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 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.What is the tension in T_1 as an expression without using T_2?

Answer 1

Write the equation for vertical equilibrium. It will have terms representing weight (mg), T1 sin theta1, and T2 sin theta2.

By using the equation of horizontal equilibrium, you can define T2 in therms of T1 and the two angles. use that fact to eliminate T2 in the first (vertical equilibrium) equation