# Rope around the earth

1. Jun 22, 2011

### Punkyc7

a rope is wrapped tightly around the earth (radius 250000). The rope is cut and 3 feet are added to it and the ends are reconnected. Again it is wrapped around the earth. How much space is now between the rope and the earth

so C$_{0}$ =2piR

and C=2pi(R+x)

so to find the height is ti 2piR+2pix-2piR=3

so

x=3/2pi

2. Jun 22, 2011

### cepheid

Staff Emeritus
250,000 whats?. Furlongs? Units are crucial -- always include them.

I take issue with the phrasing of the question. If the rope is again wrapped around the Earth (i.e. around its surface), then my automatic answer/assumption would be that there is still no space between the rope and the Earth, only now the rope goes around the Earth for slightly more than one full turn.

However, if the question is actually supposed to be, "what is the radius of a circle formed by the new rope, and how much larger is this radius than the radius of the Earth?", then what you have done below looks fine.

No surprise here. Circumference varies linearly with radius, meaning that it is proportional to it, with the constant of proportionality being 2$\pi$.

3. Jun 22, 2011

### AC130Nav

Your first job is to compute the circumference given a radius of 250000.

Your second is to compute a new radius given that circumference plus 3.

I'll leave the third step to you.

4. Jun 22, 2011

### cepheid

Staff Emeritus
Umm...no? He did the algebra and he got the answer. EDIT: he or she

EDIT2: What I'm saying here is that leaving things symbolic is fine. Plugging in numbers for R doesn't gain you anything when you can do algebraic manipulations to solve for the exact quantity you're looking for, and that is what the OP has already done.

5. Jun 22, 2011

### AJKing

Could be a trick question.

Due to the potential mass of the rope, if there was ANYWAY that you could add more to it (without it slipping into the ocean), then that length would only allow more lee-way for it to move lower elsewhere.

And when I say elsewhere, I mean, somewhere really close. It would either lower into the nearest soft body or do nothing and fall over aloof.

Anyway, this isn't helping :P.