Two squirrels sit on a rope. Squirrel A weighs $21$ oz $,$ and squirrel $B$ weighs $19$ oz $.$ The rope has a diameter of $0\mathrm{.}045$ inches, and forms angles of $=1\mathrm{.}6$ degrees and $=2\mathrm{.}9$ degrees as shown. Find the tensions in the rope and the minimum required ultimate strength of the rope. Choose the least expensive rope material that is suitable for this application from the choices below.

$\left[\begin{array}{cccc}\text{M}\text{a}\text{t}\text{e}\text{r}\text{i}\text{a}\text{l}& \{\begin{array}{ccc}\text{:}[& \text{C}\text{o}\text{m}\text{m}\text{o}\text{n}& ]\\ & \text{B}\text{r}\text{a}\text{n}\text{d}& \\ & \text{N}\text{a}\text{m}\text{e}& \end{array}& \{\begin{array}{ccc}\text{:}[& \text{A}\text{l}\text{l}\text{o}\text{w}\text{a}\text{b}\text{l}\text{e}& ]\\ & \text{S}\text{t}\text{r}\text{e}\text{s}\text{s}& \\ & (ksi)\end{array}& \{\begin{array}{ccc}\text{:}[& \text{U}\text{n}\text{i}\text{t}& ]\\ & \text{C}\text{o}\text{s}\text{t}& \\ & (cent\frac{s}{f}t)\end{array}\\ \text{A}\text{r}\text{a}\text{m}\text{i}\text{d}& \text{K}\text{e}\text{v}\text{l}\text{a}\text{r}& 81& 8\mathrm{.}96\\ \text{C}\text{o}\text{t}\text{t}\text{o}\text{n}& -& 10& 2\mathrm{.}24\\ \text{H}\text{e}\text{m}\text{p}& -& 26& 3\mathrm{.}65\\ \text{H}\text{M}\text{P}\text{E}& \text{S}\text{p}\text{e}\text{c}\text{t}\text{r}\text{a}& 87& 17\mathrm{.}1\\ \text{L}\text{C}\text{A}\text{P}& \text{V}\text{e}\text{c}\text{t}\text{r}\text{a}\text{n}& 93& 21\mathrm{.}6\\ \text{M}\text{a}\text{n}\text{i}\text{l}\text{a}& --& 23& 2\mathrm{.}45\\ \text{P}\text{B}\text{O}& \text{Z}\text{y}\text{l}\text{o}\text{n}& 145& 64\mathrm{.}6\\ \text{P}\text{o}\text{l}\text{y}\text{a}\text{m}\text{i}\text{d}\text{e}& \text{N}\text{y}\text{l}\text{o}\text{n}& 17& 1\mathrm{.}98\\ \text{P}\text{o}\text{l}\text{y}\text{e}\text{s}\text{t}\text{e}\text{r}& \text{D}\text{a}\text{c}\text{r}\text{o}\text{n}& 37& 2\mathrm{.}16\\ \text{P}\text{o}\text{l}\text{y}\text{p}\text{r}\text{o}\text{p}\text{y}\text{l}\text{e}\text{n}\text{e}& --& 12& 1\mathrm{.}59\end{array}\right]$

Disclaimer: the values above should only be used for this exercise, and not for general design purposes.

Rope Tensions:

$T_{AC}=$

$T_{AB}=$

$T_{BD}=$

Ultimate Stress:

${}_{\text{m}\text{i}\text{n}\text{i}\text{m}\text{u}\text{m}-\text{u}\text{l}\text{t}\text{i}\text{m}\text{a}\text{t}\text{e}}=$

be sure to include units with the answers above

Material Choice: