Why does adding 1 meter to a rope around the Earth create slack?

In summary, the original problem stated that someone would have to add 1 meter to a rope to make it long enough to go around the Earth. However, the clever person's way of doing it is to tie the rope tightly around the Earth's equator and then add 1 meter to the rope. This will create some slack so that any type of animal can go through it.
  • #1
LAF
31
0
First, try to use your own sense.

Take a twine (rope) and put it around a ball, or an orange (sphere).
Now you have the circumference (perimeter) of that sphere.
Take this twine and add 1m more (one more meter - it can be any unit of liner measure).
Put this one meter longer twine around the ball again, keeping it equidistant of the surface (circular orbit, ring).
The twine is aprox. 0,159m of the surface of the ball.

Take a twine (rope) and put it around the Earth equator (sphere).
Now you have the circumference (perimeter) of that sphere.
Take this twine and add 1m more (one more meter - it can be any unit of liner measure).
Put this one meter longer twine around the Earth equator again, keeping it equidistant of the surface (circular orbit, ring).
The twine is aprox. 0,159m of the surface of the earth.

Why does it hapen like this?
 
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  • #2
LAF said:
Why does it hapen like this?

I put the answer is spoiler tags, but this doesn't seem like a brain teaser, more like a homework help. Even so, I give the full answer.

Because the radius is a linear function of the circumference: r = c / 2pi
As a result, if you add 1 meter to the length of the rope (that is, to the circumference) then you will add 1 / 2pi (approx .159 meter) to the radius regardless of the original length.
 
  • #3
It´s been boring here and I just tried to show something that breaks the common sense.
Now I see I didn´t. I´ll try harder next time...
 
  • #4
LAF said:
It´s been boring here and I just tried to show something that breaks the common sense.
Now I see I didn´t. I´ll try harder next time...

You have spoiled the problem. The original one is:
Take a rope and tie it tightly around the Earth. Then add 1 meter to the rope. There will be some slack. What kind of animal will pass through the slack?
Intuitively people will say an ant or even a bacterium (I know a bacterium is not an animal, but people say it).
The real answer would be a cat or a bunny.
 
  • #5
CEL said:
You have spoiled the problem. The original one is:
Take a rope and tie it tightly around the Earth. Then add 1 meter to the rope. There will be some slack. What kind of animal will pass through the slack?
Intuitively people will say an ant or even a bacterium (I know a bacterium is not an animal, but people say it).
The real answer would be a cat or a bunny.

Your way is much better! Thanks.
 

1. What is the formula for calculating the perimeter of a circle?

The formula for calculating the perimeter of a circle is P = 2πr, where P is the perimeter and r is the radius of the circle.

2. How do I find the perimeter of a shape with multiple sides?

To find the perimeter of a shape with multiple sides, simply add up the lengths of all the sides. For example, if a square has sides of length 4, the perimeter would be 4+4+4+4 = 16.

3. What is the difference between perimeter and radius?

Perimeter refers to the total distance around the outside of a shape, while radius refers to the distance from the center of a circle to its outer edge.

4. Can the perimeter of a circle be calculated if only the radius is given?

Yes, the perimeter of a circle can be calculated if only the radius is given. As mentioned earlier, the formula for calculating the perimeter of a circle is P = 2πr. So if you know the value of r, you can calculate the perimeter.

5. How do I convert between the perimeter and radius of a circle?

To convert between perimeter and radius of a circle, you can use the formula P = 2πr. So if you have the perimeter, you can solve for r to find the radius. And if you have the radius, you can solve for P to find the perimeter.

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