Final answer:
An engineer can calculate the initial lengths of steel and aluminum beams needed to maintain a steady 0.500 meters length difference by considering their coefficients of thermal expansion and factoring in temperature variations.
Step-by-step explanation:
To ensure that a steel beam and an aluminum beam maintain a constant difference in length of 0.500 meters regardless of temperature changes, an engineer must account for the different coefficients of thermal expansion for steel and aluminum. The formula ΔL = αLΔT provides a way to determine the required initial lengths of the beams, where ΔL is the change in length, α is the coefficient of thermal expansion, L is the original length, and ΔT is the change in temperature.
Since the difference must remain constant, setting up an equation that equals the expansion of both materials to 0.500 meters and solving for their original lengths will provide the necessary dimensions for this engineering challenge.