A weight of 100 kg is suspended from the ceiling by cables t

A weight of 100 kg is suspended from the ceiling by cables that make 30 degree and 60 degree angles with the ceiling as shown in Fig. P4.31. Assuming that the weight is not moving (vector T_1 + vector T_2 + vector W = 0), find the tensions vector T_1 and vector T_2. A weight suspended from two cables for problem P4-31.

Solution

The sum of the vertical forces = weight
100=T2sin60 + T1 sin30 => 100= T20.866 +T10.5

The sume of the horzontal forces is zero.
T1cos30-T2cos60=0 (notice sign, opposite directions)

0.866T1= 0.5T2

T1= 0.577T2

substituting in first equation=> T2= 86.617

T1=49.978