the mass. In permanent magnets to unlike poles will cancel out and have zero effect on each other. But the unbalanced electron spins within the magnetic mass will produce a force to the center of the inbalance or the cancel zone.
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antonfire
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### Re: Gravity, Acceleration, or Centrifugal Force?

Do we have Marov chain bots prowling the fora now, or something?

Anyway,
Spoiler:
Ignoring GR, if you cut a spherical cavity out of a sphere (even off center), the gravitational field inside is constant. This is easy to see by subtracting two potentials. You can't tell the difference between being in such a cavity and being in an accelerating rocket.

Loosely speaking, because the Earth's center is so far away, it's easy to control whether things diverge or converge as they fall by moving small amounts of mass around. The effects of things like mountains is certainly not negligible.
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rnew
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### Re: Gravity, Acceleration, or Centrifugal Force?

MANN wrote:There are no forces or force fields in space.
Yes there are. That's why we can't see the alien spaceships.
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### Re: Gravity, Acceleration, or Centrifugal Force?

Spoiler:
Use a weighted gyroscope and uh.....duh......I mean...use a tiny centrifuge to....to spin yourself and.....then you could, uh.....You...Madness and science don't mix.
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Other times it makes you want to laugh, and you shoud.
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Crius
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### Re: Gravity, Acceleration, or Centrifugal Force?

Measure the amount of force at different heights.

Acceleration should always produce a uniform force regardless of where the measurement was taken. Gravity and centrifugal force should decay as you measure from greater height. Unless you have an impossibly large centrifuge, the force from gravity should decay at a much slower rate than a centrifuge.