Tv broadcast antennas are the tallest artificial structures on earth. in 1987, a 69.0 kg physicist placed himself and 400 kg of equipment at the top of one 610 m high antenna to perform gravity experiments. by how much (in mm) was the antenna compressed, if we consider it to be equivalent to a steel cylinder 0.175 m in radius?

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Explanation:

This is a problem where we have to assume we are in the linear region of the stress-strain curve for the antenna.

The physicist has a mass of 69 [Kg] and his equipment has a mass of 400 [Kg].

Now we just have to add those up, we end up with a mass of 469 [Kg].

The force exerted to the antenna (downwards) will be:

To find the compression we have that the relationship between strain we take the equation:

where is the young modulus, is the strain on the material, is the force exerted by the physicist+equipment, is the cross-section area of the cylinder, and is the initial longitude of the cylinder.

now the young modulus for steel is .

The cross section area for the cylinder is

The length of the antenna is

we find :