Answer to Question #172543 in Physics for Diocos

Question

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?

Answer 1

Compression:

$$\Delta L=\epsilon L.$$

Strain:

$$\epsilon=\frac \sigma E.$$

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

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

So, combine this to get the compression:

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

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