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Finding Tension using Newton's Laws

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data

    A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with the vertical, what must this angle be if the tension in each wire is equal to 0.75 of the weight of the frame. Ignore any friction between the wall and picture frame.


    2. Relevant equations

    Newton's laws of motion.

    3. The attempt at a solution

    The picture frame has a weight w.

    The question states that the tension of the wire is 0.75w. Since the picture frame has zero acceleration, it is in equilibrium. I drew a picture to clarify my thought process:

    http://i.imgur.com/oR8HST0.png

    ƩFx = 0

    ƩFx = T2cos(θ) - T1cos(θ) = 0
    This tells us that T2 = T1 = 0.75w

    ƩFy = 0

    ƩFy = T1sin(θ) + T2sin(θ) - w = 0

    ƩFy = T1sin(θ) + T1sin(θ) - w = 0

    = 2Tsin(θ) - w = 0

    = 1.5wsin(θ) = w

    = sin(θ) = (2/3)

    Taking the arcsine gives approximately 42 degrees, but the angle is 48 degrees and I can't figure out what I'm doing wrong.
     
  2. jcsd
  3. Feb 16, 2013 #2

    Doc Al

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    Staff: Mentor

    I suspect that they want the angle with respect to the vertical, not the horizontal.
     
  4. Feb 16, 2013 #3

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Mangoes! :smile:
    Nice diagram! :smile:

    But you've marked the wrong angle as θ! :cry:
     
  5. Feb 16, 2013 #4
    Oh wow...

    I even typed it and everything and still didn't pick up that vertical part in my head.

    Thanks a lot guys.
     
  6. Feb 16, 2013 #5

    SteamKing

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    Staff Emeritus
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    Usually, most pictures are hung using a single nail, so that the wires form an inverted V with respect to the picture.
     
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