Scenario $2$: Sliding Down a Ramp

A $2\mathrm{.}0-$kg block starts with a speed of $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at the bottom of a plane inclined at $\backslash (37^\{\backslash$circ$\}\backslash )$ to the horizontal. The coefficient of sliding friction between the block and plane is $\backslash (\backslash$mu$\_\{$k$\}=0\mathrm{.}30\backslash ).$ Determine the distance the block slides up the ramp before coming to a stop. The determine the speed of the block when it reaches the bottom of the ramp after sliding back down.

$-$ Draw a picture $($physical scenario diagram$)$ and identify a coordinate system for this scenario

$-$ Identify the forces acting on the block. You can draw these on the diagram or as a separate force diagram $($or both$)$

$-$ Construct a First Law of Thermodynamics equation and a Center of Mass equation for the block.

$-$ Set up the relevant integrals and$/$or Deltas for both equations $($including limits of integration as numbers or variables$)$

$-$ Choose one of the equations to solve and explain why you chose that equation.