A sailor is being rescued using a boetswain\'s chain thet is suspended from a pu

Question

A sailor is being rescued using a boetswain's chain thet is suspended from a pulley that can roll freely on the support cable ACB and is pulled at a constant speed by cable CD. Given thet a-30 and B-10 and that the combined weight of the boatswain's chair and the sailor is W= 170 lb. References eBook & Resources Section Break Difficulty: Medium 6. Required information 1000 poimts Determine the tension in the support cable ACB. (Round the final answer to the nearest whole number.) (You must provide an answer before moving to the next part.) The tension in the support cable ACB is lb.

Explanation / Answer

given alpha = 30 deg

beta = 10 deg

weight, W = 170 lb

tension in traction cable = T'

6. let tension in the support cable be T

then

T(sin(alpha) + sin(beta)) + T'*sin(alpha) = W

also,

Tcos(alpha) + T'cos(alpha) = Tcos(beta)

T' = T(cos(beta) - cos(alpha))/cos(alpha)

T = W/((sin(alpha) + sin(beta)) + (cos(beta) - cos(alpha))*sin(alpha)/cos(alpha) )

T = 170/((sin(30) + sin(10)) + (cos(10) - cos(30))*sin(30)/cos(30) ) = 229.040 lb

7. T' = 229.040 (cos(10) - cos(30))/cos(30) = 31.414 lb

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