Gravity and Earth being flat..... Help!

Chaos-Engine

My little brother hit me with a problem tonight...

"You have an inextensible string"
"YOu stretch it from Ireland to the East Coast of the USA"
"The Earth is round..."
"Does the string follow the circumfrence of the Earth all the way around to the other end(i.e. same distance form sea level all the way) or does the string make a chord to the other end(i.e. go through the sea taking the most direct route)..."


I have had a deep think about this and believe that the string will follow the circumference and not the chord model. This idea is based on the relative importance of the forces acting on the string and that teh Tension would be more superior to gravity...

Whats the answer??

Yurmasyurda

Originally posted by Chaos-Engine
My little brother hit me with a problem tonight...

"You have an inextensible string"
"YOu stretch it from Ireland to the East Coast of the USA"
"The Earth is round..."
"Does the string follow the circumfrence of the Earth all the way around to the other end(i.e. same distance form sea level all the way) or does the string make a chord to the other end(i.e. go through the sea taking the most direct route)..."


I have had a deep think about this and believe that the string will follow the circumference and not the chord model. This idea is based on the relative importance of the forces acting on the string and that teh Tension would be more superior to gravity...

Whats the answer??

The answer is = Your brothers a nerd nahh not really, I don't have an answer and I feel relief from saying that at the same time

Cake Fiend

Chord

Gordon

Surely the string would float 3 cms above the sea at all time, what a silly question?!

bonkey

Originally posted by Chaos-Engine
I have had a deep think about this and believe that the string will follow the circumference and not the chord model. This idea is based on the relative importance of the forces acting on the string and that teh Tension would be more superior to gravity...

I think your deep think was incorrect.

Lets take the two extremes :

Firstly, if you pull it "taut", then the string will try and follow a single dimension - straight line. If you check your handy globe, then you will see that this is not possible, as the string would have to cut significantly into the earths crust - which I am assuming is not permitted. So there is a limit to the tension we can apply unless our string is effectively indestructible.

Now - no tension.

Is the string bouyant? If it is bouyant, and you apply no tension (have plenty of extra length) then it will sit along the top of the water. If it not bouyant, then it will sit on the seabed - as conventional fibre-optic cables do.

In either of these cases, tensioning the cord will basically cause it to try and reduce itself to a one-dimensional path - a straight line. What happens in this case will depend on the strength of the string : will it cut through its environment, or will the environment break the string.

So - there is no real answer. You need to define the properties of the string more correctly, and look at the tension. With no tension, then the string will follow (as close as possible allowing for buoyancy) the circumference. With tension, it will attempt to straighten itself.


Now, you could take a simplified case, and look at (for example) stretching a string around football. Sure - you can stretch it to a "curcumference" model using tension - but why stop the tension there? This is where I think your answer came from....but you're limiting your tension at an abitrary point. Why? You're also removing the issue of topography - across the surface of a football and across the Atlantic Ocean are entirely different problems. A tensioned string will cut through water, even if it didnt cut through the surface of the football.

Dunno if this answers the question, but should show you some of the possibilities.

jc

Nietzschean

"You have an inextensible string"
"YOu stretch it from Ireland to the East Coast of the USA"

well for one ask yer brother how do u stretch an inextensible string you can only increase the tension it won't stretch, and as stated before unless you set what value the tension applied would be and the strength of the string there is a million different answers....and gravity really wouldn't come into this in a major way to find your answer. low but taught tension would lead it to follow the circumfrence of the earth....none bottom of sea....loads chord

nesf

Firstly, hey ppl how're things?

Secondly Bonkey's right, you need more info on the conditions of the problem. Plus, topology cannot be ignored, especially since this is a 3-D problem, veiwing it in terms of circumferences and chords won't work, simply because the forces acting on the string won't be in a "plane" they'll be perpindicular to the earth's surface, this complicates the problem, because you have to take into account the fact that one cannot easily resolve the problem in 2 dimensions.

Assuming that the string has negative buoyancy and won't cut through the earth, and that the tension is increased such that the "inextensible" string stays as such. (If we put enough tension on it will become extensible!) Now think about it in this fashion.

Take the 0-level to be at the lowest point on the sea floor, and that "sea-level" is akin to a tree line on a mountain and that we are steching this string around a curved surface from mountain A to B, at equi-distant perpendicular heights from our curve at 0-level. One can see visually that given enough of a curve that the string must cut this "sea-level" curve at some point, expecially if we tension the string as this will "force" the string to cut into the water as at some point the tension on the string will overcome the surface tension of the water, and the buoyancy forces inherent.

I find such problems as these are more easy to visualise if we take something like a chain, which we "know" will behave in a certain way.


Another way of visualising this is to imagine a sheet of paper with a string held elevated above it at some height A. Now bend the sheet so that it is curved. The string will be forced at a certian curvature or distance for a certain curve, to match the curve of the paper by running along it's surface.


I'm sorry if I've rambled on, it's just i haven't been online in ages.

Victor

Originally posted by nesf
Assuming that the string has negative buoyancy and won't cut through the earth, and that the tension is increased such that the "inextensible" string stays as such. (If we put enough tension on it will become extensible!) Now think about it in this fashion.

While I don't think there is any material that is truly inextensible, we can assume it for this example. At the same time inextensible material can still break (eg a steel beam might stretch only 0.1% under tension, but might break once it reached a stretch of 1%). You also have to factor in ocean currents (would cause squiggles in the string), sea traffic (would dictate a sea bottom string) and the mid-Atlantic ridge (a series of 'sea-mountains' where the European and North American tectonic plates meet).