$\backslash$table$[[$Load$,$Length$],[N,$lbf$,$mm$,$in$.],[0,0,75,2\mathrm{.}953],[4740,1065,75\mathrm{.}025,2\mathrm{.}954],[9140,2055,75\mathrm{.}05,2\mathrm{.}955],[12,920,2900,75\mathrm{.}075,2\mathrm{.}956],[16,540,3720,75\mathrm{.}113,2\mathrm{.}957],[18,300,4110,75\mathrm{.}15,2\mathrm{.}959],[20,170,4530,75\mathrm{.}225,2\mathrm{.}962],[22,900,5145,75\mathrm{.}375,2\mathrm{.}968],[25,070,5635,75\mathrm{.}525,2\mathrm{.}973],[26,800,6025,75\mathrm{.}75,2\mathrm{.}982],[28,640,6440,76\mathrm{.}5,3\mathrm{.}012],[30,240,6800,78,3\mathrm{.}071],[31,100,7000,79\mathrm{.}5,3\mathrm{.}13],[31,280,7030,81,3\mathrm{.}189],[30,820,6930,82\mathrm{.}5,3\mathrm{.}248],[29,180,6560,84,3\mathrm{.}307],[27,190,6110,85\mathrm{.}5,3\mathrm{.}366],[24,140,5430,87,3\mathrm{.}425],[18,970,4265,88\mathrm{.}725,3\mathrm{.}493],[,$Fracture,,$]]$

A specimen of ductile cast iron having a rectangular cross section of dimensions $4\mathrm{.}8mm15\mathrm{.}9$ mm $(\frac{3}{16}in.\frac{5}{8}in.)$ is deformed in tension. Using the load$-$elongation data shown in the following table, complete problems $($a$)$ through $($f$).$

$($a$)$ Plot the data as engineering stress versus engineering strain.

$($b$)$ Compute the modulus of elasticity.

$($c$)$ Determine the yield strength at a strain offset of $0\mathrm{.}002.$

$($d$)$ Determine the tensile strength of this alloy.

$($e$)$ Compute the modulus of resilience.

$($f$)$ What is the ductility, in percent elongation?