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Homework Help: System of equations

  1. Nov 25, 2015 #1
    1. The problem statement, all variables and given/known data
    this is actually one of the physics problems and I have boiled down the numerical to two equations.
    But I have trouble manipulating equations

    2. Relevant equations


    F and T are the two unknowns
    3. The attempt at a solution

    I brought the terms involving m to one side and the trig functions to the other
    and tried to add the the equations . But it only gets more complicated as in one eq F has a coefficient of cos(theta)+sin(theta) and in the other cos(theta)-sin(theta).same goes for coefficients of T in both equations.
  2. jcsd
  3. Nov 25, 2015 #2
    The form is like:
    Multiplying the both ##\sin\theta## and ##\cos\theta##, and the other way around, which may help.
  4. Nov 25, 2015 #3
    I did not understand this
  5. Nov 25, 2015 #4
    F(cos(θ))^2 sin(θ) +Tsin^2(θ) cos(θ)
    F sin^2(θ) cos(θ) -T cos^2(θ) sin(θ)

    what should I do?
  6. Nov 25, 2015 #5
    What I meant are ##(1)\cdot\sin\theta+(2)\cdot\cos\theta## and ##(1)\cdot\cos\theta-(2)\cdot\sin\theta.## Can you get anything from them?
  7. Nov 25, 2015 #6
    It worked !!
    How did you think about it?
    And THanks
  8. Nov 25, 2015 #7


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    I hope that tommyxu3 did not literally mean what he wrote.

    The form he gave was good.
    Here's what to do from that point.

    Multiply the first equation by ##\ \sin(\theta)\ ## and the second equation by ##\ \cos(\theta) \ ##, then add the equations to eliminate F . It's essentially the method of elimination. Then solve for T .
    Last edited: Nov 25, 2015
  9. Nov 25, 2015 #8
  10. Nov 25, 2015 #9

    Ray Vickson

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    It is easier if you simplify the symbolics: let ##s = \sin(\theta), c = \cos(\theta), A = mg, B = \frac{mv^2}{L} \cos(\theta)##. Then your equations read as
    [tex] sT = cF - A\\
    cT = -sF + B [/tex]
    [tex] \begin{array}{rcl}
    cF - sT &=& A\\
    sF + cT &=& B
    \end{array} [/tex]
    If you know about matrices and matrix inverion you can write down the solution immediately, because in matrix form the system reads as
    [tex] \pmatrix{c & s \\-s & c} \pmatrix{F\\T} = \pmatrix{A\\B} [/tex]
    A crucial simplification is that ##c^2 + s^2 = 1##, because these constants are the cosine and sine of the same angle.
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