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Uniform rectangular plate equilibrium problem

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data
    A uniform rectangular plate of width d, height h, and weight W is supported with its top and bottom edges horizontal. At the lower left corner there is a inge, and the upper right corner there is a cable. For what angle [itex]\theta[/itex] with the vertical will the tension in the cable be the least, and what is the tension?


    2. Relevant equations
    [itex]\tau=Fd[/itex]


    3. The attempt at a solution
    for the angle, it's easy,
    [itex]tan \theta = d/h[/itex]
    [itex]\theta=\arctan{d/h}[/itex]

    but I'm having trouble with the tension of the cable. I managed to derive
    [itex] \frac{Wd}{2}=Td\cos{\theta}+Th\sin{\theta}[/itex]

    which gives T as

    [itex]T=\frac{Wd}{2\left(d\cos{\theta}+h\sin{\theta})}[/itex]

    the answer given is

    [itex]T=(Wd/2)\sqrt{h^2+d^2}[/itex]

    I seem to fail to see the connection
    [itex]\sqrt{h^2+d^2}=\frac{1}{d\cos{\theta}+h\sin{\theta}}[/itex]

    can anyone show me why is this so?
     
    Last edited: Oct 16, 2009
  2. jcsd
  3. Oct 16, 2009 #2

    kuruman

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    You did only part of the problem. You found the tension at some angle θ. Now you need to find at what angle the tension has the least value, then find what the tension is.
     
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