What if there was a pole, whose length was the circumference of the Earth?

[Pshock92]

Imagine a strange event:
I've asked this question so many times, but have never received a clear cut answer:

Let's say that you had a pole, one that you were holding up vertically, that had the length of the circumference of the Earth (24,901.55 miles). Let's just pretend that, although the pole is extremely long, the pole does not wobble like long, skinny poles do. Let's also pretend that we have a stretch of land with no elevation changes and no oceans, sands, or anything. It's just a long grassland that goes all the way around.

Now, say we take our pole and we gently place it on the ground. What would happen?
I've narrowed it down to three possibilities:

1. The pole goes all the way around the Earth, and the two ends of the pole would meet - I've had a few people say this is what most likely will happen, and it's what I expected when I thought this up. I've also been told that it depends on the material of the pole.

2. Considering that the Earth is round, the straight pole would not go around the Earth, and would sort of just sit, jutting out into space - This is the common sense answer that people give me. I imagine this to be impossible: If the pole were to jutt out into space, then at one point that pole would have to get off the ground and elevate, for no particular reason. Would gravity allow that?

3. The pole would snap - This is what could happen if the pole was made of a material that would not allow it to go around the Earth. But, then again, it'd be strange to see the pole snap for no reason other than to be set on the ground.

My guess, as I've said before, is possibility one. Although the Earth is round, the landscape of it is flat (i.e. the ground we stand on is not round), so, the pole would have just flat land to rest on.

What do you think? I'd love new ideas to be brought foward!

 

[SmashtheVan]

My guess is that as the Earth spins it applies a torque at the base, and the bottom of the pole moves with the Earth. Since the center of mass would no longer be supported, it would fall towards the Earth. then two things can happen depending on the properties of the pole:

If the pole has a high resistance to bending, the pole will ultimately come to rest with the center of mass lying on the surface of the planet, with its sides sticking out straight across, out into space, with a slight bowing due to gravity(most affecting points of the pole closer to the CM)

If the pole has a very small resistance to bending, and no breakpoint, then i can imagine the wrapping around the Earth scenario

 

[diazona]

Well, the reason you're not getting a clear answer is probably that it's not a clear question. Do you mean to take into account the rotation of the Earth, or should this be an idealized non-rotating planet? In the latter case, what makes the pole move from its vertical position? And what do you mean by "the pole does not wobble" - is it rigid?

 

[Mapes]

If stood on its end, a pole this long made of any real material would http://en.wikipedia.org/wiki/Buckling#Self-buckling_of_columns" and fail. But if we imagine that this can't happen, then the pole is in only a metastable state when positioned on its end. If tipped off balance, it would wrap around the Earth, as this is the a lowest-energy configuration (the center of the pole's mass would be at the center of the Earth).

 

[Mapes]

If the pole has a high resistance to bending, the pole will ultimately come to rest with the center of mass lying on the surface of the planet, with its sides sticking out straight across, out into space, with a slight bowing due to gravity(most affecting points of the pole closer to the CM)

No material is this rigid. Think about it. It would be like a bridge, ten thousand miles long, connected only at one end. A typical 1" diameter metal pole wouldn't even make it a few hundred feet without yielding.

 

[SmashtheVan]

No material is this rigid. Think about it. It would be like a bridge, ten thousand miles long, connected only at one end. A typical 1" diameter metal pole wouldn't even make it a few hundred feet without yielding.

if the pole is supposedly unbreakable, then who's to say its not incredibly inductile either?

 

[Mapes]

if the pole is supposedly unbreakable, then who's to say its not incredibly inductile either?

Well, presumably Pshock92 is asking about realistic material properties. A quick calculation suggests that a 1" diameter rod would have to have a stiffness of 10³⁰ Pa to avoid wrapping around the Earth (calculated via the bending equation $\kappa = M/EI$, where $\kappa$, $M$, $E$, and $I$ are the curvature, bending moment, Young's modulus, and moment of inertia). This is about 10¹⁸ times stiffer than steel. Hardly "a very small resistance to bending."

 

[russ_watters]

A solid, straight rod could be of almost any known material and wrap around the earth. It doesn't have to bend much for that.

 

[DaveC426913]

The rod would only have to deflect one degree over each 60 mile length. According to http://www.1728.com/circsect.htm" , that would mean, over 30 miles to each side, the rod would only have to deflect .297 miles or 1570 feet.

That is well within the ductility of any known material and surely not enough to break it. It is probably safe to say that even the theoretically most rigid material physically possible would bend without breaking.

 

[Unit]

my take on this is that because the curvature of the Earth is so shallow in relation to the width of the pole, the pole would just warp around the entire earth, although it would look as if it was straight, just like the grassy field beneath your feet looks flat.

however, if the post was infinitely strong (haha), so that it wouldn't bend, wouldn't break, wouldn't yield under anything, it would be like balancing a thin straw on an orange.

also, inside my head I've always been imagining this pole as a hollow pole, what about all of you?

 

[DaveC426913]

also, inside my head I've always been imagining this pole as a hollow pole, what about all of you?

It doesn't matter. The only thing that matters is the tensile strength of the material and whether it is a reall material or an ideal material.

 

[qlc]

first i looked at this:
24,901.55 miles (40,075.16 kilometers).

then i found out that:
Low Earth Orbit (LEO) - Geocentric orbits ranging in altitude from 160–2,000 km (100–1,240 miles); one revolution takes 90 minutes, the speed is 8 kilometers per second.
Medium Earth Orbit (MEO) - Geocentric orbits ranging in altitude from 2,000 km to just below geosynchronous orbit at 35,786 km (22,240 miles). Also known as an intermediate circular orbit.
Geosynchronous Orbit (GEO) - Geocentric orbit with an altitude of 35,786 km (22,236 statute miles) above mean sea level. The period of the orbit coincides with the rotation period of the earth: 24 hours; the speed is 3 km/s.
High Earth Orbit (HEO) - Geocentric orbit higher than 35,786 km (22,236 statute miles)

HEO is 35,786 km and the rod`s length is 40,075.16 kilometers
now i think that the rod whould fly off to space or start to orbit around Earth rather than fall down on the Earth trought the atmosphere.
the rod is simply too long, i mean wouldn't the Earth's centrifugal force be stronger at this point than the gravitational pull between the two objects.
what ya`ll think ?

 

[Mapes]

Hi qlc, welcome to PF. Calculate the height and speed of the pole's center of mass if the pole were standing on its end (and still intact). If the speed is too slow for its orbit, the center of mass will tend to move toward the Earth, not away from it.

 

[Pshock92]

Alot of people on her are siding with my theory, and are giving good evidence for it, which is good.
Is their any possibility that the pole would just jutt out into space? If, for some unknown reason, the pole would not wrap around the Earth, what would that look like? If you were to balance a thin straw on an orange, then the two ends of the straw would not be touching the orange. They'd just be jutting out into space.
Imagine this with the pole and the Earth. What would that look like from space? What would I see if I was on the Earth right at where the pole seizes to touch ground? Would I just see a pole slanting upward into the sky? Weird.

Again, I imagine this to be somewhat impossible. But, if under crazy cirumstances, it is possible, could someone explain it?

I thought of this whole thing when I was in 7th grade, and the next day tried to explain to some friends and an adult or two. They're first reaction was that the pole would jutt out into space. When I tried to explain why this was impossible, they all laughed at me. I suggested that the pole would wrap around, and they called me crazy.

It even led to one guy to look me in the face and say, "You're an idiot. You're going to be president of the United States one day, because you are such an idiot."
Fun little anecdote.

 

[Pshock92]

A solid, straight rod could be of almost any known material and wrap around the earth. It doesn't have to bend much for that.

The exact, clear cut answer I wanted. Yay!

 

[DaveC426913]

Is their any possibility that the pole would just jutt out into space?

If it were made of an imaginary material that had an unlimited stiffeness, yes.

Note that you could theoretically do this by making a truss (i.e. a bridge with one central pier and no endpoints). Huge increase in stiffness without the correspoinding increase in weight.

If, for some unknown reason, the pole would not wrap around the Earth, what would that look like? If you were to balance a thin straw on an orange, then the two ends of the straw would not be touching the orange. They'd just be jutting out into space
Imagine this with the pole and the Earth. What would that look like from space? What would I see if I was on the Earth right at where the pole seizes to touch ground? Would I just see a pole slanting upward into the sky? Weird.

No. You would see a straight pole that disappeared into the misty horizon. It is the Earth that curves away from the pole, not the other way around. And from a six foot altitude, you cannot see the Earth curve away from you.

If you drove ten miles down the road and looked up, you'd see a line a few hundred feet in the air that ran horizontally from horizon to horizon. It would be virtually impossible to tell that one end was higher than the other.

It wouldn't be until you were in orbit that you would be able to see the curvature of the Earth, and thus how the Earth curves away from the pole.

I thought of this whole thing when I was in 7th grade, and the next day tried to explain to some friends and an adult or two. They're first reaction was that the pole would jutt out into space. When I tried to explain why this was impossible, they all laughed at me. I suggested that the pole would wrap around, and they called me crazy.

It even led to one guy to look me in the face and say, "You're an idiot. You're going to be president of the United States one day, because you are such an idiot."
Fun little anecdote.

Many, many people are intimidated by enquiring minds. Here, you have found a place where others are just like you who will appreciate and nourish an enquiring mind. We are glad to have you.

 

[Klockan3]

Imagine a strange event:
the pole does not wobble like long, skinny poles do.

To me this means that the pole is infinitely stiff and therefore will balance off the Earth's surface.

 

[Nick89]

I can imagine how weird it will look to have an infinitely rigid pole laying on the surface of the earth. It would appear to just be a very large pole lying on the ground if you are near the 'contact point'. But if you move away from the contact point, it would appear to be floating in mid air!

Of course, even the slightest touch will make the pole tip over and find a new balance point (it may even 'roll' around the Earth a few times hehe).

 

[D H]

To me this means that the pole is infinitely stiff and therefore will balance off the Earth's surface.

That's exactly how I looked at the problem. The OP essentially posited an unobtanium rod with infinite shear modulus and asked if it would bend. This is not an irresistible force / immovable object quandary. It is a resistible force versus an immovable object. The immovable object wins.

The answer would be a bit different had the OP posited the use of commercial-grade unobtanium, which has a very high, but not infinite shear modulus. Then the rod would partially wrap around the Earth. Some deformation would occur but the ends would stick out above the Earth. How much would occur bending would occur: You'll have to read the product spec.

 

[diazona]

I can imagine how weird it will look to have an infinitely rigid pole laying on the surface of the earth. It would appear to just be a very large pole lying on the ground if you are near the 'contact point'. But if you move away from the contact point, it would appear to be floating in mid air!

Of course, even the slightest touch will make the pole tip over and find a new balance point (it may even 'roll' around the Earth a few times hehe).

Actually, I would think a slight touch would make the pole rock back and forth slightly. Or roll. It depends on which way the force was applied.

 

[ESTÉRA]

Why isn't anyone not mentioning the mass of the pole?
I mean, assumeing the the pole stays vertical, with respect to grund, isn't there a possibility that the pole, due to it's huge mass, would "poke"/penetrate the Earth somewhat?

 

[Pshock92]

Many, many people are intimidated by enquiring minds. Here, you have found a place where others are just like you who will appreciate and nourish an enquiring mind. We are glad to have you.

Much thanks for the welcome and support.

 

[DaveC426913]

Actually, I would think a slight touch would make the pole rock back and forth slightly. Or roll. It depends on which way the force was applied.

A slight touch wouldn't do anything. The pole is still extremely massive. And in equilibrium. To move it would require a force to overcome that massive inertia.

Here's a fun thought experiment though. The pole that bends so that it encircles the Earth - what would it do? What if its length were slightly longer than the circumference of the Earth? How would it behave?

 

[DaveC426913]

Why isn't anyone not mentioning the mass of the pole?
I mean, assumeing the the pole stays vertical, with respect to grund, isn't there a possibility that the pole, due to it's huge mass, would "poke"/penetrate the Earth somewhat?

While true, it doesn't have any impact on the behaviour of the pole.

 

[Pshock92]

Here's a fun thought experiment though. The pole that bends so that it encircles the Earth - what would it do? What if its length were slightly longer than the circumference of the Earth? How would it behave?

My guess would be that you would have a pole in which the ends surpass each other. It's like, you put down the pole, then it would poke you in the back.

 

[Nick89]

A slight touch wouldn't do anything. The pole is still extremely massive. And in equilibrium. To move it would require a force to overcome that massive inertia.

Hmm, I suppose that makes sense. But isn't the equilibrium a very very unstable one? I imagine it like balancing a straw on an orange. Once you have it there, even the slightest touch makes it roll off. Of course, a straw isn't really a good example of a very massive object, but still :p

 

[DaveC426913]

Hmm, I suppose that makes sense. But isn't the equilibrium a very very unstable one?

The Queen Mary could be pushed by hand, but it would take a fair bit of pushing to get it moving.

 

[DaveC426913]

My guess would be that you would have a pole in which the ends surpass each other. It's like, you put down the pole, then it would poke you in the back.

Sorry, what I was getting at is, if the ends came together so that the pole was now a complete ring, what would happen? When slightly longer than the circumference of the Earth, it would actually not be able to lie on the ground - it would be too long.

It would be suspended a short distance above the ground. Assuming it was perfectly rigid, it would also be weightless. You could lift it up and it would stay there. Push it down and it would stay there. It is the inside-out version of Newton's Shell Theorem.

 

[Mapes]

Sorry, what I was getting at is, if the ends came together so that the pole was now a complete ring, what would happen? When slightly longer than the circumference of the Earth, it would actually not be able to lie on the ground - it would be too long.

It's a nifty problem to calculate the compressive stress on this ring. One approach is to equate the gravitational potential energy of the whole ring being a little lower to the strain energy penalty for the ring to compress to make this happen. (Are there other solution approaches?)

I'll leave the details up to the interested reader; I get $\sigma = \sqrt{2r\rho g E}$, where $\sigma$ is the compressive stress, $r$ the distance from the Earth's center, $\rho$ the material density, $g$ the acceleration of gravity, and $E$ the Young's elastic modulus of the ring.

Surprisingly, the answer is independent of cross-sectional area. Not surprisingly, no material in existence could survive this configuration; a yield strength of at least hundreds of GPa would be required, if my calculations are correct.

Note that even if a material's yield strength were high enough, the ring would still surely fail by compressive buckling (i.e., elastic instability), which is a different failure mechanism than simple compressive loading.

 

[diazona]

A slight touch wouldn't do anything. The pole is still extremely massive. And in equilibrium. To move it would require a force to overcome that massive inertia.

$F = ma$, I say - a slight touch (F) would produce a slight acceleration (a). So it would do something, even if the motion would be so small you couldn't measure it.

Hmm, I suppose that makes sense. But isn't the equilibrium a very very unstable one? I imagine it like balancing a straw on an orange. Once you have it there, even the slightest touch makes it roll off. Of course, a straw isn't really a good example of a very massive object, but still :p

Well, the straw-on-an-orange analogy sort of breaks down once the straw moves from the top of the orange: the straw is subject to a uniform force, but the pole would be subject to a radial force. (Point: the straw can fall off the orange, but the pole couldn't fall off the earth)

 

[DaveC426913]

$F = ma$, I say - a slight touch (F) would produce a slight acceleration (a). So it would do something, even if the motion would be so small you couldn't measure it.

Well OK. I guess the same thing could be said about the Queen Mary. A slight touch sets it moving imperceptibly?

 

[haloshade]

An other way I thought about looking at this thought experiment is if the pole was infinitely long. Would the pole keep on warping around the Earth? Or will it warp until ends meet (well sorta) and the equal force from each side would cancel any other warping and the rest of the extent will keep on jutting out into space?

Just something I thought would be interesting to add to this already interesting thought experiment.

Edit: Assume that the infinite pole is behaves the same way as the already finite pole.

 

[DaveC426913]

An other way I thought about looking at this thought experiment is if the pole was infinitely long. Would the pole keep on warping around the Earth? Or will it warp until ends meet (well sorta) and the equal force from each side would cancel any other warping and the rest of the extent will keep on jutting out into space?

Just something I thought would be interesting to add to this already interesting thought experiment.

Edit: Assume that the infinite pole is behaves the same way as the already finite pole.

Uh, you lost me. An infinitely-long pole would form a helix of infinite width. I don't see where you're going with this.

 

[haloshade]

Uh, you lost me. An infinitely-long pole would form a helix of infinite width. I don't see where you're going with this.

Well I sort of worded it wrong, I meant a helix when I suggested my first option I just didn't word it properly. Sorry about that.