An oil rig in the Gulf is held steady at its designated drilling location by thr
ID: 1484421 • 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 56000 N straight in the easterly direction. Tugboat B pulls at an angle of 47 degree north of west. Tugboat C pulls 39 degree west of south.
a) Draw a proper free-body diagram.
b) Find the magnitude of the tension of the ropes attached to tugboats B and C.
(Show your work step by step. Always use units with numbers. Always show the equation before substituting numbers. Just the right answer will not give full credit.)
Below answer with the tension in rope B.
Explanation / Answer
a )
Tugboat B pulls at an angle of 47 degree north of west.
Tugboat C pulls 39 degree west of south.
then the angle between these two is
180 - 86 = 940 ( 47 + 39 = 860 )
b)
T1 / sin47 = T2 / sin39 = 56000 / sin94
T1 / sin47 = 56000 / sin94
T1 / sin47 = 56000 / 0.9975
T1 = sin47 X 56000 / 0.9975
T1 = 0.731 X 56000 / 0.9975
T1 = 40936 / 0.9975
T1 = 41038.59 N
T2 / sin39 = 56000 / sin94
T2 / sin39 = 56000 / 0.9975
T2 = sin39 X 56000 / 0.9975
T2 = 0.629 X 56000 / 0.9975
T2 = 35224 / 0.9975
T2 = 35312.28 N