A chandelier with mass m is attached to the ceiling of a large concert hall by t

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 T_1 and makes an angle of theta_1 with the ceiling. Cable 2 has tension T_2 and makes an angle of theta_2 with the ceiling. Find an expression for T_1, the tension in cable 1, that does not depend on T_2. Express your answer in terms of some or all of the variables m, theta_1, and theta_2, as well as the magnitude of the acceleration due to gravity g. You must use parentheses around theta_1 and theta_2, when they are used as arguments to any trigonometric functions in your answer.

Explanation / Answer

LetT1 and T2 be the tension in wires 1 and 2

The horizontal components of tension

T2cos2-T1cos1 =0

T2 = T1cos1/cos2

The vertical components of tension is

T2sin2 + T1sin1 – mg = 0

substituting T2 value

{T1cos1/cos2} sin2 + T1sin1 = mg

T1 {cos1sin2 + cos2sin1}/cos2 = mg

T1 {sin(1+2)} = mgcos2

T1 = mgcos2/{sin(1+2)}

Your answer is right please submit your answer in the following format

T = mg(cos(2))/sin(1+2)

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