[itachi-san]

Bill wants to tie a rope around the earth. So he buys a rope of 40,000 KM and ties it around the world. His neighbor, Charley, wants to do the same only he wants the rope supported on sticks 1 meter above the ground uniformly.

1) How much more rope does Charley need?

2) And how much rope would he need if he used the moon instead of the earth?

[akaslickster]

2more inches of rope.

rope can't be tied around a moon or planet unless it can had been done before.

[Guest]

We worked this out in physics...

Approximately 6.28 m.

The first rope has length L=2(pi)r, from the equation for circumference, where r=the radius of the earth.

The new rope has length X=2(pi)(r+1), where r+1=the new radius.

By multiplying, we get: X= 2(pi)r + 2(pi)(1)

Since 2(pi)r=L, X=L+2(pi)(1)

Thus the new rope is 2(pi) longer, which is about 6.28 meters.

The same method applies to the moon, because earth's actual radius doesn't matter. Thus the moon rope would also be 6.28 m longer.

[Guest]

We worked this out in physics...

Approximately 6.28 m.

The first rope has length L=2(pi)r, from the equation for circumference, where r=the radius of the earth.

The new rope has length X=2(pi)(r+1), where r+1=the new radius.

By multiplying, we get: X= 2(pi)r + 2(pi)(1)

Since 2(pi)r=L, X=L+2(pi)(1)

Thus the new rope is 2(pi) longer, which is about 6.28 meters.

The same method applies to the moon, because earth's actual radius doesn't matter. Thus the moon rope would also be 6.28 m longer.

I haven't worked out the puzzle yet but it doesn't make sense that size of the sphere is irrelevant. if the circumference of the sphere were less than 6 meters then how could the the additional rope length be 6.28 meters? Radius of the sphere must matter, so I would recheck your math.

I am taking this back, I was too qick on my judgement. Math is Math!

Edited May 20, 2008 by teaser101

[itachi-san]

We worked this out in physics...

Approximately 6.28 m.

The first rope has length L=2(pi)r, from the equation for circumference, where r=the radius of the earth.

The new rope has length X=2(pi)(r+1), where r+1=the new radius.

By multiplying, we get: X= 2(pi)r + 2(pi)(1)

Since 2(pi)r=L, X=L+2(pi)(1)

Thus the new rope is 2(pi) longer, which is about 6.28 meters.

The same method applies to the moon, because earth's actual radius doesn't matter. Thus the moon rope would also be 6.28 m longer.

Well done. Exactly correct

[Guest]

about 40006 meters of rope.

[Guest]

Oh sorry 40006 KM, my bad.

[Guest]

He needs 2pi M more rope regardless of earth or moon.

r1 = first radius

r2 = second radius

extra rope needed = 2pi*r2 - 2pi*r1 = 2pi * (r2 - r1) = 2pi M

since r2 - r1 = 1 M

Edited May 20, 2008 by dave273

[Guest]

Similar to this post, which as you can see generated a lot of discussion. It didn't take long to understand the math, but I loved the puzzle because it's such a mind-blowing idea, quite contrary to my intuitive response.

[Guest]

so ...

pi*d=40000 = > d=12732.3954 km

by adding 1 meter sticks to each side, so 1 m = .001 km

so the new d=12732.3954 km + .002 km = 12732.3974 km

so the new circumference = c = pi*d=40000.006283185307179586476925287 km = 6.283185307179586476925287 m

and for those of use who loathe the metric system .006283185307179586476925287 km =247.3695 in = 20.614125 ft

so show me 2*pi m