Imagine a string tied tightly around Earth’s circular equator (of radius about 6400 km) and then add 1 m of extra length to it. Pinch it at a point and lift it up from the surface. How high can you lift it?
The radius is 6400000 meters
The circumference is 2*pi*6400000
If theta is the angle at the earth's center between one point of tangency of the string and the lifted point, then the length of the string, which is the earth's circumference plus 1, is
2*pi*6400000 - 2*6400000*theta + 2*6400000*tan(theta), with theta in radians
= 6400000*(2*pi-2*theta+2*tan(theta))
Using Wolfram Alpha to "solve 6400000*(2*pi-2*x+2*tan(x))=1+2*pi*6400000", one gets x ~= 0.00616549893597891...
The distance of your pinch point from the center of the earth is then
6400000/cos(0.00616549893597891)
which a calculator says is 6400121.64473353, so that's about 122 meters above the surface.
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Posted by Charlie
on 2018-10-29 10:26:14 |
my solution
