Determine the tension developed in the cable AB required to support the traffic

Question

Determine the tension developed in the cable AB required to support the traffic light, which has a mass of 19 kg. Take h = 4 m. Express your answer to three significant figures and include the appropriate units. Determine the tension developed in the cable AC required to support the traffic light Express your answer to three significant figures and include the appropriate units. Determine the tension developed in the cable AD required to support the traffic light Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

A = 0, 0, 4

B = 3, 4, 4

C = -6, -3, 6

D = 4, -3, 4

AB = 3i + 4j

|AB| = sqrt(3^2 + 4^2) = 5

ABcap= AB / |AB| = 0.6i + 0.8j

AC = -6i -3j + 2k and |AC| = 7

ACcap = - 0.857i - 0.429j + 0.286k

AD = 4i - 3j

ADcap = 0.8i - 0.6j

and W = - (19 x 9.8) k = - 186.2 k N

Fnet = 0 { for equilibrium}

force vector = magnitude x direction

e.g F_AB = magnitude of Fab (say F1) x ABcap (this is direction along AB)

FAB + FAC + FAD + W = 0

F1(0.6i + 0.8j ) + F2 ( - 0.857i - 0.429j + 0.286k) + F3 (0.8i - 0.6j ) - 186.2k = 0

along direction k,

0.286 F2 - 186.2 = 0

F2 = 651 N ( F2 is force in AC )

along i direction,

0.6F1 - 0.857F2 + 0.8F3 = 0

0.6F1 + 0.8F3 = 558 ..... (i)

along j direction,

0.8F1 - 0.429F2 - 0.6F3 = 0

0.8F1 - 0.6F3 = 279.3 .... (ii)

solving (i) and (ii),

F1 = 13956/25 = 558.24 N

F2 = 13941/50 = 278/.82 N

(A) F_AB = F1 = 558.24 N

(B) F_AC = F2 = 651 N

(C) F_AD = F3 = 278.82 N

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