A tugboat tows a ship at a constant velocity. The tow harness consists of a sing

Question

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 ? = 35.0? and ? = 22.0?, respectively. The tugboat pulls with a force of 12750N . What are the tensions TBC and TBD in the rope segments BC and BD?

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 ? = 35.0? and ? = 22.0?, respectively. The tugboat pulls with a force of 12750N . What are the tensions TBC and TBD in the rope segments BC and BD?

Explanation / Answer

perpendicular to the rope

Tcd*sin22 = Tbdsin35

Tcd = 1.5311 Tbd

alon the rope

Tcd*cos22 + Tbd*cos35 =F

1.5311 Tbd*cos22 + Tbd*cos35 = 12750

Tbd = 5695.0152 N

Tcd = 8719.6378 N

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