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3 unknowns, 3 equations, failure on algebraic method

  1. Sep 12, 2011 #1
    1. The problem statement, all variables and given/known data

    This example comes straight out of the book. Can someone show intermediate steps?

    Code (Text):
    Fx = 0: -0.0933Tab - 0.0846Tac + P = 0
    Fy = 0: +0.778Tab + 0.705Tac - 1962N = 0
    Fz = 0: +0.622Tab - 0.705Tac = 0
    Book solution: P = 235 N, Tab = 1401N, Tac = 1236N

    2. Relevant equations

    what method did they use

    3. The attempt at a solution

    determinants & algebraic methods failed.
     
  2. jcsd
  3. Sep 12, 2011 #2

    dynamicsolo

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    I would suggest you check your hand calculation or calculator work more carefully. Those values does work in the equations.

    Try adding the last two equations together: you should get 1.4 Tab = 1962 N , which does give the book's answer. Now 0.622 Tab = 0.705 Tac , so Tac = (0.622/0.705) Tab . Putting these values into the first equation will let you find P .

    It would help in troubleshooting if you showed what you'd done...
     
  4. Sep 13, 2011 #3

    Ray Vickson

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    The problem is sensitive to roundoff errors. When I solve the system in Maple 14 I get Tab = 1401.42857142857, Tac = 1236.43768996960 and P = 235.355914285714. Putting these in a column vector X and computing A.X gives [0, 1962, .1137e-12] (taking N=1) which is close to the actual right-hand-sides [0,1962,0]. However, rounding off to Tab = 1401, Tac = 1236, P=235 in a vector X gives A.X = [-.2789, 1961.358, .0420], which is not particularly close to [0,1962,0]. I don't know if this is what you are getting, as you have not explained exactly what you mean by failure.

    RGV
     
  5. Sep 13, 2011 #4
    Ok I posted the answer to these equations in my original post, but I wasn't trying to verify whether or not they work. They do work; what I posted is the last part of the example in my book. What I want to know is how they took on the 2nd last step those equations and somehow got that result?

    There appears to be 3 unknowns: Tab, Tac, and P. In another thread on another question I tried using Cramers rule to solve a similar question using determinants. Next I tried the algebraic solution to try and arrive at the book's result, but with 3 unknowns I kept going in circles. I ended up with 2 unknowns no matter what I did.

    The book just says ''solving these equations we obtain'' and then lists the result. Can someone please explain how to solve these equations? thanks.
     
    Last edited: Sep 13, 2011
  6. Sep 14, 2011 #5
    togo - I would start with the last two equations. Note that they contain just two variables (Tab and Tac).

    Use the last equation and solve for Tab in terms of Tac (or Tac in terms of Tab).


    Next (I'll assume you solved for Tab in terms of Tac):

    Substitute Tab expresion into the second equation so you get an equation soley in terms of Tac. Solve this equation for Tac.

    Now, using the expresion you first solved for (Tab as a function of Tac), use the value of Tac and sove for the value of Tab.

    Use the values for Tab and Tac in the first equation to solve for the value of P.
     
  7. Sep 14, 2011 #6

    vela

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    dynamicsolo already told you how to solve the equations step by step.

    If you still can't work it out on your own, you need to post details of your work, so we can see where you're going wrong.
     
  8. Sep 14, 2011 #7
    crap your right, sorry.
     
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