PROBLEM $10$: Ancient pyramid builders are balancing a uniform rectangular slab of stone tipped at an angle $\backslash (\backslash$theta $\backslash )$ above the horizontal using a rope. The rope is held by five workers who share the force equally. $($a$)$ If $\backslash (\backslash$theta:$=20\mathrm{.}0\backslash$cdot $\backslash$operatorname$\{$deg$\}\backslash )$ what force does each worker exert on the rope? $($b$)$ As increases $\backslash (\backslash$theta $\backslash ),$ does each worker have to exert more or less force than in part $($a$),$ assuming they do not change the angle of the rope? Why? $($c$)$ At what angle $\backslash (\backslash$theta$\_\{0\}\backslash )$ do the workers need to exert no force to balance the slab? What happens if exceeds this value?