1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    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
    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Power series question Date
Question regarding Power Series May 21, 2015
Power series question Dec 3, 2013
General question about differentiating power series Nov 17, 2013
Power Series Question Apr 22, 2013
Power series question. Jan 1, 2013