A 1400 kg steel beam is supported by two ropes.

A 1400 kg steel beam is supported by two ropes.

What is Tension in Rope 1 and what is Tension in Rope 2

Answer

Along the x - direction:
        T1 sin20 = T2
sin30
        0.342 T1 = 0.5T2
==> T1 / T2 = 0.5 / 0.342
              T1
= 1.461T2      ........1
Along the vertical direction
        T1cos20 + T2 cos30
=mg
   ==> 0.939T1 + 0.866T2 =
13720  .....2
Substituting 1 in 2 we get
          1.3718T2
+0.866T2 = 13720
             2.237
T2 = 13720
                       ∴
T2 = 6133.2 N
                      and
T1 = 8960.2 N

T₁sin(20) = T₂sin(30)
T₁cos(20) + T₁cos(30) = mg
T₁cos(20) + T₁sin(20)cos(30)/sin(30) =
mg
T₁cos(20)sin(30) + T₁sin(20)cos(30)
=mgsin(30)
T₁sin(20 + 30) = mgsin(30)
∴T₁ = mgsin(30)/sin(50) = 8955 N
T₂ = mgsin(20)/sin(50) = 6126 N