An Interesting Science Problem

[pumpuiman]

Imagine you have a very long piece of string. It's long enough to stretch all the way around the earth. Since the circumference of the Earth is about 40,074 kilometres, that's how much string you would need.

Imagine that you lay out this string along the ground and on top of the oceans, all the way round the Earth, and that the earth's surface was smooth and free of obstructions.

Now pull it tight, so it lays flat. The string makes a big circle that is 40,074 kilometers, or 4,007,400,000 centimeters long.

Then you realize that you have an extra meter of string in your pocket, and you want to add it to the string around the Earth ...

You'll have to cut the circle of string somewhere, as it passes in front of you on the ground. Then you'll add exactly one meter more string.

Now you want to spread out this extra bit of string around the Earth, supporting it somehow, so that the string forms a circle off the ground, all 40,074 kilometers (plus one meter) around the world.

This may take a while! But eventually, you've smoothed the string out into a perfect circle, all the way around the Earth, and slightly off the ground because of the extra 100 cm you added.

Here's the question we want to ask ...

How high off the ground would the string be?

I'm sure some of you know the answer.....I'll post it later.

Make a best guess.....try not to google it!!!

[pumpuiman]

A hint.......the size of the sphere makes no difference. A meter added to a string wrapped around a basketball will produce the exact same result!!

[pumpuiman]

Ok......no takers.......Here's the answer.

You would probably say that the string will hardly be off the ground at all. After all, you only added 100 cm, and the string's length was 4,007,400,000 cm to start with. Most people guess something like 0.00005 cm.

The very surprising answer is that the string will be 15.9 cm off the ground, all the way around the Earth!

If you think about it, this is a very large distance for so little change to the total length of the string!

Another way to look at the problem may make the answer seem more reasonable. The height of 15.9 cm is in addition to the radius of the Earth. Since the Earth's radius is about 637,800,000 cm, the change in height is in fact very tiny.

But wait, there's more ...

The size of the object you're wrapping the string around is completely irrelevant to the problem!

Imagine wrapping a string tightly around a basketball, which has a circumference of about 94 cm.

Then you add exactly 100 cm of string, and smooth out the circle all around the ball.

You will make the surprising discovery that the loop of string is once again 15.9 cm above the ball!

Whether the ball is the Earth, or a basketball, or a marble, adding one metre of string to the circumference will make the string form a loop 15.9 cm above the surface, regardless of the size of the sphere the string is wrapped around!

Here are the calculations that show the height of the string above the Earth, after you add one metre.

We first worked out the circumference of the Earth, which will be the length of the original string. It's 4,007,415,589 cm.

Next we added 100 cm, making the length of the string 4,007,415,689 cm.

Finally, we solved for the radius of this new bigger circle.

When compared to the original radius, you can see that the difference is in fact 15.9 cm.

Edited September 4, 2007 by pumpuiman

[zaza]

[meemiathai]

C=2 pi r

X is the piece of extra string

Y is the height increased

C+X = 2 pi (r+Y)

C+X = 2 pi r + 2 pi Y

X = 2 pi Y

[suegha]

Thanks for clarifying it meemiathai! I now feel so much more illuminated!

Of course if you think about it, it's obvious!!!

[gampaan]

DITTO...

[meemiathai]

Thanks for clarifying it meemiathai! I now feel so much more illuminated!

Of course if you think about it, it's obvious!!!

Cheers

I learned that when I was in university year 4.

[frikkiedeboer]

Ok......no takers.......Here's the answer.

You would probably say that the string will hardly be off the ground at all. After all, you only added 100 cm, and the string's length was 4,007,400,000 cm to start with. Most people guess something like 0.00005 cm.

The very surprising answer is that the string will be 15.9 cm off the ground, all the way around the Earth!

If you think about it, this is a very large distance for so little change to the total length of the string!

Another way to look at the problem may make the answer seem more reasonable. The height of 15.9 cm is in addition to the radius of the Earth. Since the Earth's radius is about 637,800,000 cm, the change in height is in fact very tiny.

But wait, there's more ...

The size of the object you're wrapping the string around is completely irrelevant to the problem!

Imagine wrapping a string tightly around a basketball, which has a circumference of about 94 cm.

Then you add exactly 100 cm of string, and smooth out the circle all around the ball.

You will make the surprising discovery that the loop of string is once again 15.9 cm above the ball!

Whether the ball is the Earth, or a basketball, or a marble, adding one metre of string to the circumference will make the string form a loop 15.9 cm above the surface, regardless of the size of the sphere the string is wrapped around!

Here are the calculations that show the height of the string above the Earth, after you add one metre.

We first worked out the circumference of the Earth, which will be the length of the original string. It's 4,007,415,589 cm.

Next we added 100 cm, making the length of the string 4,007,415,689 cm.

Finally, we solved for the radius of this new bigger circle.

When compared to the original radius, you can see that the difference is in fact 15.9 cm.

you got it all wrong. your math is ok, but EVERYBODYin thailand knows that the earth is FLAT, so your experiment won't work!

[zaza]

DITTO...