# Problem: Consider a cylindrical cable with a hanging weight suspended from it. 3Part (a) When the mass is removed, the length of the cable is found to be L0 = 4.79 m. After the mass is added, the length is remeasured and found to be L1 = 5.31 m. Determine Young's Modulus Y in N/m2 for the steel cable if the weight has a mass m = 95 kg and the cable has a radius r = 0.015 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, L1, L0, and r provided in part A

###### FREE Expert Solution

Part (a). Strain:

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

Young's Modulus:

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

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###### Problem Details

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 L0 = 4.79 m. After the mass is added, the length is remeasured and found to be L1 = 5.31 m. Determine Young's Modulus Y in N/m2 for the steel cable if the weight has a mass m = 95 kg and the cable has a radius r = 0.015 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, L1, L0, and r provided in part A