The problem involves two weights, $W_1$ and $W_2$, resting on inclined planes and connected by a horizontal link $AB$. Given that $W_1 = 1000 \, \text{N}$, we are to determine the maximum and minimum values of $W_2$ for which equilibrium can exist. The coefficient of friction at the contact surfaces is given as $0.36$.

Solution Outline:

1. Free Body Diagrams (FBD): Draw FBDs for $W_1$ and $W_2$. Analyze the forces acting on both weights, including friction, normal forces, and tensions.

2. Equilibrium Equations: Use the equilibrium conditions (sum of forces in horizontal and vertical directions equals zero) for both weights.

3. Friction Forces: Incorporate the friction forces using the coefficient of friction ($\mu = 0.36$). Friction force is calculated as $f = \mu N$, where $N$ is the normal force.

4. Maximum and Minimum $W_2$: Solve the equations to find the values of $W_2$ that maintain equilibrium. There will be a range defined by the frictional limits.

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Related Questions:

1. How do you calculate the normal force on an inclined plane?
2. What role does the coefficient of friction play in equilibrium problems?
3. How do you determine the direction of friction forces in a system?
4. What are the conditions for equilibrium in a system involving inclined planes?
5. How can changes in $W_1$ affect the equilibrium conditions for $W_2$?

Tip: Always check the direction of frictional forces to ensure they oppose the relative motion of the surfaces in contact.