Braingle: 'Ring Around the Earth' Brain Teaser

Ring Around the Earth

Science brain teasers require understanding of the physical or biological world and the laws that govern it.

Puzzle ID:	#8439
Fun:	(2.79)
Difficulty:	(2.68)
Category:	Science
Submitted By:	electronjohn
Corrected By:	cnmne

Imagine a smooth metal ring running around the earth's equator about the width of a sidewalk. Now imagine a metal cable wrapped around this first ring so tightly that nothing can squeeze between the cable and the ring. You may assume that the ring and cable are perfect circles even though they most likely would never be. Now this cable, which does not stretch, has three extra feet added to it and is made to magnetically float up and off of the ring so that extra three feet of slack is then equally distributed around the earth. This now gives you an equal distance between the ring and the cable anywhere you checked it around the planet. Now before you do the math, if you are going to do the math at all, what do you think the largest object is that will fit between the cable and the ring?

A) an electron (Less than 1x10-13 cm)
B) a virus (~100nm)
C) single skin cell (~20 microns)
D) a grain of sand (~200 microns)
E) a typical pearl (~9mm diameter)
F) a grape (~1 inch diameter)
G) a grapefruit (~5 inches diameter)
H) a pumpkin (~1.5 feet diameter)

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Answer

The gap comes to about 5.73 inches, which is about the size of a grapefruit! If you wrap the cable around a soccer ball and add 3 feet the gap between the soccer ball and the cable will be 5.73 inches, the same as it was for the earth. If you wrap the cable around the solar system and add 3 feet you also get a 5.73 inch gap! It does not matter what the original circumference is in this problem, the answer will always be the same!
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Comments

speedyg1000 Nov 16, 2002	wooooah...that is really weird
just_moi Nov 17, 2002	could u pleez explain a bit more? the circumference of the earth and the ball are totally different! the earths is a LOT bigger so wouldnt the extra 3 feet have to be distributed around a lot more of the ring thus less space between the cable and ring? or is this based on a scientific theory beyond the mental abilities of my humble brain?
electronjohn Nov 18, 2002	Here is the mathematical explanation for why it works. It blew my mind when I first heard about this and it took my doing the math a number of times before I believed it. So please do not feel your mental abilities are lacking. First of all you have to know the following. Circumference = 2 x Pi x radius so, Earth Circumference = 2 x Pi x r1 where r1 is the earth’s radius in feet and Pi= 3.141592654…. Circumference of modified cable = 2 x Pi x r2 where r2 is its radius. What we want to do is find the difference between the two radiuses (or is it radii?) which is (r2 – r1).
electronjohn Nov 18, 2002	Sorry, I am having trouble posting the rest of this explanation!
electronjohn Nov 18, 2002	The difference between the cable’s circumference and the earth’s circumference is 3 feet, so: 2 x Pi x r2 = 2 x Pi x r1 + 3
electronjohn Nov 18, 2002	or (2 x Pi x r2) – (2 x Pi x r1) = 3, or 2 x Pi x (r2 – r1) = 3, or (r2 – r1) = 3/(2 x Pi)
electronjohn Nov 18, 2002	which equals about 0.477 feet or about 5.7 inches.
electronjohn Nov 18, 2002	Now notice that the circumference of the initial object (i.e. earth, soccer ball, solar system, atom, etc.) is nowhere to be seen in the final equation. The only important thing here is the 3 feet added.
electronjohn Nov 18, 2002	If you are still in school and you have not covered this math yet then ask your teacher to go over it with you.
just_moi Nov 19, 2002	WOW! strange... but awesome!!!
Deucex2 Dec 03, 2002	Brilliant. Absolutely brilliant. I'm gonna run this one by my science teachers from high school wicked grin!
jonnyonline Jan 16, 2003	it's radii
jonnyonline Jan 16, 2003	i think why most people have conceptual problems with this one is because they tend to assume that the 25,000 miles of cable is applied to a soccer ball, etc. when in fact that starts taught as well.
jimbo Feb 24, 2003	If you know calculus you can start with the circumference C=2x Pi xR. The change in C (dC) = 2Pi x Change in R (dR) so the change in circumference is only affected by the change in radius and it has no component referring to R the original radius. Hence the change is constant for all circles.
curtiss82 Dec 24, 2003	Wow. That is probably one of the best teasers I have read. But I would have put it in the math section though.
vbguy101 Sep 02, 2006	Simply find it by figuring the radius of acircle 3 ft(36 in) in circumference 36/2pi=5.73 in. Correct! Actually, it's 5.7295645530939648586707410236822 in
vbguy101 Sep 02, 2006	I used Windows Calculator, and I DID NOT run out of room.
mosca Jul 15, 2007	Really great teaser! I got it ok, but had never seen this type of problem! I'm going to pass this on to our Army math tutor for her enjoyment!
Zag24 Jan 19, 2009	I've seen this before, but I like the way you tell it -- with the list of choices. (Also, I agree that this belongs in math, not science.)
RAUL Sep 04, 2010	This seems to involve a lot of PI and I love pumpkin PI.