Final answer:
To determine the diameter of the rod, calculate the stress and strain experienced. Use the elastic modulus of steel to solve for the diameter.
Step-by-step explanation:
The diameter of the rod can be determined by considering the conditions for it to not stretch more than 1.0 cm when a 2.5 × 104-kg truck passes by. We can use the concept of stress and strain to calculate the necessary diameter.
First, we need to calculate the stress that the rod experiences. The stress is given by the force applied divided by the cross-sectional area of the rod. In this case, the force is the weight of the truck, and the cross-sectional area can be calculated using the formula for the area of a cylinder, which is A = πr2 (where r is the radius).
Next, we can calculate the strain, which is the change in length divided by the original length. In this case, the change in length is 1.0 cm and the original length can be determined using the formula for the circumference of a cylinder, which is C = 2πr.
Finally, the stress and strain are related by the elastic modulus of the material. For steel, the elastic modulus is typically around 200 GPa. By rearranging the equation for stress and strain, we can solve for the diameter of the rod.