An eccentric billionaire (and presidential candidate) builds a steel band (steel

Question

An eccentric billionaire (and presidential candidate) builds a steel band (steel = 1.2X10-5 K-1) around the world at the equator. As initially constructed, this band sits on the surface of the planet and forms a perfect ring of radius R = 6371 km. Since the billionaire doesn’t believe in global warming, he orders his engineers not to build any expansion joints into the structure. If the mean temperature of the planet rises 0.40 oC by 2040, how high off the ground will this ring sit then, in meters?

Explanation / Answer

r final = rinitial (dt + 1)

Where

dt = change in temperature

= linear expansion coefficient

Therefore, r final = rinitial (dt + 1) = 6371 (0.4 * 1.2X10-5 + 1) = 6371.03058 km

The new radius is 6371.03058 km

It will therefore be (6371.03058 km - 6371) = 0.03058 km

This means 30.58 m above the surface of the earth.

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