Answer to Question #172543 in Physics for Diocos

Question #172543

TV broadcast antennas are the tallest artificial structures on Earth. In 1987, a 79-kg physicist placed himself and 392 kg of equipment at the top of a 556-m-high antenna to perform gravity experiments. By how much was the antenna compressed, if we consider it to be equivalent to a steel cylinder 0.33 m in radius?


1
Expert's answer
2021-03-26T11:41:22-0400

Compression:


ΔL=ϵL.\Delta L=\epsilon L.

Strain:


ϵ=σE.\epsilon=\frac \sigma E.

Stress under force F=(m+M)g:


σ=FA=(m+M)gπR2.\sigma=\frac FA=\frac{(m+M)g}{\pi R^2}.

So, combine this to get the compression:


ΔL=L(m+M)gπR2E=3.75105 m.\Delta L=L\frac{(m+M)g}{\pi R^2E}=3.75·10^{-5}\text{ m}.

*Young's modulus of steel is E=21011 Pa.E=2·10^{11}\text{ Pa}.


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