Question

A chandelier with mass is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (notindicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier.Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension and makes an angle of with the ceiling. Cable 2 has tension and makes an angle ofwith the ceiling.

Find an expression for T1, the tension in cable 1, that does not depend on T2.

Answer 1

In vertical direction,

T₁sinθ₁+T₂sinθ₂=mg

And in the horizontal direction,

T₁cosθ₁=T₂cosθ₂

Solving both the equations and solving for T₁ and T₂

T₁=m*g*cos(θ₂)/sin(θ₁+θ₂)
T₂=m*g*cos(θ₁)/sin(θ₁+θ₂)