The required uni$-$directional composite modulus for an IM$-$carbon$-$fiber$/$epoxy composite is $140$ GPa in the longitudinal or fiber direction. $($a$)$ Estimate what volume fraction of fibers are needed, utilizing Ef $=290$ GPa and Em $=1\mathrm{.}5$ GPa. $($b$)$ If the applied stress is $1100$ MPa, then estimate the stress in the fibers and the matrix. $($c$)$ Plot the stress$-$strain curves of the fiber, matrix, and the composite in the

same plot. $($d$)$ Estimate the strength of the composite if fibers fail at $3\mathrm{.}5$ GPa