Final answer:
The question involves calculating the resolved shear stress on the slip system of a gold single crystal with FCC structure when subjected to a normal stress, a process that uses Schmid's law and an understanding of crystallography.
Step-by-step explanation:
The question asks for the resolved shear stress on the most-likely slip system in a gold single crystal when a normal stress of 25.7 MPa is applied in the [001] direction. In materials science and engineering, this involves understanding the crystal structure of a material and applying geometric relationships to determine the stress on different planes and directions inside the crystal. For face-centered cubic (FCC) structures like gold, the primary slip system is {111}<110>, meaning that the shear stress must be resolved onto the {111} planes in the <110> direction.
To calculate the resolved shear stress, one would typically use the Schmid's law, which states that the resolved shear stress, τ, is equal to the applied normal stress, σ, multiplied by both the cosine of the angle between the normal stress direction and the slip direction, λ, and the cosine of the angle between the normal stress direction and the slip plane normal, μ: τ = σ * cos(λ) * cos(μ).