An oil rig in the Gulf is held steady at its designated drilling location by thr
ID: 1352145 • Letter: A
Question
An oil rig in the Gulf is held steady at its designated drilling location by three tugboats (see figure). Tugboat A pulls with 52000 N straight in the easterly direction. Tugboat B pulls at an angle of 38 degree north of west. Tugboat C pulls 43 degree west of south.
Below answer with the tension in rope B.
Three ropes are connected to each other as shown in the figure. The tension in rope A, which hangs straight from the ceiling, is 451 N. Rope B has an angle of 31 degree with respect to vertical. Rope C has an angle of 19 with respect to horizontal.
Below answer with the tension in rope C.
Explanation / Answer
Three ropes are connected to each other as shown in the figure.
TA = tension in rope A
TB = tension in rope B
TC = tension in rope C
summation of forces on horizontal axis, we have
TB cos 310 = TC cos 190
TB = TC cos 190 / cos 310 { eq.1 }
summation of forces on vertical axis, we have
TB sin 310 = (451 N) - TC sin 190
TB = (451 N) - TC sin 190 / sin 310 { eq.2 }
equating eq.1 & 2, we get
TC cos 190 / cos 310 = (451 N) - TC sin 190 / sin 310
(0.945) TC / (0.857) = (451 N) - (0.325) TC / (0.515)
(0.486) TC = (0.857) [(451 N) - (0.325) TC]
(0.486) TC = (386.5 N) - (0.278) TC
(0.764) TC = (386.5 N)
TC = (386.5 N) / (0.764)
TC = 505.9 N