Homework H$\mathrm{.}4.$A

Given: Particle P $($of mass $m)$ moves along a rough surface $($with a coefficient of kinetic friction of ${}_k$ between P and the surface$).$ At one instant when P is at a position on the path that has a radius of curvature of $,P$ has a speed of $v$ with the velocity vector for P being oriented at a clockwise angle of $$ from the vertical.

Find: For this position,

$($a$)$ Determine the normal component of force of the path acting on particle P $.$

$($b$)$ Determine the rate of change of speed of particle $P.$

Use the following parameters in your analysis: ${}_k=0\mathrm{.}2,m=4kg,=0\mathrm{.}5m,=36\mathrm{.}87$ and $v=30\frac{m}{s}.$