Given,
The mass is supported by the cables, m=100 kg
The angle made by one of the cables, θ=40°
Where T₁ and T₂ are the tension in the cables.
At equilibrium, the net force on the mass will be zero. That is, net horizontal force and net vertical force will be equal to zero.
Considering the vertical forces,
[tex]mg=T_1\sin \theta[/tex]On substituting the known values,
[tex]\begin{gathered} 100\times9.8=T_1\sin 40\degree \\ \Rightarrow T_1=\frac{100\times9.8}{\sin 40\degree} \\ =1524.6\text{ N} \end{gathered}[/tex]Considering the horizontal forces,
[tex]T_2=T_1\cos \theta[/tex]On substituting the known values,
[tex]\begin{gathered} T_2=1524.6\times\cos 40\degree \\ =1167.9\text{ N} \end{gathered}[/tex]Thus the tension in the horizontal cable is 1167.9 N
