Final answer:
To find the stress in the steel post, the force due to the mass of the load is calculated and divided by the cross-sectional area of the post. This results in a stress value of approximately 2.27 MPa.
Step-by-step explanation:
The question is asking to find the stress in a vertical solid steel post that is supporting a load. The stress can be calculated using the formula σ = F/A, where σ is the stress, F is the force applied, and A is the cross-sectional area of the post. The force can be calculated from the mass of the load (m = 8000 kg) and the acceleration due to gravity (g = 9.8 m/s²), using F = mg. The cross-sectional area (A) of the post can be found from its diameter (d = 21 cm), A = π(d/2)².
Firstly, calculate the force:
F = mg = 8000 kg × 9.8 m/s² = 78400 N.
Next, calculate the cross-sectional area:
A = π(d/2)² = π(0.21 m/2)² = 0.0346 m².
Finally, calculate the stress:
σ = F/A = 78400 N / 0.0346 m² = 2266018.25 Pa or approximately 2.27 MPa.