Final answer:
To find the diameter of the steel rod that does not stretch more than 1.0 cm under a load, one must use the formulas for stress, strain, and Young's modulus and solve for the cross-sectional area to get the diameter.
Step-by-step explanation:
To determine the required diameter of a steel cylindrical rod that will not stretch more than 1.0 cm under the weight of a 2.5 × 104-kg truck, the concepts of stress, strain, and Young's modulus need to be applied. Using the formula for stress (σ) which is the force (F) divided by the area (A), and strain (ε) which is the change in length (ΔL) divided by the original length (L), and knowing that Young's modulus (E) is the ratio of stress to strain (E = σ/ε), we can combine these to find the diameter (d) of the rod required to support the truck without exceeding the maximum allowed strain.
The calculation will involve finding the cross-sectional area that corresponds to the required diameter and ensuring that the maximum stress the rod can withstand without stretching more than 1.0 cm is not exceeded by the weight of the truck.