Mechanics: could someone check my diagram please?

[knowlewj01]

Homework Statement

A uniform rod of length 2a and weight W rests at an angle of 60° to the horizontal with one end hinged to a horizontal plane and one end resting on a cylinder of radius a and weight W that is itself resting on the horizontal plane. The axis of the cylinder is perpendicular to the vertical plane containing the rod. The contacts between the rod and the cylinder and between the cylinder and the ground are rough. Find the ratio of the frictional force to the normal reaction force at the point of contact of: i) the cylinder with the plane and ii) the rod with the cylinder

Homework Equations

The Attempt at a Solution

I have uploaded my diagram, just wondering if i have all the forces there and the correct directions. Thanks

 

[knowlewj01]

I think there should be a normal reaction from the plane on the rod but i can't decide wether it should be perpendicular to the plane or the rod. any ideas?

 

[Phrak]

Is this a dynamic or static problem? You show the cylinder rotating.

-The normal force of the cylinder on the rod should be at it's point of contact along a line passing through the center of the cylinder.

-The rod is hinged to the surface.

-The weight of the rod should pass through it's center.

-The frictional force between the rod and the cylinder is missing.

 

[knowlewj01]

the system is in equilibrium and in limiting friction such that
F=\muR

is the normal reaction of the rod on the floor perpendicular to the floor? i think this is right, then to solve the problem i should resolve and take moments.

 

[Phrak]

the system is in equilibrium and in limiting friction such that
F=\muR

is the normal reaction of the rod on the floor perpendicular to the floor? i think this is right, then to solve the problem i should resolve and take moments.

Yes it is. But I don't know what 'limiting friction' means.

There are two forces on the end of the rod. There is a vertical normal force of the floor on the rod at the point of contact, and a static frictional force directed in the negative x direction upon the end of the rod.

 

[ChrisBaker8]

But the question says one end is hinged to the horizontal. Doesn't that mean you count them as one object? (ie no normal force or friction)

 

[Phrak]

But the question says one end is hinged to the horizontal. Doesn't that mean you count them as one object? (ie no normal force or friction)

Yes, that's a better way of looking at it. The magntude and direction of the force at the hing is unknown. It has to be found as a result of the other forces.