Question

A chandelier with mass m is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated 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 T₁ and makes an angle of θ₁ with the ceiling. Cable 2 has tension T₂ and makes an angle of θ₂ with the ceiling.

Part A 

Find an expression for T₁, the tension in cable 1, that does not depend on T₂.
Express your answer in terms of some or all of the variables m, θ₁, and θ₂, as well as the magnitude of the acceleration due to gravity g.

Answer 1

Part A Answer

Just use this formula:

T₁ = (cos(θ₂) * m * g) / sin(θ₁ + θ₂)

T₂ = (cos(θ₁) * m * g) / sin(θ₁ + θ₂)