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A tugboat tows a ship at a constant velocity. The tow harness consists of a single tow cable attached to the tugboat at point A that splits at point B and attaches to the ship at points C and D. The two rope segments BC and BD angle away from the center of the ship at angles of ϕ = 25.0 ∘ and θ = 23.0 ∘, respectively. The tugboat pulls with a force of 3700 lb . What are the tensions TBC and TBD in the rope segments BC and BD?

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Manetho

Explanation:

perpendicular to the rope

Tcd×sin23 = Tbd×sin25

Tcd = 1.08160 Tbd

along the rope

Tcd×cos23 + Tbd×cos25 =F

1.08160×Tbd×cos23 + Tbd×cos25 = 3700 lb

Tbd (1.08160×cos23°+cos25°)=3700

Therefore, Tbd = 1945.3965 lb

Tcd = 1945.3965×1.0816 = 2104.14085 lb.

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