Find the minimum and maximum of a ratio for equilibrium

AI Thread Summary
The discussion focuses on determining the minimum and maximum ratio of l/d for a rod in equilibrium, considering static friction at points A and B. The user has calculated the forces acting on the rod just before sliding occurs but is uncertain about the next steps. They need to express the solution as an inequality involving the coefficient of static friction (μ_s) and the angle (θ). There is a suggestion to incorporate four forces and three torques into the calculations. The conversation emphasizes the importance of these calculations to establish the required ratio for equilibrium.
Aleph_null
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Homework Statement



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Consider the rod as shown in the figure. The coefficient of static friction at A and B is \mu_s. I'm trying to find how big and how small the ratio l/d can be for the rod to still be in equilibrium. I have calculated how big all forces are acting upon the rod in the case just before sliding happens, but I'm not sure how to proceed.

Homework Equations



Just before sliding happens the friction force F is F = \mu_s * F_n, where F_n is the normal force.

The Attempt at a Solution

 
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They want the solution as an inequality in terms of \mu_s and theta, .i.e they want a LS and RS as LS < l/d < RS .
 
Aleph_null said:
I have calculated how big all forces are acting upon the rod in the case just before sliding happens, but I'm not sure how to proceed.

Have you? Could you show us that calculation? Did it involve 4 forces and 3 torques all written in terms of l, d, and θ?
 

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