# Uniform cylinder force diagram

1. Nov 2, 2012

### diorific

1. The problem statement, all variables and given/known data

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.

3. 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?

2. Nov 2, 2012

3. Nov 2, 2012

### haruspex

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.