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Anders
Anders asked in Science & MathematicsPhysics · 7 years ago

If you tie a rope firmly around the equator of the earh (40000 KM), how much more rope to have it suspend 1 meter above ground?

So, lets say that 40000 km worth of rope fits snugly around the equator of the earth. Now, if I want to elevate the rope to 1 meter above ground all around the earth's circumference, how many extra meters of rope would I need?

Update:

I'm also assuming in this question that the earth is a perfect sphere.

3 Answers

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  • lunchtime_browser
    Lv 7
    7 years ago
    Favorite Answer

    Call the radius of the Earth R metres. Its circumference is therefore 2πR metres and that is the length of a rope on the ground.

    When the rope is 1 m above the surface, the rope makes a circle of (R + 1) metres, so its circumference is 2π(R + 1) metres.

    The difference in length (x) is therefore:

    x = 2π(R + 1) - 2πR

    multiply out the brackets.

    x = 2πR + 2π - 2πR

    x = 2π metres

    x = 6.28.. metres

  • civil_av8r
    Lv 7
    7 years ago

    40000 km = circumference... find the radius

    2*pi*r = 40000 km

    r = 40000 km / 2*pi

    If you add 1m to the radius, find the new cirumference

    2*pi*r = 2*pi*(40000 km / 2*pi + .001 km) = 40000.00628 km

    So, you added 6.28 m to the length.

  • jimmymae2000
    Lv 7
    7 years ago

    Add about 2PI meters of rope (6.28 m).

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