# Find the minimum and maximum of a ratio for equilibrium

• Aleph_null
In summary, the conversation discusses a rod in equilibrium with a coefficient of static friction at points A and B, and the goal of finding the ratio l/d for the rod to remain in equilibrium. The speaker has calculated the forces at play just before sliding occurs, but needs help proceeding with the solution. The desired solution is an inequality in terms of the coefficient of static friction and the angle θ. The calculation likely involved 4 forces and 3 torques written in terms of l, d, and θ.
Aleph_null

## Homework Statement

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

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?

## What is meant by "equilibrium" in this context?

Equilibrium refers to a state in which opposing forces or factors are balanced, resulting in a stable system. In the context of finding the minimum and maximum of a ratio for equilibrium, it means determining the point at which the ratio is most balanced.

## Why is finding the minimum and maximum of a ratio important for equilibrium?

In order to maintain a stable and optimal system, it is important to know the range of values that the ratio can take. If the ratio falls below the minimum or goes above the maximum, the system may become unbalanced and lead to inefficiency or even failure.

## What factors influence the minimum and maximum of a ratio for equilibrium?

The minimum and maximum of a ratio for equilibrium can be influenced by a variety of factors, such as external forces, internal components, and environmental conditions. These factors can affect the balance of the system and thus impact the range of values for the ratio.

## How can we calculate the minimum and maximum of a ratio for equilibrium?

The exact method for calculating the minimum and maximum of a ratio for equilibrium will depend on the specific system and variables involved. Generally, it involves analyzing the relationships between different components and using mathematical or computational methods to determine the most balanced ratio.

## What are the potential implications if the minimum and maximum of a ratio for equilibrium are not properly determined?

If the minimum and maximum of a ratio for equilibrium are not accurately determined, it can lead to an unstable system and potential inefficiency or failure. This can have consequences ranging from minor setbacks to major disruptions, depending on the significance of the system and its role in a larger context.

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