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 architectur al

Jaden Easton

Jaden Easton

Answered question

2021-02-06

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 architectur al 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 T1 and makes an angle of θ1 with the ceiling. Cable 2 has tension T2 and makes an angle of 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 someor all of the variables m,θ1, and θ2, as well as the magnitude of the acceleration due to gravity g.

Answer & Explanation

bahaistag

bahaistag

Skilled2021-02-07Added 100 answers

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2021-09-30

The answer above is incorrect, the actual answer is mgsin(θ1)+tan(θ2)cos(θ1)

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-11Added 2605 answers

Apply Newton's and law,

T1cosθ1=T2cosθ2

T2=T1cosθ1cosθ2

T1sinθ1+T2sinθ2=mg

T1[sinθ1+(cosθ1cosθ2)sinθ2]=mg

T1=mg[sinθ1+(cosθ1cosθ2)sinθ2]=mgcosθ2sinθ1cosθ2+cosθ1sinθ2

T1=mgcosθ2sin(θ1+θ2)

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