Hanging Chandelier (A question about Tension Force)

  1. Hanging Chandelier (Solved)

    1. The problem statement, all variables and given/known data
    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 T1 and makes an angle of (theta1) with the ceiling. Cable 2 has tension T2 and makes an angle of (theta2) 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, (theta1) , and (theta2) , as well as the magnitude of the acceleration due to gravity .

    2. Relevant equations
    No equation


    3. The attempt at a solution
    I figured that Net Force=0 and therefore
    Net Force x = T2cos(theta2) - T1cos(theta1)=0
    Net Force y = T1sin(theta1) + T2sin(theta2) - mg=0

    I came up with these equations and I know that they are right. I just don't know how to eliminate T2.

    Can anyone help me with this?

    This is the figure : http://session.masteringphysics.com/problemAsset/1010934/37/MFS_1l_3_v1_a.jpg
     
    Last edited: Feb 24, 2011
  2. jcsd
  3. I figured that T2 = (T1cos(theta1)/(cos(theta2)

    Which makes the Net Force y equation T1sin(theta1)+(T1cos(theta1))/(cos(theta2))=mg

    Then I just solved for T1 and I got T1=(mgcos(theta2)-T1sin(theta1))/(cos(theta2)

    Which is not the right answer. It says my answer should not depend on T1.

    Where is my mistake?
     
  4. I figured out my mistake. For some reason I thought :

    Net Force y equation was T1sin(theta1)+(T1cos(theta1))/(cos(theta2))=mg instead of

    T1sin(theta1)+(T1cos(theta1))(sin(theta2))/(cos(theta2))=mg

    Then T1(Sin(theta1)+(cos(theta1)(tan(theta2)=mg

    T1=mg/(Sin(theta1)+(cos(theta1)(tan(theta2)

    I tried it. It's the right answer.
     
    Last edited: Feb 24, 2011
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