Final answer:
To determine the root axial stress at a specific point in a steel rod, use the formula for normal stress due to the weight of the object: σ = P × g × h × A. Apply this to a cylindrical rod to find the stress at any given point along its length due to its own weight.
Step-by-step explanation:
Determining the root axial stress at a specific point requires knowledge of the material properties, geometry, and the applied load conditions. For a cylindrical steel rod fixed vertically, with its weight acting downwards due to gravity, the normal stress σ can be calculated using σ = P × g × h × A, where P is the steel density, g is the acceleration due to gravity, h is the height of the cylinder above the point of interest, and A is the cross-sectional area.
For point (a), located 1.0 m from the lower end of a steel rod that has a density of 7.8 g/cm³, a diameter of 5.0 cm, and a length of 2.0 m, we can calculate the volume of the rod above point a as V = π × (d/2)² × h, then the mass as m = P × V, and finally the stress as σ = m × g / A. Point (b) follows the same procedure, but with h adjusted to 1.5 m from the lower end.