What Are the Key Forces Acting on a Cylinder on an Inclined Plane?

AI Thread Summary
A uniform cylinder on an inclined plane is in equilibrium, supported by a cord under tension and subject to static friction. To determine the minimum coefficient of friction for equilibrium, a force diagram is essential, incorporating the cylinder's weight, normal force, tension, and friction. The discussion emphasizes the need for three equations: two for horizontal and vertical force balance, and one for torque balance. There are concerns about the accuracy of the force diagram, particularly the direction and line of action of the normal force. Properly resolving these forces is crucial for solving the problem accurately.
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Homework Statement



A uniform cylinder of mass m and radius R rests in equilibrium against a
rough plane that is inclined at an angle α to the horizontal. The cylinder
is supported by a cord under a constant tension, wrapped round it, so that
the cord leaves the surface of the cylinder tangentially and is horizontal;
the plane of the cord is perpendicular to the axis of the cylinder. The axis
of the cylinder is horizontal, and all the forces act in the same vertical
plane.
Model the cord as a model string, and take the coefficient of static friction
between the cylinder and the plane as μ. The object of this question is to
find the minimum value of the coefficient of friction for the cylinder to be
in equilibrium.
https://skydrive.live.com/redir?resid=4CDF33FFA97631EF!1040
I'm having problems drawing the force diagram.


The Attempt at a Solution



I've made two diagrams, but I think they are both wrong.
https://skydrive.live.com/redir?resid=4CDF33FFA97631EF!1041
Can you help?
 
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You have four unknown forces. You only need to figure out (in principle) the ratios between them, so that's 3 degrees of freedom. That means you need three equations. Horizontal and vertical force balance gives two, and torque balance gives the third. So you will be needing the second diagram.
The only problem I see with it is how you've drawn N. The direction looks a bit off (maybe just a drawing inaccuracy) and the line of action is not right.
The line of action of W isn't quite clear, but it's probably OK.
 
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