Suppose a metal band stretched around the Earth at the equator. The length of this circular band would be 24901.143 miles (131478035 feet). If this band were to be lengthened by 6 feet and the band were suspended evenly around the Earth above the equator, would you expect there to be a noticeable space between the new band and the surface of the Earth? Find the distance between the lengthened metal band and the surface of the Earth in feet.
I have no clue how to start this so if somebody can just tell me how to get started I should be able to finish...Thanks!
Hello, mathkid2007!
This is a classic (old) problem with a surprising answer.
Suppose a metal band stretched around the Earth at the Equator.
The length of this circular band would be 24901.143 miles (131478035 feet).
If this band were to be lengthened by 6 feet and the band were suspended evenly
around the Earth above the equator, would you expect there to be a noticeable space
between the new band and the surface of the Earth?
Find the distance between the lengthened metal band and the surface of the Earth in feet.
Never mind the numbers they gave us . . .
Let be the radius of the earth.
Then the circumference around the Equator is: .
Now is increased by 6 feet.
There will be a corrsponding increase in the radius; call it .
We have: .
. . Then: .
. .Hence: .
Therefore: .
The band will be about a foot above the surface of the earth.
Note: Since the radius drops out of the problem,
. . . . .the original radius does not matter.
If you wrapped a string around a basketball, then extended the string by 6 feet,
. . the new string would be about a foot from the basketball.