How Does Friction Affect the Motion of a Cylinder on Planks?

[sArGe99]

Homework Statement

http://s287.photobucket.com/albums/ll123/amalnathm/th_untitled.jpg

A uniform solid cylinder of mass m rests on two horizontal planks. A thread is wound on the cylinder. The hanging end of the thread is pulled vertically down with a constant force F. Find the maximum magnitude of force which does not bring about any sliding of the cylinder, if the coefficient of friction between the cylinder and the planks equal k. Which is the acceleration of the axis of the cylinder rolling down the inclined plane.

Homework Equations

The Attempt at a Solution

Direction of forces is giving me the headache again.

Force equation
F + mg - 2f = ma

Torque equation
(F - 2f) X R = I \alpha
f = k. (mg+F)
F - 2k (mg+F) = M a r / 2
F(1 - 2k) = 2kmg + M a r/2
F = (2kmg + m a r/2) / (1-2k)

 

[sArGe99]

I need a bit of help with this please..

 

[sArGe99]

BUMP! Just keeping it on the top.