Jump to content
BrainDen.com - Brain Teasers
  • 0


itachi-san
 Share

Question

Bill wants to tie a rope around the earth. So he buys a rope of 40,000 KM and ties it around the world. His neighbor, Charley, wants to do the same only he wants the rope supported on sticks 1 meter above the ground uniformly.

1) How much more rope does Charley need?

2) And how much rope would he need if he used the moon instead of the earth?

Link to comment
Share on other sites

9 answers to this question

Recommended Posts

  • 0

We worked this out in physics...

Approximately 6.28 m.

The first rope has length L=2(pi)r, from the equation for circumference, where r=the radius of the earth.

The new rope has length X=2(pi)(r+1), where r+1=the new radius.

By multiplying, we get: X= 2(pi)r + 2(pi)(1)

Since 2(pi)r=L, X=L+2(pi)(1)

Thus the new rope is 2(pi) longer, which is about 6.28 meters.

The same method applies to the moon, because earth's actual radius doesn't matter. Thus the moon rope would also be 6.28 m longer.

Link to comment
Share on other sites

  • 0
We worked this out in physics...

Approximately 6.28 m.

The first rope has length L=2(pi)r, from the equation for circumference, where r=the radius of the earth.

The new rope has length X=2(pi)(r+1), where r+1=the new radius.

By multiplying, we get: X= 2(pi)r + 2(pi)(1)

Since 2(pi)r=L, X=L+2(pi)(1)

Thus the new rope is 2(pi) longer, which is about 6.28 meters.

The same method applies to the moon, because earth's actual radius doesn't matter. Thus the moon rope would also be 6.28 m longer.

I haven't worked out the puzzle yet but it doesn't make sense that size of the sphere is irrelevant. if the circumference of the sphere were less than 6 meters then how could the the additional rope length be 6.28 meters? Radius of the sphere must matter, so I would recheck your math.

I am taking this back, I was too qick on my judgement. Math is Math!

Edited by teaser101
Link to comment
Share on other sites

  • 0
We worked this out in physics...

Approximately 6.28 m.

The first rope has length L=2(pi)r, from the equation for circumference, where r=the radius of the earth.

The new rope has length X=2(pi)(r+1), where r+1=the new radius.

By multiplying, we get: X= 2(pi)r + 2(pi)(1)

Since 2(pi)r=L, X=L+2(pi)(1)

Thus the new rope is 2(pi) longer, which is about 6.28 meters.

The same method applies to the moon, because earth's actual radius doesn't matter. Thus the moon rope would also be 6.28 m longer.

Well done. Exactly correct

Link to comment
Share on other sites

  • 0

He needs 2pi M more rope regardless of earth or moon.

r1 = first radius

r2 = second radius

extra rope needed = 2pi*r2 - 2pi*r1 = 2pi * (r2 - r1) = 2pi M

since r2 - r1 = 1 M

Edited by dave273
Link to comment
Share on other sites

  • 0

Similar to this post, which as you can see generated a lot of discussion. It didn't take long to understand the math, but I loved the puzzle because it's such a mind-blowing idea, quite contrary to my intuitive response.

Link to comment
Share on other sites

  • 0

so ...

pi*d=40000 = > d=12732.3954 km

by adding 1 meter sticks to each side, so 1 m = .001 km

so the new d=12732.3954 km + .002 km = 12732.3974 km

so the new circumference = c = pi*d=40000.006283185307179586476925287 km = 6.283185307179586476925287 m

and for those of use who loathe the metric system .006283185307179586476925287 km =247.3695 in = 20.614125 ft

so show me 2*pi m

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...