The 200kg crate is held in equilibrium in the position shown

The 200-kg crate is held in equilibrium in the position shown below. The pulleys are frictionless. How much tension must the men apply in each of the cables AB and AC?

Solution

force = 200 kg * 9.8m/s^2 = - 1960 N

Tab cos 50 = Tac cos 30

Tab (.642) = Tac (.866)

Tab = Tac (.866)/(.642) = 1.349Tac

and Tab sin 50 + Tac sin 30 = 1960 N

.766 Tab + .5 Tac = 1960

or

.766 (1.349 Tac) + .5 Tac = 1960

1.0332 Tac + .5Tac = 1960

1.5332 Tac = 1960

T_ac = 1278.37 N

T_ab = 1.349* 1278.37 = 1724.52 N