Problem $2)$ You are testing a polymer fiber to generate stress$-$strain data and determine if it is a suitable candidate for tendon replacement. You obtain the following data points.

for

The initial fiber length is $35$ mm and the cross$-$sectional area of the fiber is $2\backslash (\backslash$mathrm$\{$mm$\}^\{2\}\backslash ).$ The figure shows that the relation between force $\backslash ((\backslash$mathrm$\{$Y$\})\backslash )$ and fiber length for this polymer is linear with the following best linear fit:

$\backslash (\backslash$mathrm$\{$Y$\}=0\mathrm{.}275\backslash$mathrm$\{$X$\}-9\mathrm{.}625\backslash )$ where X in mm and Y in N

a$)$ Calculate the force required to exert a strain of $0\mathrm{.}1$ on the fiber. $(10$ points$)$

b$)$ Determine the energy stored $($in Joules$)$ in the fiber at $0\mathrm{.}1$ strain. $(10$ points$)$

c$)$ Derive an equation to relate stress to strain for this polymer fiber with stress in $\backslash (\backslash$mathrm$\{$N$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash )$ or Pa $.(5$ points$)$