Around the world in 6 inches

Uncle Dad

Lay a rope around the equator. Now lengthen it by 6 inches.

This gives you enough slack to raise the rope by 1 inch from the ground AROUND THE WHOLE PLANET. :eek:

locum-motion

Approximating the circumference as 25,000 miles(*1), the radius of the earth is 252,101,429 inches.
If your lengthened rope is 25,000miles & 6" long(*2), then the radius of its circle is 252,101,430 inches.

Wow, you're right! I didn't expect you to be!


(*1) 1,584,000,000 inches
(*2) 1,584,000,006 inches


(Calculated using whatever the value of Pi that's stored in the iPhone's Calculator app is.)

Uncle Dad

Surprising, eh? The same thing works for a circle of any size because the formula for the circumference is linear. It would work for a circle the size of our galaxy or the whole universe.

If you add 2pi (ok, it's not 6 exactly but 6.283..) to 2pi*r you get,

2pi*r + 2pi.

Which is of course the same as,

2pi*(r+1).

That's an extra inch in radius, regardless of what you started with!

Capt'n Midnight

Since this is science rather than maths

work out what temperature you would need to heat the rope by to give you that extra inch/mile and then translate it into the temperature profile of our atmosphere

http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html

Lbeard

Capt'n Midnight wrote: »

work out what temperature you would need to heat the rope by to give you that extra inch/mile and then translate it into the temperature profile of our atmosphere

But the temperature would change at different locations depending on time of day, year, weather on the day.

Average atmospheric temperature is not like the average temperature in a cup of tea.

OCorcrainn

At first when I saw the thread title I thought it read "Around the world with 6 inches".