two squirrels 03

Two squirrels sit on a rope. Squirrel A weighs 25 oz, and squirrel B weighs 21 oz. The rope has a diameter of 0.06 inches, and forms angles of $\theta$ = 3 degrees and $\phi$ = 3.1 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.

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$	Material	Common	Allowable	Unit	$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$
		Brand	Stress	Cost
		Name	(ksi)	(cents/ft)
	Aramid	Kevlar	75	8.96
	Cotton	--	9	2.24
	Hemp	--	24	3.65
	HMPE	Spectra	80	17.1
	LCAP	Vectran	86	21.6
	Manila	--	21	2.45
	PBO	Zylon	134	64.6
	Polyamide	Nylon	16	1.98
	Polyester	Dacron	35	2.16
	Polypropylene	--	11	1.59

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:

$\sigma_{minimum-ultimate}$ =

be sure to include units with the answers above

Material Choice: Aramid Cotton Hemp HMPE LCAP Manila PBO Polyamide Polyester Polypropylene