I'm trying to do the following in LaTeX:

[![My equation system on paper](https://i.stack.imgur.com/dl08V.jpg)](https://i.stack.imgur.com/dl08V.jpg)

The box at the end doesn't have to be there. I've tried using `cases`, from the amsmath package, but it doesn't align correctly with the equations on top, nor is the formatting very pretty:

[![latex equation](https://i.stack.imgur.com/mZweg.png)](https://i.stack.imgur.com/mZweg.png)

This is the code I used:

```
\begin{align*}
    \sum \vec{F} &= ma \\
    \vec{R_n} + \vec{Fg} + \vec{F_a} &= ma \\

    \begin{cases}
        \vec{F_a} &= ma_c\\
        \vec{R_n} - \vec{F_g} &= 0
    \end{cases}  

    \begin{cases}
        uR_n &= m\frac{v^2}{r}\\
        R_n &= mg
    \end{cases}  

    \begin{cases}
        ug &= \frac{v^2}{r}\\
        R_n &= mg
    \end{cases}  

    \begin{cases}
        \sqrt{ugr} &= v\\
    \end{cases}
\end{align*}

```

Thanks in advance, I'm a LaTeX beginner :)