Rope around the earth problem

[Sinbad]

Nope, 6 feet slack in a rope of 132 000 000 feet is but 0.0000045% of slack.

Not even noticeable at all it's way too small to even be felt or seen anywhere apart from the 2 points of origin.

Uncorrect.

Do the maths properly.

circumference = pi x d
Therefore diameter = circumference/pi

If you increase the circumference by 1 foot (lengthening the rope by 1 foot) you increase the diameter by 1/pi feet, and thus the radius by 1/2pi feet.

 

[Sinbad]

Or to put it another way...
The diameter of a circle of circumference say 10000km is 10 000 000/pi m
3183098.8618379067153776752674503m


Diameter of a circle of circumference 10 000.001km is 10 000 001/pi m
3183099.1801477928991683468052178

Difference is 0.32m in diameter, or 0.16m in radius. Which is 1/(2pi). So adding 1 meter to the rope (circumference) adds 16cm to the radius (height above the original circle)

Similarly, a 1m rope produces a circle of 0.16m radius.

 

[Hamish McPanji]

Nope, 6 feet slack in a rope of 132 000 000 feet is but 0.0000045% of slack.

Not even noticeable at all it's way too small to even be felt or seen anywhere apart from the 2 points of origin.

Look at the mathematical proof of this and come back

 

[skeptic_SA]

A variation of this problem was discussed during an episode of S1 of House of Lies. Found it quite interesting.

Suppose you tie a rope around the earth at the equator (circumference approx. 25,000 miles).
Let's say you pull the rope as tight as it will go and then add back 6 feet of slack before tying the knot.
If the extra rope is distributed evenly around the globe will there be enough
space between the rope and the surface of the earth for a worm to crawl under?

Assume the earth is a perfect sphere and the rope does not stretch.

Lol... A round earth. Pffffffft...

 

[Swa]

Ok... length of the equator is about 40,075,036m
r = C / 2pi = 6,378,140.074m

Add 6 feet or 1.8288m and you have
r = 40,075,037.8288 / 2pi = 6,378,140.365m

Rather surprising but 6 feet adds about 291mm radius to such a large rope.

 

[Sinbad]

Ok... length of the equator is about 40,075,036m
r = C / 2pi = 6,378,140.074m

Add 6 feet or 1.8288m and you have
r = 40,075,037.8288 / 2pi = 6,378,140.365m

Rather surprising but 6 feet adds about 291mm radius to such a large rope.

Indeed. It's very counterintuitive, but it's a fact.

 

[StrontiumDog]

Can someone explain this to me like i'm a 5 year old because clearly i have no clue.

 

[Sinbad]

Can someone explain this to me like i'm a 5 year old because clearly i have no clue.

If you add six feet to the length of a rope around ANY circle, you add 291mm to the radius of the circle it encloses.

 

[MartyMarts]

Hmmm... maths.
More importantly, why rope though? Why not fibre - doesn't stretch either and can be useful after the 'experiment'.

 

[Pitbull]

Uncorrect.

Do the maths properly.

circumference = pi x d
Therefore diameter = circumference/pi

If you increase the circumference by 1 foot (lengthening the rope by 1 foot) you increase the diameter by 1/pi feet, and thus the radius by 1/2pi feet.

Nothing wrong with my maths. We worked out two different things... 6 feet change in the rope is a total change to the length of the rope of just 0.0000045%. You calculated the circumference of the rope. I calculated the change in length. Yours is the correct one though