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Suspend your disbelief for a moment,
If you tied a length of string around the full circumference of the Earth so it was taught, then made it one metre longer so it floated at a uniform height around the whole Earth, how high would it float? Assume the Earth is a perfect sphere 12,756.3km in diameter.
If you can't work it out, take a guess. Remember that it's a piece of string going around the whole Earth - how high off the ground would it be if you made it 1 metre longer?
If you tied a length of string around the full circumference of the Earth so it was taught, then made it one metre longer so it floated at a uniform height around the whole Earth, how high would it float? Assume the Earth is a perfect sphere 12,756.3km in diameter.
If you can't work it out, take a guess. Remember that it's a piece of string going around the whole Earth - how high off the ground would it be if you made it 1 metre longer?
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This is the long way to solve it:
The diameter, d, of the Earth is 12756300m
:: d = 12756300
The circumference, c, of the Earth, and hence the length of the original string, is d * 3.141 (pi)
:: c = 12756300 * 3.141 = 40067538.3m (40 million metres)
Now we lengthen the string by 1m. The new length of the string shall be called c'
:: c' = 40067538.3 + 1 = 40067539.3
The diameter of the new, longer string c' = pi * d'
:: d' = c' / pi = 40067539.3 / 3.141 = 12756300.31837
Therefore, the difference in diameter, x = d' - d = 12756300.31837 - 12756300 = 0.31837
This is the increase in diameter of the string - we want the radius, which only gives us the height gain on one side.
r = x / 2 = 0.31837 / 2 = 0.159m = 15.9cm
Bar a rounding error, I declare sideshow buzz the winnar! My putting him down earlier was a trick - I believed the answer to be about 30cm, but either is quite incredible when you consider it. Lengthen the circumference of the Earth by just one metre, and its diameter would grow by 15cm.
Well, I thought it was swish (sorry buzz).
The diameter, d, of the Earth is 12756300m
:: d = 12756300
The circumference, c, of the Earth, and hence the length of the original string, is d * 3.141 (pi)
:: c = 12756300 * 3.141 = 40067538.3m (40 million metres)
Now we lengthen the string by 1m. The new length of the string shall be called c'
:: c' = 40067538.3 + 1 = 40067539.3
The diameter of the new, longer string c' = pi * d'
:: d' = c' / pi = 40067539.3 / 3.141 = 12756300.31837
Therefore, the difference in diameter, x = d' - d = 12756300.31837 - 12756300 = 0.31837
This is the increase in diameter of the string - we want the radius, which only gives us the height gain on one side.
r = x / 2 = 0.31837 / 2 = 0.159m = 15.9cm
Bar a rounding error, I declare sideshow buzz the winnar! My putting him down earlier was a trick - I believed the answer to be about 30cm, but either is quite incredible when you consider it. Lengthen the circumference of the Earth by just one metre, and its diameter would grow by 15cm.
Well, I thought it was swish (sorry buzz).
Its ok,
just out of interest what was the short way of doing it?
just out of interest what was the short way of doing it?
sideshow buzz wrote:
> 15.9045cm ? above the surface of the earth
Sideshow Won.... he got it right.
> 15.9045cm ? above the surface of the earth
Sideshow Won.... he got it right.
The short way is to do it using algebra.
c = circumference of string before lengthening
c' = circumference of string after lengthening
r = radius of string arc before lengthening
r' = radius of string arc after lengthening
n = pi (closest symbol I could find)
It's fair to say:
c = 2nr
and
c' = 2nr'
But, we know that c' = c + 1. Therefore by substitution we get:
c + 1 = 2nr'
2nr + 1 = 2nr'
We also know that the magical difference we're after, x = r' - r. Therefore:
2n(r'-x) + 1 = 2nr'
2nr' - 2nx + 1 = 2nr'
Subtract 2nr' from both sides gives:
-2nx + 1 = 0
2nx = 1
Therefore:
x = 1/(2n)
We have also proved that the gap x does not change with r. x would be 1/(2n) whether the string was originally 1 or 1 million metres long.
c = circumference of string before lengthening
c' = circumference of string after lengthening
r = radius of string arc before lengthening
r' = radius of string arc after lengthening
n = pi (closest symbol I could find)
It's fair to say:
c = 2nr
and
c' = 2nr'
But, we know that c' = c + 1. Therefore by substitution we get:
c + 1 = 2nr'
2nr + 1 = 2nr'
We also know that the magical difference we're after, x = r' - r. Therefore:
2n(r'-x) + 1 = 2nr'
2nr' - 2nx + 1 = 2nr'
Subtract 2nr' from both sides gives:
-2nx + 1 = 0
2nx = 1
Therefore:
x = 1/(2n)
We have also proved that the gap x does not change with r. x would be 1/(2n) whether the string was originally 1 or 1 million metres long.
Miserableman wrote:
> And PointlessBabble, pick on someone your own age
Blah. :P
You any idea how few people around my own age there are here? I'm part of wrinkly brigade in comparison to the 15yrs of age standard.
I picked on Tony once... but then that doesn't really count, coz he tried picking on me first.
I really don't see why I can't just pick on whoever's available for picking on. I mean, Scouse has the whole "internet bully" thing going on, and that pretty much licenses him to do it to anyone. It's just shamefully unfair that I should be singled out due to my differing age range. Equal rights, damn you. :P
> And PointlessBabble, pick on someone your own age
Blah. :P
You any idea how few people around my own age there are here? I'm part of wrinkly brigade in comparison to the 15yrs of age standard.
I picked on Tony once... but then that doesn't really count, coz he tried picking on me first.
I really don't see why I can't just pick on whoever's available for picking on. I mean, Scouse has the whole "internet bully" thing going on, and that pretty much licenses him to do it to anyone. It's just shamefully unfair that I should be singled out due to my differing age range. Equal rights, damn you. :P
I might be older than you. You can pick on me if you want, I don't mind
Pointless Babble wrote:
> Blah. :P
> You any idea how few people around my own age there are here? I'm part
> of wrinkly brigade in comparison to the 15yrs of age standard.
Sorry, I had assumed that you were about 14. I'm 22, if it helps.
> Blah. :P
> You any idea how few people around my own age there are here? I'm part
> of wrinkly brigade in comparison to the 15yrs of age standard.
Sorry, I had assumed that you were about 14. I'm 22, if it helps.
No Ros, you're around the same age as me, and since Miserable has admitted to being in the same demographic - I will now resume my picking on him. Of course, volunteers are always welcome. ;)
This has been a public service announcement brought to you by Babble Inc.™
This has been a public service announcement brought to you by Babble Inc.™
Is this the demographic of "those too old to play with Barbie dolls?"
Cindy would rock Barbie in a fight anyway
Cindy would rock Barbie in a fight anyway
I dunno... didn't they start messing around with the vital statistics on those things a few years ago?
Besides, in this day and age, when any moderately reknowned individual can give toy companies a profit; you can get effigys of just about anyone. I wouldn't be surprised if there was a lolo ferrari doll out there somewhere, and with a pair of...
...teeth that big, she pretty much wipes the floor with Barbie and Cindy. ;)
Besides, in this day and age, when any moderately reknowned individual can give toy companies a profit; you can get effigys of just about anyone. I wouldn't be surprised if there was a lolo ferrari doll out there somewhere, and with a pair of...
...teeth that big, she pretty much wipes the floor with Barbie and Cindy. ;)
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