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Calculus-based Physics Question

  1. May 22, 2015 #1
    1. The problem statement, all variables and given/known data


    • The figure shows a heavy weight suspended by a cable and pulled to one side by a force F. We want to know how much force F is required to hold the weight in equilibrium at a given distance x to one side (say to place a cornerstone correctly). From elementary physics, T cos θ = W , and T sin θ = F .
      1. (a) Find F/W as a series of powers of θ.

      2. (b) Usually in a problem like this, what we know is not θ, but x

        and l in the diagram. Find F/W as a series of powers of x/l.

      2. Relevant equations

      Tcos(theta) = W
      Tsin(theta) = F
      sin(theta) = (x/l)
      cos(theta) = sqrt(l^2-x^2) = sqrt(1-(x/l)^2)[/B]

      3. The attempt at a solution

      The first part was a relatively simple solve, it was just a power series of the tangent function.

      The second part is what I am stuck on.

      I have (F/W) = (x/l)(1/sqrt(1-(x/l)^2)), but I have no clue how to turn the right side of this equation into a power series. Should I just create 2 different functions (one where x is a function of l and another where l is a function of x) and write 2 power series, or is there a way that I am not seeing? I have also tried just letting theta = arcsin(x/l) and substituting that into the power series I found in part 1, but that solution was incorrect. I am at a complete loss. Any help would be much appreciated.

      Thanks in advance!
     
    Last edited by a moderator: May 22, 2015
  2. jcsd
  3. May 22, 2015 #2
    Never mind, I solved it. It was a simple binomial expansion that I was overlooking.
     
  4. Aug 28, 2015 #3
    I am still struck at the second part. can you please explain how you have solved it.
    Thanks in advance
     
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