A chandelier with mass m is attached to the ceilingof a large concert hall by tw

Question

A chandelier with mass m is attached to the ceilingof a large concert hall by two cables. Because the ceiling iscovered with intricate architectural decorations (not indicated inthe figure, which uses a humbler depiction), the workers who hungthe chandelier couldn't attach the cables to the ceiling directlyabove the chandelier. Instead, they attached the cables to theceiling near the walls. Cable 1 has tension T1and makes an angle of 1 with theceiling. Cable 2 has tension T2 and makes anangle of 2 with the ceiling. Find an expression forT1, the tension in cable 1, that does notdepend on T2. Express your answer in terms of someor all of the variables m, 1,and 2, as well as the magnitude of theacceleration due to gravity g.

Explanation / Answer

Sum you forces in the y-direction: T1sin(theta 1) + T2sin(theta 2) = mg Sum your forces in the x-direction: T1cos(theta 1) + T2cos(theta 2) = 0 Solve for T2: T2 = T1cos(theta 1) / cos(theta 2) Plug back into equation: T1sin(theta 1) + T1cos(theta 1)tan(theta 2) = mg Solve for T1: T1 = m*g / [sin(theta 1) + cos(theta 1)tan(theta 2)]

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