Question

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 11*10-6 /degree C. This means, for example, that a 1-meter bar of steel that increases its temperature by 1 degree C will expand 11*10-6 meters (11 micrometers)

Answer 1

Answer:

The Height is  H = 70.02 m

Explanation:

We are given that the

                         Initial length is  = $40000\ Km$ = $40,000 *10^{3} m$

from what we are told in the question the circumference of the circle is = $40,000 Km$

  This means that the Radius would be :

         Let C denote the circumference

      So  

               $C = 2 \pi r$

      =>     $r = \frac{C}{2 \pi}$

               $r = \frac{40,000}{2 \pi } = \frac{40,000*10^{3}}{2 *3.142} = 6.365*10^6 m$

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

Hence

       The final length would be

                            $40000*10^3 *(T + \alpha )$

Where T is the change in  temperature  $\alpha$ is the Coefficient of linear expansion for steel

  let $L_{final}$ denote the final length

   So

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

                  $= 40000440 \ m$

 Now the Height is mathematically represented as

         $Height(H) \ = \frac{change \ in \ radius \ }{2 \pi}$

                       $= \frac{(40000440-40000*10^3)}{2*3.142}$

                       $= 70.02m$