How Do Newtonian Forces Affect the Interaction Between Two Blocks?

[Nicolaus]

Homework Statement

Block B (1kg) is held in contact with block A (3kg). When block B is let go, A is pushed to the right with a force of 160N. Static friction is .50 between the 2 blocks.
Block A pushes on B such that B is not touching the surface upon which A is moving on. It's held in the air with only the normal force from A supporting it.
Find the force of friction on Block B, the normal force exerted by A on B, and vertical force exerted by B on A.

Homework Equations

Newtonian forces of friction, gravity, etc

The Attempt at a Solution

For the Normal force of A on B:
to find a: Fnet = 160N = m(A+B)a --> a = 160/4 = 40m/s^2
mAa = F - F(BonA)
FBonA = 160 - (3x40) = 40N = FAonB from Third Law

For Force of Friction on B: Since friction would be working against gravity and there is no vertical motion, wouldn't the force of friction be mBg, its weight?
The Max Ff would be Ff=μN = .50(40)=20N.
Not sure about the vertical force of B on A.

 

[Simon Bridge]

For Force of Friction on B: Since friction would be working against gravity and there is no vertical motion, wouldn't the force of friction be mBg, its weight?

How can friction oppose gravity - isn;t this the normal force or did you leave out part of the description?