Final answer:
To find h where aluminum plates carry half the load, apply mechanical stress principles considering the aluminum's properties and stress limits. The problem needs more data, such as the wire's cross-sectional area, for an exact solution.
Step-by-step explanation:
To determine the value of h if the portion of the load carried by the aluminum plates is half of the portion of the load, we need to apply the concept of mechanical stress and consider the properties of the material.
From the information given, an aluminum wire with a density (ρ) of 2.7 g/cm³ is suspended and the stress at its upper end reaches the proportionality limit at 8.0 × 10⁷ N/m². We would use the formula for stress, which is σ = F/A, where σ is the stress, F is the force, and A is the cross-sectional area, and combine this with the formula for force due to gravity, F = m × g where m is mass and g is the acceleration due to gravity.
In this scenario, the weight (or the force due to gravity) of the aluminum wire itself is what creates the stress in the wire. Therefore, the length of the wire (h) directly affects the weight and the resulting stress at the upper end of the wire. To solve for h, we would need to equate the maximum stress that can be handled by the aluminum (8.0 × 10⁷ N/m²) to the stress caused by the weight of the wire itself. This value is contingent on further information such as the cross-sectional area of the wire.