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Asked: 2022-04-10T07:25:08+00:00 In:

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

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A chandelier with mass 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 and makes an angle of the ceiling. Cable 2 has tension and makes an angle of the ceiling.

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

♦ Relevant knowledge
Two supporting cables are used to hang an object. At the junction point, three forces work.

The tension forces in the cables create two forces. One force is called the weight force.

The sum of all forces in the horizontal and vertical directions should equal zero to achieve equilibrium for the object.

 

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1 Answer


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

    In vertical direction

    T1sinth1+T2sinth2=mg

    In the horizontal direction.

    T1costh1=T2costh2

    Both the equations and solving T 1 andT 2 are solved

    T1=m*g*cos(th2)/sin(th1+th2) T2=m*g*cos(th1)/sin(th1+th2)

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