Determine all possible angles θ for equilibrium, 0∘<θ<90∘.

Question

Mathematics

Alisha Saunders

23 November, 04:22

Determine all possible angles θ for equilibrium, 0∘<θ<90∘.

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Answers (1)

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Andrew · Answer 1

If the tension of a cable AB and BC is represented as Fab and Fac, using the equilibrium equations equation 1:Fab cos 40 degrees - Fac cos x = 0where x is the angle we are looking for, 0.766Fab - Fac cox x = 0equation 2:-200 + Fab sin 40 degress + Fac sin x = 00.643Fab + Fac sin x = 200solving the tension we getFab = 311.04lbFac = 238.26 lb

substitute 30 degrees to x on equation 1 and 2, we getFab = 184.31lb, Fac = 163lb

substitute 45 degrees to x on equations 1 and 2, we getFab = 141.9lb, Fac = 153.77lb

substitute 60 degrees to equation 1 and 2, we getFab = 101.5lb, Fac = 155.55lb

substitute 90 degrees to x on eqn 1 and 2 we getFab = 0lb, Fac = 200lb

There 90 is not a possible answer.

Possible angles are 30 degrees, 45 degrees and 60 degrees