Science Homework...HELP!?

Question

You tied a string perfetly around the equator. Then you added 1 meter to it. How much larger would the radius of the earth become and how far off the ground would the string be?

please help...i dont get it...and please show work or tell me exactly how to do it.

Answer 1

Let r = radius of earth in feet

Then the circumfence(c) is
c = 2r(pi)

Now we add one to it which gives us a bigger circumfence C
so
C = 2r(pi) + 1

C is also equal to 2R(pi) where R is the radius of the new circle created.

C = 2R(pi) = 2r(pi) + 1

Solve for R

R = r + 1/(2pi)

This means that R is 1/(2pi) feet bigger than r

1/(2pi) is about 2 inches.

So the string would be about 2 inches off the ground all around the earth.

Answer 2

It's hard to explain this problem via a text message, but I will try my best...

You have the circumferance of the earth, if you add one meter to it, it's going to effect the radius.

Here are some formulas that will help find the answer that you are looking for:

Radius: r
Diameter: d
Circumference: C
Area: K

d = 2r
C = 2 Pi r = Pi d

K = Pi r2 = Pi d2/4
C = 2 sqrt(Pi K)

K = C2/4 Pi = Cr/2

Basically you have to determine the constants of your formula. One being the circumference of the Earth at the equator + 1 meter.

That would be your C.

C = (Pi)d, and d/2 = r

That would give you your radius.

How far would the string be off the ground???

Well Subtract your original diameter from your new diameter and divide that by 2.

d1 - d2 / 2

Hope this could be of some help.

Answer 3

The radius of the earth will, of course, not change. The radius of the circle described by the string, however, will; it will increase by 1/(2 pi) meters. So, if the string were supported at a uniform height above the surface, it would be about six inches above the ground.