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 architectur al

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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 architectur al 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 $$\displaystyle{T}_{{1}}$$ and makes an angle of $$\displaystyle\theta_{{1}}$$ with the ceiling. Cable 2 has tension $$\displaystyle{T}_{{2}}$$ and makes an angle of $$\displaystyle\theta_{{2}}$$ with the ceiling.
Find an expression for $$\displaystyle{T}_{{1}}$$, the tension in cable 1, that does not depend on $$\displaystyle{T}_{{2}}$$.
Express your answer in terms of someor all of the variables m,$$\displaystyle\theta_{{1}}$$, and $$\displaystyle\theta_{{2}}$$, as well as the magnitude of the acceleration due to gravity g.