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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 θ₁ of with the ceiling. Cable 2 has tension and makes an angle θ₂ ofwith the ceiling.

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

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

Balancing of Forces:

If a body has reached equilibrium, then the sum of all forces and torque exerted on it is equal to 0.

Answer and Explanation:

A chandelier of mass m is attached by two cables to the ceiling in a large concert hall. Cable 1 has tension T₁ and makes an angle θ₁ with the ceiling. Cable 2 has a tension T₂ and makes an angle θ₂ with the ceiling.

The diagram shows the angles created by the two cables as well as tension when the chandelier of weight W was hung from them.

Now, balancing force along the X direction

Similarly, balancing force along the Y direction

=> Value is independent of T₂ (Answer)

Last words

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