Hotch's...errr...Monday Afternoon Teaser?

[Hotch]

As we're all gagging for more madness...

Imagine you put rope going all the way around the equator.

Then imagine somebody then trips over your rope and sues you, luckily you're rich (assumed from the ability to buy a rope 60,000km long).

To prevent further mishaps, you decide to prop the rope up 3 metres into the air, so no more people will trip over it.

How much more rope do you need...then times that number be a thousand as I made a mistake and am dumb...? (roughly)

Assumptions:

Assume the world is a perfect sphere.
The circumference of the earth is 60,000km.
Rope is inextensible (no stretching).
Rope is infinitesimally small (it's a wonder how that person tripped on it).

 

[Skill Leverage]

Three questions:

1. How fast is the earth spinning?
2. Are we on Daylight Savings Time?
3. Can dogs look up?

Jokesies.....

 

[Hotch]

Three questions:

1. How fast is the earth spinning?
2. Are we on Daylight Savings Time?
3. Can dogs look up?

Jokesies.....

1-900mph (roughly), go go galaxy song
2-Yes, it's winter (in England at least)
3-If they lie on their back sure

 

[Skill Leverage]

At first glance I'm assuming we are just adding 6m to the diameter of our circle of rope, so our answer is Pi.(D+6)... I'm sure there's more to it than that though.

EDIT: Sorry, how much MORE rope do we need... Pi.(D+6) - Pi.D... we can calculate D from (60,000/Pi)....as I said, sure there's more to it than that.

 

[Mr. Charts]

A rope around the earth........
I think I'll skip this one.

 

[Hotch]

I've made a mistake in the poll.....Uh oh!

they should all be in Meters, not KM

*sad panda*

 

[Skill Leverage]

Ohhhhh I just got that....lol nice Charts

 

[trendie]

does the rope traverse oceans?
the waves will jiggle the rope up and down and thus require constantly changing lengths of rope.

can the rope trip up an oil-tanker?

is the rope parallel to the poles? if not, the changing seasons, and temperature, will cause expansion and contraction of the rope and thus the length involved. (think railway tracks, and why they arent one long length of metal. or indeed, electricity cables, between pylons)

 

[fifty2aces]

As we're all gagging for more madness...

Imagine you put rope going all the way around the equator.

Then imagine somebody then trips over your rope and sues you, luckily you're rich (assumed from the ability to buy a rope 60,000km long).

To prevent further mishaps, you decide to prop the rope up 3 metres into the air, so no more people will trip over it.

How much more rope do you need? (roughly)

Assumptions:

Assume the world is a perfect sphere.
The circumference of the earth is 60,000km.
Rope is inextensible (no stretching).
Rope is infinitesimally small (it's a wonder how that person tripped on it).

C=2*pi*r

So radius of earth = 60,000 / (2 * 3.14) = 9554.14km

Radius of earth + rope = 9554.14 + 3 = 9557.14km

Circumference of new rope = 2 * 3.14 * 9557.14 = 60018.84km

Extra rope = 60018.84 - 60,000 = 18.84km

 

[Skill Leverage]

Is that what I said Fifty... I'm too fried to look again...

 

[fifty2aces]

Is that what I said Fifty... I'm too fried to look again...

Yeah, you were heading in the right direction, and you'd already avoided making the obvious mistake.

 

[Hotch]

does the rope traverse oceans?
the waves will jiggle the rope up and down and thus require constantly changing lengths of rope.

can the rope trip up an oil-tanker?

is the rope parallel to the poles? if not, the changing seasons, and temperature, will cause expansion and contraction of the rope and thus the length involved. (think railway tracks, and why they arent one long length of metal. or indeed, electricity cables, between pylons)

Nice, then again, mots of these are solved by it being inextensible (guess you can read it differently). Really a farce as I buggered up the poll, but oh well, thread will probably turn out just as amusing.

 

[Hoggums]

OK - I've got nothing better to do.

The diameter of the earth is 12,715.43km. The circumference of a circle is defined as pi*diameter

If you wanted the rope 3m above ground then the diameter needs to be an extra 6m (3m at either end)

For on the ground pi * 12715.43 = 39946.70Km
For 3m above .. pi * (12715.43 + 6) = 39,965.55Km

Difference between the two is... 18.85Km

So I win a prize?

EDIT - Doh - I've raised the rope 3Km in my calculation!! I'll go crawl back to my space.

 

[Skill Leverage]

Thank God.

 

[fifty2aces]

OK - I've got nothing better to do.

The diameter of the earth is 12,715.43km. The circumference of a circle is defined as pi*diameter

If you wanted the rope 3m above ground then the diameter needs to be an extra 6m (3m at either end)

For on the ground pi * 12715.43 = 39946.70Km
For 3m above .. pi * (12715.43 + 6) = 39,965.55Km

Difference between the two is... 18.85Km

So I win a prize?

If the circumference of the earth is 60000, how is the diameter ~= 12000?

edit: Just realised you used the correct value, but the question in this thread assumes the earth is 60,000km in circumference.

 

[Hotch]

I can't even type either, meant 2 metres, but yeah!

Prizes for everyone! we're all intelligent (bar me), and all the world's ills are solved.

 

[trendie]

I am being my usual thick self.

For every metre you raise the height (radius), you need 2[pi] extra rope.
I thought the extra would be (3 x 2[pi]) metres. Approx 18.42 metres.

 

[Skill Leverage]

Trendie that's the circ. of a rope 3 metres in radius.

 

[Skill Leverage]

It might also be right though, i literally cannot think at the moment

 

[fifty2aces]

I am being my usual thick self.

For every metre you raise the height (radius), you need 2[pi] extra rope.
I thought the extra would be (3 x 2[pi]) metres. Approx 18.42 metres.

Same answer I got, with less work. (Also your units should be km)