If we had a piece of rope that fitted snugly all around the equator, we then addedd 6 inches in length?

Question

how much space would appear between the rope and the earth all the way round?

Answer 1

Only a man would add inches....

Answer 2

The correct answer was put forward by Paul H. The rope initially fits snuggly around the earths circumference but it is not rigid, so if the length of the rope is increased it will not stand above the ground, it cannot, unless the rope has no mass or is supported in some way.
If you tie a piece of string around a glass, tight and snug, it has a certain radius and a cetain circumference. If you increase the length of the string slightly it doesn't just stand there like a hallow around the glass, it falls or slips down the glass because gravity says so.
Even if the material changed and we had, for example, a metal strap around the earth, like the strap on a beer barrel, increaseing the length of the strap would not cause it to stand proud from the earth by a set distance all the way around unless it was supported in some way, it may stand away from the earth at some points but would be in contact at others (assuming no deflection in the material which over the distances in question would deffinately occur).
In terms of the mathmatical equation northstar is absolutely right, increasing a circumference of any size by 6 inches leads to a 0.954806 inch increase in its radius. It does not matter how big the circle is, the increase is constant. So if we get rid of gravity and all the other laws that prevent the pure maths working on a rope you would have slightly less than an inch gap all the way around.
Hope that helps.

Answer 3

The circumference of a circle of radius r is 2πr. So the radius of a circle with a circumference 6 inches longer is:

(2πr + 6)/2π = r + 3/π = r + 0.95

So about 0.95 inches of space would appear between the rope and the earth all the way around.

Answer 4

It doesnt matter what the circumference or radius of the earth is. You could wrap a rope around a ping pong ball and extend that 6 inches, the result would be the same. ie. 0.95 inches.

Thus...
Circumerence = 2πr, or radius = C/2π
C+6 = 2π(r + n) (n being increase in radius)
C/2π + 6/2π = r +n

as r=C/2π...
r + 6/2π = r + n

6/2π = n = .95

tada!!

This is hard to imaging though isn't it... that the vastness of the earth makes no difference. So, look at it this way... Increase the radius by 1 inch, and the circumference (C=2πr) increases by 2π inches everytime.

Answer 5

There would be no space between the rope and the earth as long as it is pulled snuggly. The extra 6 in wouldnt matter.

Answer 6

AT any given point on the earths surface it would lift to the full 6" providing nobody else was touching the rope.

Answer 7

About 2 inches. Increasing the circumference changes the diameter by C/Pi.

Answer 8

The Earth's circumference can only be estimated.
The Earth's radius can only be estimated.
Therefore to that logic, the radius + x can only be estimated.
x would therefore be an estimate.
I estimate that the distance you're after would be so small that even scientists would class it as insignificant. You'd also have to take into account the effect the sea had on the string too (not that that would amke the finding significant)!

Answer 9

if you moved the rope as you walked around the earth then the answer would be 6inchs

Answer 10

I too did the calcs, not beleiving the 0.95 inch would be right. Well, it is right. I woulda lost on Jeopardy if I didn't do the calcs.

Answer 11

None, because gravity would pull the rope down to Earth.