TV broadcast antennas are the tallest artificial structures on Earth. In 1987, a 72.0-kg physicist placed himself and 400 kg of equipment at the top of a 610-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 0.150 m in radius?

1.894 * 10^-4 m

Explanation:

mass of the man = 72 kg, mass of the equipment = 400 kg

total mass on top of the antenna = 72 + 400 = 472 kg

total weight of the man and equipment = total mass * acceleration due to gravity (g, 9.81 m/s²) = 472 * 9.81 = 4630.32 N

to calculate the ΔL (how much the antenna was compressed), we use the formula below

E = stress / strain = (F/A) / (ΔL/L) = FL / ΔLA where F is the force in Newton, A is the surface area of the circular face of the antenna in m²

E = 2.1 * 10^11 N/m² which is the young modulus of steel

A = πr² = 3.142 * (0.150²) = 0.071m²

make ΔL the subject of the formula

ΔL = FL / AE

substitute the values into the equation

ΔL = (4630.32 * 610) / (0.071 * 2.1 * 10^11) = 1.894 * 10^-4 m