Consider a 40,000 km steel pipe in the shape of a ring that fits snuggly all around the circumference of the Earth. We are heating now the ring so its temperature increased by 1 degree C. Now, the pipe will no longer be snug. How high the ring will now stand above ground level? (Make as many simplifications as necessary). Data: Coefficient of linear expansion for steel is 1110-6 /degree C. This means, for example, that a 1-meter bar of steel that increases its temperature by 1 degree C will expand 1110-6 meters (11 micrometers)

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okpalawalter8 okpalawalter8 · Answer 1 · 2020-03-16T05:31:51+01:00

Answer:

The Height is H = 70.02 m

Explanation:

We are given that the

Initial length is = [tex]40000\ Km[/tex] = [tex]40,000 *10^{3} m[/tex]

from what we are told in the question the circumference of the circle is = [tex]40,000 Km[/tex]

This means that the Radius would be :

Let C denote the circumference

So

[tex]C = 2 \pi r[/tex]

=> [tex]r = \frac{C}{2 \pi}[/tex]

[tex]r = \frac{40,000}{2 \pi } = \frac{40,000*10^{3}}{2 *3.142} = 6.365*10^6 m[/tex]

We are told that 1-meter bar of steel that increases its temperature by 1 degree C will expand [tex]11*10^{-6}[/tex] meters

Hence

The final length would be

[tex]40000*10^3 *(T + \alpha )[/tex]

Where T is the change in temperature [tex]\alpha[/tex] is the Coefficient of linear expansion for steel

let [tex]L_{final}[/tex] denote the final length

So

[tex]L_{final} =40000*10^{6} *[1+ 11*10^{-6}][/tex]

[tex]= 40000440 \ m[/tex]

Now the Height is mathematically represented as

[tex]Height(H) \ = \frac{change \ in \ radius \ }{2 \pi}[/tex]

[tex]= \frac{(40000440-40000*10^3)}{2*3.142}[/tex]

[tex]= 70.02m[/tex]