How Does Friction Affect Motion in AP Physics Problems?

[dwangus]

AP Physics Question about friction?

Homework Statement

Please explain everything through... I'm so lost :(
Mass B is on top of Mass A which is on top of the floor.
B=2kg, A=4kg, gravity assumed to be 10m/s^2
Coefficient of friction between B and A is 0.2 kinetic, 0.4 static
Coefficient between A and the floor is 0.
A force is solely being applied to B.
1. Make a FBD of each of the two masses!
2. Max force that will allow them to move as one?
3. Acceleration of each mass if F = 40N?
4. Acceleration of each mass if the coefficient of friction (static and kinetic) between the floor and A is 0.2?
Questions 5-7 is assumed that a force is solely being applied to A.
5. Max force that will allow them to move as one?
6. Acceleration of each mass if F = 40N
7. What is the acceleration of each mass if the coefficients between A and the floor is 0.2?
Questions 8-11 is assumed the same, with the force solely being applied to A, but the static and kinetic friction is 0.4 and 0.3 respectively between all surfaces.
8. Biggest Force that will allow them to move as one?
9. Magnitude and direction of force of friction on each mass in #8?
10. Acceleration of each mass if the force is 10N? 30N? 60N?
11. Magnitude and direction of force of friction on each mass in #10 in each case?

I'm sure that by answering a couple of them I'll understand the rest, but I don't know how to get started... everytime I attempt this, I always get the wrong answer...

Homework Equations

F=MA
Friction=μk/s x Fn
mass of A/mass of B = acceleration of B/ acceleration of A
?

The Attempt at a Solution

I really don't know...

 

[Simon Bridge]

I don't like subscripts and I don't like putting numbers into equations too early

lets say mass B has value m and mass A have value M.
lets make gravity = g ... so the weights are mg and Mg respectively.
the floor is frictionless.
friction can be μ until we know what kind it is - then I'll just have to live with a subscript.

A horizontal force is applied to B - call it F.
There will be friction - call if little f so that f=μN ... it will help discussion to start with just f as friction.

Lets go one step at a time:

Step 1 says make a free-body diagram for the two masses.
OK: pick a direction to be positive, and put an arrow showing that on your diagram.

draw a box for mass B, alone, and put only the forces that are acting on it.
what are they and what are their directions?