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Rope trick

+11
411
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+122

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?

#1
+109
+5

d = 12 472km

r = 6 236km

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

(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
Sort:

#1
+109
+5

d = 12 472km

r = 6 236km

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

(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
+26544
+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
+122
+3