a$)$ If a factor of safety $(\backslash (\backslash$mathbf$\{$n$\}\backslash ))$ of $3$ is desired based on the Tresca criterion, find the diameter of pulleys C and D $.$ Justify your answer, i$.$e$.,$ show all appropriate internal reaction and cross$-$section diagrams, etc., needed to support your calculations.

b$)$ If $\backslash (\backslash$mathrm$\{$n$\}=3\backslash )$ is desired based on the von Mises criterion, find the diameter of pulleys C and D$.$

Hint: The pulley diameters only affect the torque caused by the tensions $\backslash (\backslash$mathrm$\{$T$\}\_\{1\}\backslash )$ to $\backslash (\backslash$mathrm$\{$T$\}\_\{4\}\backslash ).$