A triangular object lies at rest on the ground, pressed up against a wall. Above it is a box fixed to the wall by

a wire. Above the box rests a trapezoidal object. The box has mass m while both the triangular and trapezoi$-$

dal objects have mass $2$m$.$ The only surface with friction is the interface between the box and the trapezoid.

$($a$)$ Treating each object as a point particle, draw a free$-$body$-$diagram for all three objects. Scale each

force vector relative to each other.

$($b$)$ Identify all Newton$$s third law force pairs.

$($c$)$ Find an expression, in terms of the wedge angle $,$ for the coefficient of friction that would just

barely keep the trapezoidal object from sliding.

$($d$)$ Find an expression for the tension in the cable as a function of and m$.$

$($e$)$ Use the Proportionality sense$-$making technique to check your expression for the tension in part $($d$).$

Does the tension increase or decrease as the angle increases? Is this the behavior you would ex$-$

pect? Explain.