Final answer:
To calculate the normal stress in a cylindrical rod, one must find the weight of the rod portion above the point in question and divide it by the cross-sectional area. Parts c and d of the question relating to rod deformation and modulus of elasticity cannot be answered without additional information about the rod and material properties.
Step-by-step explanation:
The problem presented involves the concepts of stress, strain, and elasticity applied to cylindrical rods, which are within the field of materials engineering or mechanical engineering. To address the question regarding normal stress at a specific point on a vertically positioned cylindrical steel rod, we must apply the formula for stress, σ = F/A, where F is the force exerted by the weight of the rod above the point in question, and A is the cross-sectional area of the rod.
a. To find the normal stress at 1.0 m from the lower end of the rod, we first calculate the volume of the upper half of the rod (V = πr^2h), then determine its mass (m = Vρ, where ρ is the density of steel), and finally calculate the weight (F = mg, where g is the acceleration due to gravity). The stress is then found by dividing this weight by the cross-sectional area (A = πr^2).
b. Similarly, for the stress at 1.5 m from the lower end, we calculate the volume, mass, and weight for the upper 0.5 m of the rod and again apply the stress formula.
For parts c. and d., rod deformation and modulus of elasticity (Young's modulus) would typically require additional information such as the length of the rod, the material properties (specifically the modulus of elasticity), and the applied forces. However, these are not provided in the given scenarios. Therefore, generalized concepts can be discussed but no specific calculations can be performed without this information.