$1$ Weight$-$Critical Design

In this problem, consider the following potential materials: $304$ stainless steel, $6061$ aluminum, titanium, brass, copper, lead, concrete, acrylic, rubber, porcelain, granite, marble, oak, pine, balsa, cotton, nylon, silk, kevlar, carbon$-$fiber composites, diamond, and graphene. $($For some materials like cotton and nylon, you may need to search for values when formed in a rope.$)$

$1\mathrm{.}1$ Stiffness$-$to$-$Weight Ratio

Stiffness$-$to$-$weight is a common design variable. Look up Young's modulus $E$ and density $$ for these materials and rank them in order of decreasing $\frac{E}{}.$ Can you draw any conclusions from this list?

$1\mathrm{.}2$ Strength$-$to$-$Weight Ratio

Strength$-$to$-$weight is a common design variable. Look up ultimate tensile strength ${}_u$ and density $$ for these materials and rank them in order of decreasing $\frac{{}_u}{}.$ Can you draw any conclusions from this list?