Short Answer 
The maximum frictional forces for blocks A and B are calculated to be 160 N and 120 N, respectively, allowing both blocks to move together due to A’s higher friction. The common acceleration of both blocks is determined to be 2 m/s¬≤.
Step 1: Understand the Frictional Forces
First, calculate the maximum frictional forces acting on both blocks. For block A, the maximum frictional force is given by:
- f₁ max = μ₁ N₁ = (0.8)(20g) = 160 N
For block B, also calculate the normal force:
- N‚ÇÇ = N‚ÇÅ + 10g = 300 N
Then calculate the maximum frictional force for block B:
- f₂ max = μ₂N₂ = (0.4)(300) = 120 N
Step 2: Analyze the Conditions for Acceleration
Next, compare the maximum frictional forces to determine whether both blocks can accelerate together. Since f‚ÇÅ max (160 N) is greater than f‚ÇÇ max (120 N), this implies that the frictional force on block A is sufficient to prevent slipping. This means both blocks will move together under the influence of the applied force.
Step 3: Calculate the Common Acceleration
Now, calculate the common acceleration of both blocks. Use the formula:
- ac = (Applied Force – f‚ÇÇ max) / (mB + mA)
Substituting the values, we get:
- ac = (180 Р120) / (20 + 10) = 2 m/s²
Thus, the acceleration of the lower block (B) concerning the upper block (A) is 2 m/s².