I disagree with the answer to this homework question. Here it goes.
The coefficient of static friction is 0.60 between the two blocks in figure. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force F⃗ causes both blocks to cross a distance of 5.0m , starting from rest.
What is the least amount of time in which this motion can be completed without the top block sliding on the lower block?
Here's how I did it. I calculated the maximum force that won't cause the blocks to slide. The answer I got was 23.52N. So far the cannonical answer agrees with me.
Now I subtract the force of friction on the bottom block (13.72N) from the total tension on the rope and get 9.8N . The answer still agrees with me.
Here's where it diverges. To find the acceleration I take the net force (9.8N) and using F=ma where m = (mass of top block + mass of bottom block = 7kg), I get an acceleration of 1.4m/s^2
The answer key uses F=ma, but instead of taking m as mass of both blocks they take m to be the mass of the bottom block alone so they get an acceleration of 3.27m/s^2. Why are they doing this?