Advanced — Friction on Two BlocksHardQuestion 30275
Question
Block A (3 kg) is on block B (5 kg) on a rough floor (μ_floor = 0.2). μ between A and B = 0.4. Force 40 N on A. (g = 10). Do they move together?
- AYes, a = 5 m/s²
- BNo, A slides on BCorrect
- CYes, a = 4 m/s²
- DNo, B slides on floor only
Correct answer
No, A slides on B
Explanation
If together: a = (40 − 0.2×8×10)/8 = (40−16)/8 = 24/8 = 3 m/s². Friction needed on A from B = 3×3 = 9 N. Max friction between A and B = 0.4×3×10 = 12 N. So if together, friction is fine. But check B: friction from A on B (forward) = 9 N, friction from floor = 0.2×8×10=16 N backward. Net on B = 9−16 = −7 N → B doesn't accelerate forward at 3 m/s². The system analysis needs to be done simultaneously to determine if they slip. This is a complex multi-body problem.