Problem 5. Consider a reference glass fibers-epoxy composite material with a volume fraction of epoxy of 35%. Evaluate the following: (a) What is the volume fraction of carbon fibers that you have to add to the initial material to double the value of EL (longitudinal composite modulus), while maintaining the volume fraction of epoxy to 35% ? (b) What is the reduction of the density achieved with the carbon fibers? (c) What is the ultimate strength (u) of the two composites? \begin{tabular}{|l|cccc|} \hline Material & E[GPa] & [/] & [g/cm3] & u[MPa] \\ \hline Epoxy matrix & 3.5 & 0.34 & 1.2 & 52.5 \\ Glass fiber & 70 & 0.21 & 2.5 & 700 \\ Carbon fiber & 350 & 0.21 & 1.8 & 700 \\ Kevlar fiber & 147 & 0.23 & 1.5 & 1300 \\ Boron fiber & 390 & 0.22 & 2.63 & 2800 \\ \hline \end{tabular}