Final answer:
To calculate the normal stress in a steel rod, use the formula σ = F/A, considering the density, volume of the material above the point of interest, and the cross-sectional area.
Step-by-step explanation:
To calculate the normal stress in a steel rod, you must determine the force acting perpendicularly to a given cross-sectional area. The stress (σ) is found by the formula σ = F/A, where F is the force in newtons and A is the cross-sectional area in square meters.
Consider a steel rod of density P = 7.8 g/cm³, which is 2.0 m long with a diameter of 5.0 cm. The rod is vertical, so the force acting on a cross-section is due to the weight of the rod above that point. The weight (W) can be found by W = V • P • g, where V is the volume, P is density, and g is the acceleration due to gravity (approximately 9.81 m/s²).
For part (a), the volume of the rod above the 1.0 m mark is a cylinder of height 1.0 m. The cross-sectional area (A) is given by A = π(d/2)². Substituting the given values into the formula for stress yields the calculation for the normal stress at 1.0 m from the lower end.
Likewise, calculating for part (b) at 1.5 m from the lower end, the height changes, impacting V and thus W. Then apply the stress formula again with the adjusted force.