Answer:
1.894 × 10^-4 m
Step-by-step 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