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1. The problem statement, all variables and given/known data

Two particles A and B of mass [tex]m[/tex] and [tex]3m[/tex] respectively, A collides with B. Find the coefficient of restitution [tex]e[/tex] if [tex]\textbf{v}_{A}[/tex] is purely in the [tex]\textbf{j}[/tex]-direction.

Velocity of each particle before collision.

[tex]\dot{\textbf{r}}_{A}=9 \textbf{i}+5\textbf{j}[/tex]

[tex]\dot{\textbf{r}}_{B}=2 \textbf{i}+2\textbf{j}[/tex]

The x and y velocity components before collision

[tex]\dot{x}_{A}[/tex], [tex]\dot{y}_{A}[/tex], [tex]\dot{x}_{B}[/tex] and [tex]\dot{y}_{B}[/tex]

The x and y velocity components after collision

[tex]\dot{X}_{A}[/tex], [tex]\dot{Y}_{A}[/tex], [tex]\dot{X}_{B}[/tex] and [tex]\dot{Y}_{B}[/tex]

2. Relevant equations

The common tangent is the [tex]\textbf{j}[/tex] axis.

[tex]\dot{y}_{A}\textbf{j}=\dot{Y}_{A}\textbf{j}[/tex] and [tex]\dot{y}_{B}\textbf{j}=\dot{Y}_{B}\textbf{j}[/tex]

[tex](\dot{X}_{A}-\dot{X}_{B})\textbf{i}=-e(\dot{x}_{A}-\dot{x}_{B})\textbf{i}[/tex]

[tex]m\dot{\textbf{r}}=m\textbf{v}[/tex]

3. The attempt at a solution

With the values above I find the velocities after collision

[tex]\textbf{v}_{A}=(-\frac{21}{4}e+\frac{15}{4})\textbf{i}+5\textbf{j}[/tex]

[tex]\textbf{v}_{B}=(\frac{7}{4}e+\frac{15}{4})\textbf{i}+2\textbf{j}[/tex]

How do I find [tex]e[/tex] if [tex]\textbf{v}_{A}[/tex] is purely in the [tex]\textbf{j}[/tex]-direction?

If I use(which is in the i-direction)

[tex](\dot{X}_{A}-\dot{X}_{B})=-e(\dot{x}_{A}-\dot{x}_{B})[/tex]

I get [tex]e=0[/tex], a totally inelastic collision.

Thanks in advance.

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# Homework Help: Linear momentum

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