Equilibrium in 2D Video Lessons

Concept

# Problem: Hanging Chandelier (Figure 1 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 Ti and makes an angle θ1 with the ceiling. Cable 2 has tension T2 and makes an angle θ2 with the ceiling.Find an expression for T1, the tension in cable 1, that does not depend on T2.Express your answer in terms of some or all of the variables m, θ1, and θ2, as well as the magnitude of the acceleration due to gravity g. You must use parentheses around θ1 and θ2, when they are used as arguments to any trigonometric functions in your answer.

###### FREE Expert Solution

The forces are balanced in the vertical direction.

Therefore:

$\overline{){\mathbf{\Sigma }}{\mathbf{F}}{\mathbf{=}}{\mathbf{0}}}$

${\mathbit{T}}_{\mathbf{1}}\mathbit{s}\mathbit{i}\mathbit{n}{\mathbit{\theta }}_{\mathbf{1}}\mathbf{+}{\mathbit{T}}_{\mathbf{2}}\mathbit{s}\mathbit{i}\mathbit{n}{\mathbit{\theta }}_{\mathbf{2}}\mathbf{=}\mathbit{m}\mathbit{g}$

The forces are also balanced in the horizontal direction.

Fnet = 0

${\mathbit{T}}_{\mathbf{1}}\mathbit{c}\mathbit{o}\mathbit{s}{\mathbit{\theta }}_{\mathbf{1}}\mathbf{=}{\mathbit{T}}_{\mathbf{2}}\mathbit{s}\mathbit{i}\mathbit{n}{\mathbit{\theta }}_{\mathbf{2}}$

${\mathbit{T}}_{\mathbf{2}}\mathbf{=}{\mathbit{T}}_{\mathbf{1}}\mathbf{\left(}\mathbit{c}\mathbit{o}\mathbit{s}{\mathbit{\theta }}_{\mathbf{1}}\mathbf{\right)}\mathbf{/}\mathbf{\left(}\mathbit{c}\mathbit{o}\mathbit{s}{\mathbit{\theta }}_{\mathbf{2}}\mathbf{\right)}$

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###### Problem Details

Hanging Chandelier (Figure 1 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 Ti and makes an angle θ1 with the ceiling. Cable 2 has tension T2 and makes an angle θ2 with the ceiling.

Find an expression for T1, the tension in cable 1, that does not depend on T2.

Express your answer in terms of some or all of the variables m, θ1, and θ2, as well as the magnitude of the acceleration due to gravity g. You must use parentheses around θ1 and θ2, when they are used as arguments to any trigonometric functions in your answer.

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Equilibrium in 2D concept. You can view video lessons to learn Equilibrium in 2D. Or if you need more Equilibrium in 2D practice, you can also practice Equilibrium in 2D practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Couder's class at NOTRE DAME.