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Hi, I'm a freshman intending to major in mathematics and CS.

You can find my course notes typeset in $\LaTeX$ here

Week 1

The gravitational force is equal to $10m$ downwards, and so the normal and frictional forces must sum to the opposite the gravitational force $(0, -10m)$. This gives us the equation $N \cdot (1/2, \sqrt{3}/2) + \mu \cdot (-\sqrt{3}/2, 1/2) = (0, 10m)$, where $N$ and $\mu$ are the magnitude of the normal and frictional forces respectively. Solving this system of linear equations gives us $\mu = 5m$ and $N = 5\sqrt{3}m$, implying that the normal and frictional forces are $F_N = (5\sqrt{3}m/2, 15m/2)$ and $F_\mu = (-5\sqrt{3}m/2, 5m/2)$ respectively.