Final answer:
To find the expression for T1, the tension in cable 1, we can use trigonometry and the equilibrium condition. The expression is T1 = (mg - T2*sin(theta2)) / sin(theta1).
Step-by-step explanation:
To find an expression for T1, the tension in cable 1, we can use trigonometry and the equilibrium condition. The forces acting on the chandelier are its weight mg and the tensions T1 and T2 in the cables. Let's consider the vertical forces. The vertical component of T1 is T1*sin(theta1) and the vertical component of T2 is T2*sin(theta2). Since the chandelier is not accelerating vertically, the sum of the vertical components of the tensions must equal the weight mg. This can be expressed as:
T1*sin(theta1) + T2*sin(theta2) = mg
Solving for T1:
T1 = (mg - T2*sin(theta2)) / sin(theta1)