A little maths teaser

[TVC]

This one was on University Challenge, so I won't claim credit:

Lay a rope all the way round the Earth so that the two ends are just touching and there is no slack in the rope.
Now, raise the rope one metre off the ground all the way around the Earth.
How big will the gap between the two ends of the rope be?


Put your hands up and no shouting out!
If you have an answer then post it so that the text is formatted to the same colour as the background and can only be read by highlighting, like this:

So it won't spoil it for others.

Enjoy.

 

[Archie_tect]

Pi x additional diameter [2m] so ends will be 6.284m apart.

 

[Peteaud]

What month is it?

Is the tide in or out?

 

[threebikesmcginty]

My screen is set to CC 'darker' so I could read what you've both written! Anyway my answer as below...

Hey! Who gives a shit!!!

 

[TVC]

Archie: 10/10
Peteaud: It doesn't matter
3BMcG: Just what I expected from you.

 

[threebikesmcginty]

3BMcG: Just what I expected from you.

So, do I get a 'like'?

 

[deptfordmarmoset]

I'm no good at this sort of stuff but doesn't the answer calculate the distance of an arc? The gap would be a straight line.

 

[TVC]

Marmoset: it does, but the difference will not be significant, no points for being a smartypants
3BMcG: You would have got a like if you'd has a sensible stab at the answer.
Tadpole: If you say so.

 

[Archie_tect]

Can I have the rope when you're done?
An approx cost per foot is 80p... that's a lot of money! + you'd have to splice it every 100 foot or so, that's another foot and £2 per splice!
We're on a winner here TVC. [Where did you find it?]

 

[Archie_tect]

String's no use, it would stretch.... but you could start with string and slowly build up to thicker ropes....

 

[threebikesmcginty]

You'll get no more likes from me you Leicester dwelling fried spud muncher.

 

[Archie_tect]

Here 3BMcG, hold this rope a minute.

 

[Archie_tect]

Didn't he used to be a Chinaman?

 

[Gary E]

6.283 (ish) m

 

[thom]

I refer the honourable gentleman to the following post and subsequent replies.
Now we know where their questions come from ;-)

In fact the answer you'll have is slightly wrong on 2 counts:
1) the distance depends on the shape of the body - you reasonably assume the rope traces a circle round the earth for the purposes of the question but in reality, the peaks and dips in the earth invalidate this and the formula used - you need to know the exact description of the earth's surface where the rope lies
2) there is a small amount of curvature that even under the assumption that the earth is round, the distance between the two ends is just slightly less