Consider a 40,000 km steel pipe in the shape of a ring that fits snuggly all aro

ID: 2126027 • Letter: C

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)

Initial length = 40000 km

Initial radius = 40000/2*pi

Final length = 40000(1+11*10^-6) = 40000.44

Final radius = 40000.44/2*pi

Hieght = Change in radius = [ 40000.44 - 40000 ] / 2*pi = 0.44/2*pi = 0.07006 km

= 70.06 m

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