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

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The discussion revolves around calculating the maximum force that can be applied to a uniform solid cylinder resting on two planks without causing it to slide, given a coefficient of friction k. The participant is struggling with the direction of forces and has set up equations for force and torque to analyze the problem. They derived a force equation and expressed it in terms of mass, gravitational force, and acceleration, but seek assistance in refining their approach. The equations indicate a relationship between the applied force, friction, and the resulting motion of the cylinder. The participant is looking for clarification on their calculations and the overall dynamics involved.
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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)
 
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I need a bit of help with this please..
 
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