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A piece of rope is placed on the ground at the equator and runs all the way round the Earth.It is then cut, and 1 metre is added.Now we ask everyone around Earth to stand equally placed apart and lift the rope,how high will they be able to lift it?

Mathcad  May 11, 2015

Best Answer 

 #1
avatar+109 
+5

d = 12 472km

r = 6 236km

p = d * pi = $${\mathtt{12\,472}}{\mathtt{\,\times\,}}{\mathtt{\pi}} = {\mathtt{39\,181.943\: \!575\: \!571\: \!901\: \!270\: \!1}}$$

 

Let's add a meter:

(1m = 1/1000km)

 

$${\mathtt{39\,181.943\: \!58}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{1\,000}}}} = {\mathtt{39\,181.944\: \!58}}$$

 

And back to the diameter:

 

$${\frac{{\mathtt{39\,181.944\: \!58}}}{{\mathtt{\pi}}}} = {\mathtt{12\,472.000\: \!319\: \!719\: \!393\: \!786\: \!5}}$$

 

We have ~3.197 Meter more.

We can lift it now by 1.5985 Meter on each side. 

xerxes  May 11, 2015
 #1
avatar+109 
+5
Best Answer

d = 12 472km

r = 6 236km

p = d * pi = $${\mathtt{12\,472}}{\mathtt{\,\times\,}}{\mathtt{\pi}} = {\mathtt{39\,181.943\: \!575\: \!571\: \!901\: \!270\: \!1}}$$

 

Let's add a meter:

(1m = 1/1000km)

 

$${\mathtt{39\,181.943\: \!58}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{1\,000}}}} = {\mathtt{39\,181.944\: \!58}}$$

 

And back to the diameter:

 

$${\frac{{\mathtt{39\,181.944\: \!58}}}{{\mathtt{\pi}}}} = {\mathtt{12\,472.000\: \!319\: \!719\: \!393\: \!786\: \!5}}$$

 

We have ~3.197 Meter more.

We can lift it now by 1.5985 Meter on each side. 

xerxes  May 11, 2015
 #2
avatar+26720 
+3

If h is the height it can be lifted, then we have:

 

Original circumference = pi*d  where d is diameter of the earth.

New circumference = pi*(d+2h)  since the new diameter is d+2h.

 

New - Old circumference:  pi*(d + 2h) - pi*d = 1m so that pi*2h = 1m  or h = 1/(2pi) m or h ≈ 0.159m

 

(xerxes, your next to last line should say "We have ∼0.3197 meters more).

.

Alan  May 11, 2015
 #3
avatar+122 
+3

sorry xerxes,answer is simply     1metre/2pi.

Here's the solution; let Earth's circumference be 2pi R. New circumference then is 2pi (R + delta R) where delta R is the height we want to find.

so 2pi R + 1 metre= 2pi(R+ deltaR),the 2pi R 's cancel out,giving 2pi delta R = 1 metre,so delta R,the height,is 1 metre /2pi. We did not need to know the Earth's circumference in order to solve the problem.

Mathcad  May 11, 2015

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