# Solving Chandelier Tension Problem: Find T1 Expression without T2

• Amria
In summary, the problem involves finding an expression for T1, one of the tensions in the cables holding up a chandelier in a concert hall. The chandelier is attached to the ceiling by two cables, which are not directly above the chandelier due to intricate decorations on the ceiling. Using the equations of sum of forces in the x and y directions, T1 can be expressed in terms of T2 and the angles of the cables with the ceiling. By isolating the T1 terms and factoring out T1, the expression for T1 can be solved algebraically.
Amria

## Homework Statement

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 T1 that does not include T2

## Homework Equations

I have found that the

Sum of the forces of in the x direction is T2cos(theta2) - T1cos(theta1) = 0

Sum of the forces in the y direction is T1sin(theta1) + T2sin(theta2) - mg = 0

## The Attempt at a Solution

from the first equation, T2= T1cos(theta1)/cos(theta2)

would then T1sin(theta1) + T1cos(theta1)/cos(theta2)*sin(theta2) - mg = 0?
Any ideas how to solve algebraicly for T1?

To start, isolate the T1 terms on one side of your equation. That might make things a bit clearer.

yes. T1sin(theta1) + T1cos((theta1)/cos(theta2))*sin(theta2) - mg = 0...then u factor out the T1 and u should be able to do it on ur own from there.

## 1. What is the "Chandelier Tension Problem" and why is it important?

The "Chandelier Tension Problem" refers to the challenge of finding the expression for tension in a chandelier's support rod (T1) without knowing the tension in the other support rod (T2). This problem is important because it is a common scenario in physics and engineering, where one must solve for unknown forces in a system to ensure structural stability and safety.

## 2. What are the variables involved in solving this problem?

The variables involved in solving the Chandelier Tension Problem are the tension in the two support rods (T1 and T2), the angles at which the support rods are attached to the chandelier, and the weight of the chandelier itself.

## 3. What is the formula for finding T1 expression without T2?

The formula for finding T1 expression without T2 is T1 = (W * sinα) / (sinα + sinβ), where W is the weight of the chandelier, α is the angle at which T1 is attached, and β is the angle at which T2 is attached.

## 4. Can this problem be solved using any other methods?

Yes, there are other methods for solving the Chandelier Tension Problem, such as using vector analysis or using the principle of static equilibrium. However, the formula mentioned above is the most commonly used method as it is a straightforward and efficient approach.

## 5. Are there any limitations to this formula?

While the formula for finding T1 expression without T2 is accurate in most cases, it does have some limitations. It assumes that the support rods are massless and that the chandelier's weight is evenly distributed. It also does not take into account any external forces acting on the chandelier. Therefore, it is important to consider these factors and make appropriate adjustments when using this formula in practical applications.

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