# [SOLVED] Conservation of linear momentum

• July 3rd 2008, 03:04 AM
moolimanj
[SOLVED] Conservation of linear momentum
Another darned Physics (or Psycho) question. Any help greatly received.
• July 3rd 2008, 03:30 AM
flyingsquirrel
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 $E_{\text{after}}-E_{\text{before}}=E_{c,C}-E_{c,A}+E_{c,B}$.
• July 3rd 2008, 10:26 AM
thermalwarrior
mst209..............................
• July 3rd 2008, 01:05 PM
moolimanj
great minds think alike
• July 3rd 2008, 03:05 PM
thermalwarrior
can you post a few pointers for solving this for the variables???
• July 3rd 2008, 03:23 PM
mr fantastic
Quote:

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
• July 3rd 2008, 11:22 PM
flyingsquirrel
Quote:

Originally Posted by thermalwarrior
can you post a few pointers for solving this for the variables???

Rewrite the left hand side as follows :

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