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Solved: Consider a 40,000-km steel pipe that forms a ring
Chapter 15, Problem 4P(choose chapter or problem)
Problem 4P
Consider a 40,000-km steel pipe that forms a ring to fit snugly all around the circumference of the Earth. Suppose people along its length breathe on it so as to raise its temperature 1°C. The pipe gets longer. It also is no longer snug. How high does it stand above ground level? (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 = 2πr. The result is surprising!)
Questions & Answers
QUESTION:
Problem 4P
Consider a 40,000-km steel pipe that forms a ring to fit snugly all around the circumference of the Earth. Suppose people along its length breathe on it so as to raise its temperature 1°C. The pipe gets longer. It also is no longer snug. How high does it stand above ground level? (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 = 2πr. The result is surprising!)
ANSWER:
Solution:
For steel, α = 11 × 10-6/°C. Remember that ΔL = Lα ΔT.
ΔL = 40,000 km × 11×10-6/°C × 1°C
= 0.44 km = 440 meters
Lfinal = 40,000,000 m + 440 m
= 40,000,440 m
C = 2πr