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!

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

    Tsin(theta)=Fcos(theta)-mg
    and
    Tcos(theta)=(mv^2/Lcos(theta))-Fsin(theta)

    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:
    $$T\sin\theta-F\cos\theta=...$$
    $$T\cos\theta+F\sin\theta=...$$
    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
    $$T\sin\theta-F\cos\theta=...(1)$$
    $$T\cos\theta+F\sin\theta=...(2)$$
    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

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper

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

Have something to add?
Draft saved Draft deleted



Similar Discussions: System of equations
  1. System of equations (Replies: 1)

  2. System of Equations (Replies: 1)

  3. System of Equations (Replies: 6)

  4. System of equations (Replies: 3)

  5. System of Equations (Replies: 17)

Loading...