1. Standard memberPBE6
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    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. Standard memberAgerg
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    08 Oct '09 15:411 edit
    nevermind...I asked a yes/no question that only has one answer if this question is solveable
  3. Standard memberPBE6
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    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
    Never you mind about that.
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    08 Oct '09 17:071 edit
    Originally posted by PBE6
    Never you mind about that.
    My highly unchecked answer is:

    (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. Standard memberPBE6
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    08 Oct '09 17:16
    Originally posted by mtthw
    My highly unchecked answer is:

    (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.
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    09 Oct '09 13:081 edit
    Originally posted by PBE6
    That's what I got too.
    Good. I won't bother checking it, then. 🙂
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    10 Oct '09 08:18
    doesn't an insertion of 100m increase the radius by 100m / (2*pi) = approx. 16 m?
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    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.
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    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 😳
  10. Standard memberuzless
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    20 Oct '09 06:09
    Originally posted by mtthw
    My highly unchecked answer is:

    (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.
    I'm you could have done this as a ratio too.
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    20 Oct '09 17:04
    6731.0318km
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