**Part (a). **Strain:

$\overline{)\frac{\mathbf{\u2206}\mathbf{L}}{{\mathbf{L}}_{\mathbf{0}}}{\mathbf{=}}\frac{\mathbf{F}}{\mathbf{A}\mathbf{Y}}}$

Young's Modulus:

$\begin{array}{rcl}\mathbf{Y}& \mathbf{=}& \frac{\mathbf{F}{\mathbf{L}}_{\mathbf{0}}}{\mathbf{A}\mathbf{\u2206}\mathbf{L}}\\ & \mathbf{=}& \frac{\mathbf{m}\mathbf{g}{\mathbf{L}}_{\mathbf{0}}}{\mathbf{\pi}{\mathbf{r}}^{\mathbf{2}}\mathbf{(}{\mathbf{L}}_{\mathbf{1}}\mathbf{-}{\mathbf{L}}_{\mathbf{0}}\mathbf{)}}\\ & \mathbf{=}& \frac{\mathbf{\left(}\mathbf{95}\mathbf{\right)}\mathbf{(}\mathbf{9}\mathbf{.}\mathbf{81}\mathbf{)}\mathbf{(}\mathbf{4}\mathbf{.}\mathbf{79}\mathbf{)}}{\mathbf{\pi}{\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{015}\mathbf{)}}^{\mathbf{2}}\mathbf{(}\mathbf{5}\mathbf{.}\mathbf{31}\mathbf{-}\mathbf{4}\mathbf{.}\mathbf{79}\mathbf{)}}\end{array}$

Consider a cylindrical cable with a hanging weight suspended from it. 3

Part (a) When the mass is removed, the length of the cable is found to be *L*_{0} = 4.79 m. After the mass is added, the length is remeasured and found to be* L _{1}* = 5.31 m. Determine Young's Modulus Y in N/m

Part (b) If we were to double the radius of the wire and re-suspend the weight, what would happen to the stress in the cable?

Part c) If this cable is pulled down a distance *d* in m from its equilibrium position it acts like spring when released. Write an express determining the spring constant *k* of this material using the cable-specific variables Y, *L _{1}*,

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