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Power series in real world situation

  1. Aug 15, 2011 #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. Tcosθ=W and Tsinθ=F. Find F/W as a power series of θ. Often in a problem like this, what we know is not θ, but x and l. Find F/W as a series of powers in x/l.

    l is the length if the cable
    W is weight
    T is the tension in the cable


    2. Relevant equations



    3. The attempt at a solution

    no idea...
     
  2. jcsd
  3. Aug 15, 2011 #2

    HallsofIvy

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    The first obvious thing to do is to see that F/W= (T sin(θ))/(Tcos(θ))= tan(θ).

    Can you expand that as a power series- say, a Taylor series?
     
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