# Earth belt

PBE6
Posers and Puzzles 08 Oct '09 14:27
1. PBE6
Bananarama
08 Oct '09 14:27
Imagine a belt big enough to circle the entire Earth with a little slack left over. This slack can be taken up by inserting a 100 m tall stake into the Earth and letting the belt rest on top of it as it circles the Earth.

Q: If the belt were returned to its original circular shape, what would be its radius?

(Assume the Earth is a sphere with a radius of 6371 km, that the belt traces a great circle on the Earth, and that the belt does not stretch.)
2. Agerg
The 'edit'or
08 Oct '09 15:411 edit
nevermind...I asked a yes/no question that only has one answer if this question is solveable
3. PBE6
Bananarama
08 Oct '09 16:46
Originally posted by Agerg
nevermind...I asked a yes/no question that only has one answer if this question is solveable
4. 08 Oct '09 17:071 edit
Originally posted by PBE6

(R = radius of Earth = 6173000m, r = 100m)

1 + R/pi{sqrt[(1 + r/R)^2 - 1] - arccos(R/R+r)}

Which works out as an increase in radius of about 12cm compared to the radius of the Earth.

Plausible? Maybe. I'll try and check it later.
5. PBE6
Bananarama
08 Oct '09 17:16
Originally posted by mtthw

(R = radius of Earth = 6173000m, r = 100m)

1 + R/pi{sqrt[(1 + r/R)^2 - 1] - arccos(R/R+r)}

Which works out as an increase in radius of about 12cm compared to the radius of the Earth.

Plausible? Maybe. I'll try and check it later.
That's what I got too.
6. 09 Oct '09 13:081 edit
Originally posted by PBE6
That's what I got too.
Good. I won't bother checking it, then. ðŸ™‚
7. 10 Oct '09 08:18
doesn't an insertion of 100m increase the radius by 100m / (2*pi) = approx. 16 m?
8. 10 Oct '09 09:43
Originally posted by Mephisto2
doesn't an insertion of 100m increase the radius by 100m / (2*pi) = approx. 16 m?
Inserting 100m into the belt would do that, but that's not the scenario being described. You need to work out what the length of the belt needs to be to go over the top of the mast.
9. 10 Oct '09 10:10
Originally posted by mtthw
Inserting 100m into the belt would do that, but that's not the scenario being described. You need to work out what the length of the belt needs to be to go over the top of the mast.
yes, my (s)lack of understanding English properly made me go wrong ðŸ˜³
10. uzless
The So Fist
20 Oct '09 06:09
Originally posted by mtthw