[SOLVED] Conservation of linear momentum

**moolimanj** · July 3rd 2008, 02:04 AM

Another darned Physics (or Psycho) question. Any help greatly received.

**flyingsquirrel** · July 3rd 2008, 02:30 AM

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 $E_{\text{after}}-E_{\text{before}}=E_{c,C}-E_{c,A}+E_{c,B}$ .

**thermalwarrior** · July 3rd 2008, 09:26 AM

mst209..............................

**moolimanj** · July 3rd 2008, 12:05 PM

great minds think alike

**thermalwarrior** · July 3rd 2008, 02:05 PM

can you post a few pointers for solving this for the variables???

**mr fantastic** · July 3rd 2008, 02:23 PM

Originally Posted by moolimanj

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

**flyingsquirrel** · July 3rd 2008, 10:22 PM

Originally Posted by thermalwarrior

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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