Part $($b$)$

Using the coordinate system provided in the problem image, find an expression for the component of the force of gravity in the $y$ direction in terms of given quantities and variables available in the palette.

Part $($c$)$

Write an expression for the magnitude of the maximum friction force in terms of given quantities and variables available in the palette.

Part $($d$)$

Assuming the static friction is maximized, write an expression, using only the given parameters and variables available in the palette, for the sum of the forces along the plank.

Part $($e$)$

In terms of the given parameters and variables available in the palette, write an expression for the maximum angle that the board can make with respect to the horizontal before the block starts moving.

Part $($f$)$

Enter a value, in degrees, for the maximum angle.

${}_{\text{m}\text{a}\text{x}}=$A block with a mass of $m=1\mathrm{.}07kg$ rests on a wooden plank. The coefficient of static friction between the block and the plank is ${}_s=0\mathrm{.}87.$ One end of the board is attached to a hinge so that the other end can be lifted forming an angle, $,$ with respect to the ground. Assume the $x$ axis is parallel to the surface of the plank and directed up the incline, as shown.

Part $($a$)$

Please use the interactive area below to draw the Free Body Diagram for this block, assuming it is in static equilibrium. If necessary, use $F_s$ for the force of static friction and $F_k$ for the force of kinetic friction.

$$ Correct!

Part $($b$)$

Using the coordinate system provided in the problem image, find an expression for the component of the force of gravity in the $y$ direction in terms of given quantities and variables available in the palette.

Part $($c$)$

Write an expression for the magnitude of the maximum friction force in terms of given quantities and variables available in the palette.