A tugboat tows a ship at a constant velocity The tow harness

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 phi = 29.0 degree and theta = 19.0 degree, respectively. The tugboat pulls with a force of 1700 lb . What are the tensions TBC. and TBD in the rope segments BC and BD?

Solution

T_BCcos()+T_BDcos()=F

T_BCsin()T_BDsin()=0

cos(29) = 0.874 cos(19)=0.945 F =1700 sin29=0.484 sin19=0.325

T_BC(0.874)+T_BD(0.945)=1700 -------------------------1

T_BC(0.484)-T_BD(0.325)=0   multiplying by 2.9

T_BC(1.403)-T_BD(0.945)=0   ---------------------------------2

Adding eqn 1 and 2, we get

T_BC(2.277) = 1700

T_BC = 1700/2.277 =746.59