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Math Help - [SOLVED] Conservation of linear momentum

  1. #1
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    [SOLVED] Conservation of linear momentum

    Another darned Physics (or Psycho) question. Any help greatly received.
    Attached Thumbnails Attached Thumbnails [SOLVED] Conservation of linear momentum-particles.bmp  
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    Super Member flyingsquirrel's Avatar
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    Hi

    The first question can be answered using... the conservation of the linear momentum of the two particles : we know their mass and their velocity, we also know that the mass of the coalesced particle is m_A+m_B=4m hence

    \vec{p}_{\text{before}}=\vec{p}_{\text{after}} \Longleftrightarrow\vec{p_A}+\vec{p_B}=\vec{p_C} \Longleftrightarrow m\begin{pmatrix} 2\\3\end{pmatrix}+3m\begin{pmatrix} 6\\-5\end{pmatrix}=4m\begin{pmatrix} v_x\\v_y\end{pmatrix}

    And this can be solved for v_x and v_y.

    For the second question you've to compute the kinetic energy of the three particles since you're asked to evaluate E_{\text{after}}-E_{\text{before}}=E_{c,C}-E_{c,A}+E_{c,B}.
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    mst209..............................
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    great minds think alike
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    can you post a few pointers for solving this for the variables???
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    Quote Originally Posted by moolimanj View Post
    Another darned Physics (or Psycho) question. Any help greatly received.
    This question links nicely with this htread: http://www.mathhelpforum.com/math-he...ors-t-0-a.html
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  7. #7
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by thermalwarrior View Post
    can you post a few pointers for solving this for the variables???
    Rewrite the left hand side as follows :

    m\begin{pmatrix} 2\\3\end{pmatrix}+3m\begin{pmatrix} 6\\-5\end{pmatrix}=\begin{pmatrix} 2m+18m\\3m-15m\end{pmatrix}=\begin{pmatrix} 20m\\-12m\end{pmatrix}=4m\begin{pmatrix} 5\\-3\end{pmatrix}
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