Imagine a 40,000-km steel pipe that forms a ring to fit

Chapter 7, Problem 41TAS

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Imagine a \(40,000-km\) steel pipe that forms a ring to fit snugly entirely around the circumference of Earth. Suppose that people along its length breathe on it so as to raise its temperature by \(1^{\circ} \mathrm{C}\). The pipe gets longer—and is also no longer snug. How high does it stand above ground level? Show that the answer is an astounding \(70 \ m\) higher! (To simplify, consider only the expansion of its radial distance from the center of Earth, and apply the geometry formula that relates circumference \(C\) and radius \(r: C=2 \pi r\).)

                               

Equation Transcription:

Text Transcription:

40,000-km

1 degree C

70 m

C

r: C = 2pi r

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