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

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)

Explanation / Answer

GIVEN

Initial length Lo = 40,000 km = 40,000*10^3 m = 40*10^6 m

circumference of circle = 2*pi*r0 = L0

r0 = L0/(2*pi) = 4000000/(2*pi) = 636619.8 m

change in temperature dT = 1 oC

coefficient of linear expansion alpha = 11*10^-6 /degree

change in radius dr = r0*alpha*dT = 636619.8*11*10^-6 = 7 m

the ring will atand 7m above the ground level

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