Question

Problem 1.

An oil rig in the Gulf is held steady at its designated drilling location by three tugboats (see figure). Tugboat A pulls with 53000 N straight in the easterly direction. Tugboat B pulls at an angle of 27 degree north of west. Tugboat C pulls 31 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.

Problem 2.

Three ropes are connected to each other as shown in the figure. The tension in rope A, which hangs straight from the ceiling, is 336 N. Rope B has an angle of 35 degree with respect to vertical. Rope C has an angle of 20 with respect to horizontal.

a) Draw a proper free-body diagram.

b) Find the magnitude of the tension of the ropes 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 C.

Problem 3.

Answer 1

1) Force in the vertical direction is :

F_y = Bsin27^o - Ccos31^o = 0

therefore B = 1.89C ......................[1]

and Force in the horizontal direction:

F_x = 53000 - Bcos27^o - Csin31^o = 0

53000 - 0.891B - 0.515C..........................[2]

Using equation [1] we get:

53000 - 0.891(1.89)C - 0.515C = 0

=> C = 24102 N

therefore B = 1.89 x 24102 = 45552.78 N

Problem 2)

Force in the vertical direction :

F_y = 336 - Bcos35^o - Csin20^o = 0 ...................................[1]

Force in horizontal direction :

F_x = Bsin35^o - Ccos20^o = 0

B = 1.6383 C ...........................[2]

Substituting equation [2] in equation [1] we get:

336 - 1.6383C cos35^o - Ccos20^o = 0

C = 147.26 N

therefore B = 1.6383 x 147.26 = 241.25 N

Problem 3) The net Force on the mass is zero. Therefore the sum of all forces pointing to left equals sum of forces pointing to right. Also, the vector sum over all forces is zero.