# Thread: [SOLVED] Conservation of linear momentum

1. ## [SOLVED] Conservation of linear momentum

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

2. 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 $\displaystyle m_A+m_B=4m$ hence

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

And this can be solved for $\displaystyle v_x$ and $\displaystyle v_y$.

For the second question you've to compute the kinetic energy of the three particles since you're asked to evaluate $\displaystyle E_{\text{after}}-E_{\text{before}}=E_{c,C}-E_{c,A}+E_{c,B}$.

3. mst209..............................

4. great minds think alike

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

6. Originally Posted by moolimanj
Another darned Physics (or Psycho) question. Any help greatly received.

7. Originally Posted by thermalwarrior
can you post a few pointers for solving this for the variables???
Rewrite the left hand side as follows :

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