First, define .

Then, draw all forces that works on the rod. The total force and torque on the rod must be zero, because it is in equilibrium.

For x-component,

For y-component,

And for torque, we can take an arbitrary point on the rod because it is in equilibrium. In this case, we take the contact point to the floor.

Solving these three equations, and we get the relation between and ,

Because and may have different values, the coefficient of friction of wall and floor must be the greatest value between these two values, and , to keep the value of both not higher than the coefficient of friction.

Then draw a graph with as x-axis and as y-axis (can be or ).

From the graph, we can conclude that it reach its minimum value when .

And the equation (4) will become

Solve for ,

That's my solution.
If you have any question, correction, or comment, please leave a comment below.
Thank you.

Solution - Minimum FrictionSocialTwist Tell-a-Friend


Anonymous said... @ March 6, 2009 at 9:19 PM

i dont understand why you can draw the graph.. explain please

Copycat91 said... @ March 7, 2009 at 2:41 PM

From equation (4), I try all possible value of \mu_w and compare its value with \mu_f. The greater value of these two \mu (either it is \mu_w or \mu_f), is the coefficient of friction.
And I was looking for the value of \mu_w so that the coefficient of friction is minimum.

In order to do so, it would be easier if I draw a graph.

Anonymous said... @ May 1, 2009 at 9:56 PM

oh I don't understand too, about the graph, Could you explain it please!

Anonymous said... @ May 6, 2012 at 5:25 PM

hi cant see the images is there any way to resolve this?

Anonymous said... @ September 24, 2012 at 11:04 AM

i cant see as well!

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