Step-by-Step Solution
Step 1
We are given with the density of Aluminium ${\rho _{Al}} = 5.26\;{\rm{slug/f}}{{\rm{t}}^3}$
We are asked to compute the density of Aluminium in SI units.
Step 2
“slug” is the unit of mass, and $1\;{\rm{slug}}$ is equal to $14.59\;{\rm{kg}}$ of SI units. Whereas, “ft” or feet is the unit of length, and $1\;{\rm{ft}} = 0.3048\;{\rm{m}}$.
Step 3
Now, convert the units.\[\begin{array}{c} {\rho _{Al}} = 5.26\;\left( {\frac{{{\rm{slug}}}}{{{\rm{f}}{{\rm{t}}^{\rm{3}}}}}} \right)\left( {\frac{{14.59\;{\rm{kg}}}}{{1\;{\rm{slug}}}}} \right){\left( {\frac{{1\;{\rm{ft}}}}{{0.3048\;{\rm{m}}}}} \right)^3}\\ = 2710.89\;{{{\rm{kg}}} \mathord{\left/ {\vphantom {{{\rm{kg}}} {{{\rm{m}}^3}}}} \right. } {{{\rm{m}}^3}}} \end{array}\]