Magnitude of tension vectors

Question

A  pound object hangs from two cables with angles below the horizontal of  and  respectively. Determine the magnitudes of the tension vectors,  and .

Answer 1

Draw a parallel to the upper horizontal line passing through the T₂T₁ connection. Due to opposite angles of parallel lines, the T₂ angle is 28° with the second horizontal line and the T1 angle is 32°.

Summing forces in the x and y directions.

∑F_x = 0 -->T_2x - T_1x = 0

∑F_y = 0 -->T_2y + T_1y - mg = 0 mg = 600lbs

T_2x = T₂cos(28) T_2y = T2sin(28)

T_1x = T1cos(32) T_1y = T1sin(32)

x:

cos(32)T₁-cos(28)T₂ = 0 T1 = cos(28)T₂/cos(32) = 1.0412T₂

y:

sin(28)T₂ + sin(32)(1.0412T₂) -600 = 0 --> 0.4695T₂ + 0.5299(1.0412)T₂ = 600

T₂ = 600/1.02125 = 587.514

T₁ = (1.0412)(587.514) = 611.72