Show formulas and complete solutions. Your solution MUST match your force vectors for each part. You must include a free$-$body diagram with each part's relevant force vectors.

Note: Make swre your free$-$body diagrams and force vectors match your equations for each case. Follow the same method for each part by analyzing the forces on both the block on the incline and the hanging block. You must account.for gravity, tension in the string, friction, and the normal force in your calculations.

A $\backslash (5-\backslash$mathrm$\{$kg$\}\backslash )$ block is placed on a ramp $\backslash (30^\{\backslash$circ$\}\backslash )$ above the horizontal. As shown in the figure, it is connected to a hanging block by a light string over an ideal pulley at the top edge of the ramp. The string pulls on the $\backslash (5-\backslash$mathrm$\{$kg$\}\backslash )$ block parallel to the inclined surface.

Now, consider friction between the surfaces and the $5-$kg block on the ramp for all parts below. The static and kinetic coefficients of friction are given as:

$-\backslash (\backslash$mu s$=0\mathrm{.}2\backslash )($static coefficient of friction$)$

$-\backslash (\backslash$mu $\backslash$mathrm$\{$k$\}=0\mathrm{.}1\backslash )($kinetic coefficient of friction$)$

To solve each part of the problem, you must first copy the figure onto your paper.

$1.$ Use a ruler to draw all force vectors acting on both the $\backslash (5-\backslash$mathrm$\{$kg$\}\backslash )$ block and the hanging block.

$2.$ Label all the force vectors clearly.

$3.$ Start with the equation Fnet$=$ma to solve each part.

$4.$ The equations you derive must match the force vectors in your free$-$body diagrams