Physics Question#2

Question

TV broadcast antennas are the tallest artificial structures on Earth. In 1987, a 70-kg physicist placed himself and 344 kg of equipment at the top of a 647-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 0.15 m in radius?

Round your answer to 5 decimal places

Answer 1

Let

m = 414 kg be the total mass compressing the antenna,

h = 647 m be the height of the antenna,

r = 0.15 m be the radius of the antenna,

g = 9.81 m/s² be gravitational acceleration,

E = 200 GPa = 2×10⁸ N/m² be the Young's modulus of steel.

The mass m applies vertical force

F = mg

The cross section of the antenna is

S = πr²

Let Δh be the compression of the tower to be calculated.

By the definition of Young's modulus

Δh/h = F/(S×E)

Therefore

Δh = (h×F)/(S×E)

= (h×m×g)/(πr²×E)

Substituting actual numbers

Δh = (647×414×9.81)/(π×0.15²×2×10⁸) = 0.18587 m

The antenna was compressed about 19 cm.