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Power series question involving classical mechanics

  1. May 4, 2010 #1
    1. The problem statement, all variables and given/known data
    A heavy weight is suspended by a cable and pulled to one side by a force F. How much force is required to hold the weight in equilibrium at a given distance x to one side.
    From classical mechanics, TcosX= W and TsinX=F. Find F/W as a power series of X(angle).

    Often in a problem like this, what we know is not X, but x(displacement) and l(length of string).

    Find F/W as a series of powers in x/l


    2. Relevant equations

    TcosX=W
    TsinX=F

    3. The attempt at a solution

    How do I calculate the power series for tanX? I've searched online but the people at yahoo answers got it wrong
    http://en.wikipedia.org/wiki/Taylor_series
    Wikipedia gives the answer but no route to it.

    SinX= x/l

    cosX= ((l-x)(l+x))^0.5/l

    F/W = x/(l-x)(l+x)^0.5??????
     
  2. jcsd
  3. May 4, 2010 #2

    vela

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    You want things in terms of x/l. The sine already is, but the cosine isn't. Rewrite it slightly, like this

    [tex]\cos X = \frac{\sqrt{l^2-x^2}}{l}} = \sqrt{1-\left(\frac{x}{l}\right)^2}[/tex]

    and go from there.
     
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