Equilibrium cylinder and plank on incline

[joemama69]

Homework Statement

A horizontal stick of mass m has its left end attached to a free pivot on a plane (inclined at angle θ), while it’s right end rests on a cylinder also of mass m which in turn rests on the plane, as shown. The coefficient of friction between the cylinder and both the stick and the plane is μ

(a) Assuming that the system is at rest, what is the normal force from the plane on the cylinder?

(b) What is the smallest value of μ (in terms of θ) for which the system doesn’t slip anywhere?

Homework Equations

The Attempt at a Solution

is my free body diagram correct on the attachment. I realize that the Ns and the us are different

 

[AEM]

Your free body diagram looks okay. I'd be a little more careful to make the normal forces and frictional forces perpendicular and locate them at the points of contact between the surfaces. I'd make mgcos(Q) perpendicular to the inclined plane, but then I'm a fussy old professor. I'd show the attachment of the horizontal stick to the pivot at the end of the inclined plane.

I guess you can summarize it by I'd be a little more complete and a little more careful. You cut down on errors that way. (Plus it impresses the person who grades your homework.)

 

[sxr001]

I know this is from a few years ago, but can someone explain to me why that bottom friction force is pointed up the plane. It seems strange...