Setup: Block A (mass m) on top of Block B (mass M) on a surface. Force F applied on one block.

Step 1: Check if blocks move together. Assume they move together: a = $\frac{F}{m+M}$. Required friction on A = ma (if F is on B) or = Ma (if F is on A... depends on which block). Compare with $f_{max}$ = $mu_s$ * m * g (between A and B).

Step 2: If $f_{required}$ <= $f_{max}$: Blocks move together at a = $\frac{F}{m+M}$.

Step 3: If $f_{required}$ > $f_{max}$: Blocks slide relative to each other.

• Write separate FBDs with $f_k$ = $mu_k$ * m * g between them
• Solve for individual accelerations

Common error: Using static friction when blocks are sliding, or kinetic when they're not.