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from Newsletters and Commentaries
PUZZLER: A Rope Around the Earth
This puzzler is a classic:
A rope fits snugly around the equator of the Earth. Ten feet is added to its length. When the extended rope is wrapped about the equator, it magically hovers at uniform height above the ground. How high off the ground?
A second rope fits snugly about the equator of Mars and ten feet is added to its length. How high off the ground does this extended rope hover when wrapped about the planet's equator?
A third rope fits snugly about the (tiny) equator of a planet the size of a pea. When ten feet is added to its length, how high off the equator does it hover?
Comment. The answers to these questions are surprising in three ways: they are the same, they can be computed with no knowledge of the radius of the planet under consideration, and the shared answer is surprisingly large, about 1.6 feet. (Adding just ten feet to a rope the length of the circumference of the Earth produces enough space under which to roll!)
This problem provides a wonderful activity for students. Using a length of rope as a radius, draw a circle on the ground with sidewalk chalk. Lay a long rope about its circumference and add ten feet to its length. Have a group of students—evenly spaced about the circle—attempt to wrap this extended rope about the original circle with a gap of constant width.
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