Question

figure: s.yimg.com/tr/i/0f803deaf4944fffa178bdd3c40e958c_A.png

The weight of the cylinder is 40 lb, the ropes are fixed at B, C, and D.

o x direction force equation of equilibrium? TAB + TAC + TAD + WA = 0
o y direction force equation of equilibrium? TAB + TAC + TAD + WA = 0
o z direction force equation of equilibrium? TAB + TAC + TAD + WA = 0
o Tensile force along AB, TAB ? lb
bTensile force along AC, TAC ? lb

Answer 1

Because tension is necessarily positive, I'd write the x-equation of equilibrium as

Tad*sin60º*sin30º - Tac*sin60º*sin30º = 0.

There is no AB term, and no W term.

(This assumes that A is on the y-axis.)

So Tad = Tac

For the y-axis

Tab*cos45º - Tad*sin60º*cos30º + Tac*sin60º*cos30º = 0

0.707*Tab - 0.75*Tad - 0.75*Tad = 0

Tab = 2.123*Tad

Vertically

Tab*sin45º + Tad*cos60º*cos30º + Tac*cos60º*cos30º - 40lb = 0

2.123*Tad + Tad*0.433 + Tad*0.433 = 40 lb

Tad = 40lb / 2.99 = 13.4 lb ◄

Tac = 13.4 lb ◄

Tab = 2.123*13.4lb = 28.4 lb ◄