|
June 9, 2004
Roping Earth
Imagine a rope tied around Earth's equator like a ring on a person's finger. Now imagine lifting off this very long rope, cutting it somewhere so as to add exactly 1 meter of extra rope. Then imagine placing this longer rope back around Earth at the equator.
Because it is longer than the original rope by 1 meter, a gap between the rope and Earth's surface will form all the way around. How wide is the gap between the rope and Earth's surface?
Show the hint for this puzzle
Hide the hint for this puzzle
The circumference of a circle of radius r is 2(pi)r, where pi has a value of about 3.14.
Show the answer to this puzzle
Hide the answer to this puzzle
About 16 centimeters.
Let R be Earth's radius and g the width of the gap. The distance from Earth's center to the rope is R + g. So, the rope's new length is 2(pi)(R + g). This new length is equal to the rope's original length, 2(pi)R, plus 1 meter (or 100 centimeters).
2(pi)(R + g) = 2(pi)R + 100
2(pi)R + 2(pi)g = 2(pi)R + 100
2(pi)g = 100
g = 100/2(pi)
Given that pi is about 3.14, the gap g is about 16 centimeters.
Notice that it doesn't matter how long the original rope is. If you tied a rope around a basketball instead of Earth and added an extra meter to the rope, the resulting gap would still be about 16 centimeters.
Talk Back:
Do you have any comments about this puzzle? Send them
to us using the form below.
|
SNK RSS Feed 
