Annoying truths

[Peerie Maa]

I'm with TLT on this one, but if any of you math wizards want to test out your theories in real world applications can I at least get the contract to supply the rope?

Will you be looking for sisal, manila hemp, hemp. cotton, coir, perhaps low stretch polypropylene. Just let me know the actual length of cordage you think you'll need and I can get you a price*.

*Special discounts available to WBF members.

Polyprop is the only buoyant cordage, so it self-selects in this case.

[Peerie Maa]

Its turtles all the way to the bottom so the correct answer is 3.14 m + 2 x infinity

No it is not, it is 4 foot, assuming that it does already go round the turtles.

[sandtown]

OK, so one more . . .

Neither Gunz nor nuclear arms keep you safe.

[gypsie]

Is it Henry the 8th's foot or Elisabeth the first's?

[P.I. Stazzer-Newt]

I read the math explanation. Makes sense. Don’t like it.

The Rope Around The Earth Problem
Take a rope tied tautly around a basketball. Now the rope must be lengthened so that there is a one foot gap between the ball and the rope at all points, as if the rope is hovering a foot away around the entirety of the ball. How much must the rope be lengthened to accomplish this? 6.28 Feet.

Now take a rope around tied tautly around the equator of the earth. We have the same goal for the one foot hovering gap around the entirety of the earth. How far must the rope be lengthened? 6.28 Feet.

There is a real mystery here, why are some (any) annoyed by this?

[Paul Pless]

There is a real mystery here, why are some (any) annoyed by this?

simple really, reds confronted by (confounded by) truth, any truth, not their own

[Chris Woodward]

How much rope do you need to tie up the damn goats?

[George Jung]

Similar trajectory as the Monte Hall thread! Psychology, boyos!

[Too Little Time]

Now take a rope around tied tautly around the equator of the earth. We have the same goal for the one foot hovering gap around the entirety of the earth. How far must the rope be lengthened? 6.28 Feet.

I am sitting here wondering how easy it is to stretch a rope of that length enough to add 6 ft to its length. I don't think it is hard.

[Jim Mahan]

I am sitting here wondering how easy it is to stretch a rope of that length enough to add 6 ft to its length. I don't think it is hard.

Go ahead and give it a tug, then get back to us, Atlas.

[oldcodger]

I am sitting here wondering how easy it is to stretch a rope of that length enough to add 6 ft to its length. I don't think it is hard.

You make a good point, the strain dL/L, 6 feet / (24,901.461 miles x 5280) = .00000004563 is miniscule so the force is similarly small for the steady state of keeping it stretched.


However getting it there is the issue. If it had any weight at all in effect you have to shift the weight of 24,461 miles of rope on average 18 inches. The rope at the opposite side of the world does not move, each end moves 3 feet so average 18 inches.


See my post #54


.

[Jim Mahan]

Start with the rope on a spool, big enough to hold twenty-four thousand miles of rope, on a station in orbit above the equator. Use on board rockets to push the orbiting spool opposite the direction of Earth's spin. Then pay it out. As long as it's speed is fast enough relative to the Earth's rotation below it should remain effectively in orbit until you have the entire rope end to end suspended in orbit, eigheen inches above the ground, going a thousand miles an hour. It's gonna make a noise and a big mess when it slows down and falls.

Okay, who got high at recess? Jimmy?!

[sandtown]

I am sitting here wondering how easy it is to stretch a rope of that length enough to add 6 ft to its length..

Shoot, my halyards do that constantly !!

[oldcodger]

My post #51 is a fine example of posting when half asleep past your bed time. Hopefully this is not a post when I am not fully woken up.

I stand by line 1 "You make a good point, the strain dL/L, 6 feet / (24,901.461 miles x 5280) = .00000004563 is miniscule so the force is similarly small for the steady state of keeping it stretched."

The second line

"However getting it there is the issue. If it had any weight at all in effect you have to shift the weight of 24,461 miles of rope on average 18 inches. The rope at the opposite side of the world does not move, each end moves 3 feet so average 18 inches."

makes the faulty assumption that the entire rope needs stretching uniformly.

Whereas it only needs to be stretched locally which if it was polypropylene or even bungee would be easy.

[Nicholas Carey]

I am, for whatever it's worth, highly amused at the length and breadth of this discussion.

The fact that so many here have such a breadth of knowledge is a large part of what keeps me here.

[Paul Pless]

is twodot about to propose an irrational argument?

[TomF]

Reminds me of Dorothy Parker's comment. "If all the girls attending [the Yale prom] were laid end to end, I wouldn't be at all surprised."

[Keith Wilson]

Are we taking it for granted that the circumference of a circle always equals 2πr? Or ever equals 2πr?

You'd better. Otherwise you're going to have a hard time building anything that fits together.

Oh, and engineering textbooks are full of infinitely rigid bodies, and zero-stretch ropes. This is a geometry problem, not mechanics.

[sp_clark]

I get that, what I can't ever figure out is how to get the pi symbol out of my keyboard.

On a Mac it's option + p: π.

What you get though depends on what font you're using, so that will affect the appearance of the character: π π π π π. for example.

For a web page display it also depends on what fonts are installed on the viewer's system.

I don't use a PC much anymore but when I did I recall ALT+277 in Word tossed up the symbol for pi so there's that.

You want more, go to: https://www.wikihow.com/Type-the-Pi-Symbol

[Peerie Maa]

Are we taking it for granted that the circumference of a circle always equals 2πr? Or ever equals 2πr?

Well Bergholt Stuttley Johnson did build a machine with the value of Pi set to exactly 3.

[Keith Wilson]

There actually was a bill introduced in the Indiana legislature in 1897 that would have set pi (at least in the state of Indiana) as equal to 3.2. Really. It didn't pass. (Read about it here.)

[Jim Mahan]

Another way to think about this. Take the circumference of the Earth and make a square big enough to accomodate it, put the rope on the outside of the square. Now increase the distance of the rope away from the circle to eighteen inches further from center. So the sides of the square are now eigheen inches times two away from each other on either side of the circle. Ninety degrees is the same, also eighteen inches, times two, one for each opposing side. So the square is bigger by thirty-six inches square. It doesn't matter how long the sides are, the net is the same. Earth's diameter is seven thousand nine hundred twenty-six miles at the equator. So the sides of the square, and the length of the rope is seven thousand nine hundred twenty-six miles and six feet.

[Paul Pless]

instead of a square what if we used an enneadecagon?

[Jim Mahan]

Now you're just showin off.

[Keith Wilson]

instead of a square what if we used an enneadecagon?

Or an octatriacontagon, twice as good!

[Peerie Maa]

Another way to think about this. Take the circumference of the Earth and make a square big enough to accomodate it, put the rope on the outside of the square. Now increase the distance of the rope away from the circle to eighteen inches further from center. So the sides of the square are now eigheen inches times two away from each other on either side of the circle. Ninety degrees is the same, also eighteen inches, times two, one for each opposing side. So the square is bigger by thirty-six inches square. It doesn't matter how long the sides are, the net is the same. Earth's diameter is seven thousand nine hundred twenty-six miles at the equator. So the sides of the square, and the length of the rope is seven thousand nine hundred twenty-six miles and six feet.

If the sides of the square are moved 18 inches out, the rope will be 8 times 18 inches longer, 12 feet.

[TomF]

Or an octatriacontagon, twice as good!

I think there's a vaccine for that.

[ShorelineJohn]

I found this to be a great thread, better than the Monty Hall problem. (And really good homework)The part I am trying to solve is, given the rope around the equator how far north or south does one need to move the rope to have it be 1 foot away from earth.

Post #17 Question.
I think it can be figured out with Geometry without calculus. Eratosthenes calculations are a clue, It is an "Annoying Truth" that I don't already know how to do this.

[Beowolf]

Considering that looking both ways before crossing the street is considered a challenge in this discussion, it’s no wonder that resolving 8th grade algebra has stretched to two pages.

Sweet Baby Jesus in a Chicken Basket.

[Beowolf]

I found this to be a great thread, better than the Monty Hall problem. (And really good homework)The part I am trying to solve is, given the rope around the equator how far north or south does one need to move the rope to have it be 1 foot away from earth.

My math comes in around 100 miles. Although with sig-figs being what they are, I can only say that it’s somewhere in that neighborhood.

[oldcodger]

Now, to calculate how far north along the surface of the earth...that will take a lot more calculation, but is roughly the same distance.

Using your figures, tan of the angle will be 6466/20902200 = .0003093454278

Angle is .01772418686 degrees.

The distance on surface of the earth will be the circumference of the earth times the angle divided by 360

2 x Pi x 20902200 x .01772418686 / 360 = 6465.999794 so quite close to 6466

[Peerie Maa]

Using your figures, tan of the angle will be 6466/20902200 = .0003093454278

Angle is .01772418686 degrees.

The distance on surface of the earth will be the circumference of the earth times the angle divided by 360

2 x Pi x 20902200 x .01772418686 / 360 = 6465.999794 so quite close to 6466

Are you a mate of the Egyptian Eratosthenes of Cyrene ?

[oldcodger]

Are you a mate of the Egyptian Eratosthenes of Cyrene ?

No I am not a polymath, just a nerd with some interests.

I enjoy visualizing things but that let me down big time with Pure Maths.

[Peerie Maa]

No I am not a polymath, just a nerd with some interests.

I enjoy visualizing things but that let me down big time with Pure Maths.

There must be something in our Cumbrian water.

[rayman]

can I ask the simple question-why, and who cares??