Question

A chandelier with mass mmm 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 T1T1T_1 and makes an angle of θ1θ1theta_1 with the ceiling. Cable 2 has tension T2T2T_2 and makes an angle of θ2θ2theta_2 with the ceiling.

Find an expression for T1T1T_1, the tension in cable 1, that does not depend on T2T2T_2.

I have been trying to answer this one question and can't seem to get a correct order if someone can please help me.

Answer 1

This is the diagram which I made by reading the question.....Let me know if there is anything wrong !!!!!!1

so,

In x - direction, we have

T1 cos 1 = T2 * cos 2

T2 = T1 cos 1 / cos 2 ------------- (1)

and

In y - direction, we have

T1 sin 1 + T2 sin 2 = mg ----------- (2)

put (1) in (2), we have

T1 sin 1 + (T1 cos 1 / cos 2) sin 2 = mg

using trigonometry, sin 2 / cos 2 = tan 2

so,

T1 sin 1 + T1 cos 1 tan 2 = mg

so,

T1 = mg / ( sin 1 + cos 1 tan 2)

or

In proper format