How Good Is Your Intuition? (Mind-Teaser)
 

There is a wire, whose length is 10 feet longer than the circumference of the earth at the equator. The wire is formed into a circle, slipped over the earth, and placed at the equator. Assume the equator is also circular and smooth (no mountains or oceans). Can you fit your finger between the wire and the earth?

ok, what's the trick?

how cold is it?

what kinda "circle" - the kind with left over wire?

what kinda "Earth" - the kind with flat poles? slightly pear shaped? wire orientation re part 1?

Don't be a woolly-minded liberal.

There is no thermal expansion or contraction.

The wire is joined end to end. If I meant a circlip or a split ring, I would have said so.

The equator is circular and the wire is placed over the equator.

ok, then "No" - because I am too far away from it to reach mah fanger ovah theah

NO... Even though the wire is 10 feet longer than it has to be the thickness of the wire would mean it would be very tight against the Earth.
(Standing proud of the Earth by half it's thickness)

yes. if there is ten feet of slack you should be able to pull it up nearly 5 feet at a single point. giving you more than enough space to stick your finger under it.

Ok guys, play it straight. As stated, the wire is a circle, the earth's equator is a circle. No stretching, deforming, digging a hole in the earth, etc. This is a test of your sense of geometry and scale, not your ability to invent loopholes :-)

then, there is no way.

depends on the thickness of the wire

but then.. if it is too thin, it'd just cut right thru your finger...

This is a bunch of BS.....

No because of pi?

Easily. There will be approximately a 3 feet gap.

10/(2*pi) ft of gap?

What he is saying is that there is a circle with the circumference of the earth and then there is another circle with the circumference of the earth +10 feet. If you put them concentric to one another, will you be able to fit your finger between the two circles ..

I just did the math - no intuition here. Let's see what you think ...

G

Yes, you could.

This could be easily proven algebraically, but I'm too tipsy.

The problem does not state that the wire has the be evenly gapped around the earth (which is assumed)- if this were the case, no way. But if the wire was zero mass and zero thickness, it could easily be pulled taught until all the slack was in once place, and the wire met, with 5 feet of slack overlapping for a total of 10 feet of slack. Plenty of room for a finger.

He doesn't say they have to stay concentric to each other.

Maybe not concentric but the new circle has to include the old. But they have to be circles, not a circle and a 10 foot loop. ;)

G

eeh, When I think of 'wire' I think something that can be bent around. If it has to stay a circle, why not just call it a circle? Oh, I see, it's part of the sensory intuition of the problem...

there's lots of slack on a ski lift cable. But you won't catch me putting my finger under it.

with no intuition and no exact math (just reason)... if you split the wire (wrapped tightly around) in two halves (180° apart) then splice in a couple five foot Sections, much of the wire would be a couple feet off the surface. ...Now imagine splicing in that 10' section in quarters,... spliced in at 90° apart. . those original arcs are pushed off more than a finger.