Free body diagrams for boxes, inclined planes and springs

[Like Tony Stark]

Homework Statement

FIRST PICTURE
The body $A$ has a mass of $6 kg$. It lies on the body $B$ which has a mass of $14 kg$. There is no friction between these two bodies. Draw the free body diagram for both of them

SECOND PICTURE
A body $A$ of $m=9.2 kg$ slides down a body $B$ of $m=17 kg$. $B$ doesn't move because of the force applied by the spring, which suffers a deformation of $9 cm$. The friction between the two bodies is negligible. Draw the free body diagrams, determine the acceleration of $A$ with respect to $B$ and the elastic constant of the spring.

Relevant Equations

$W=m.g$
$W_x=m.sin(\alpha)$
$W_y=m.cos(\alpha)$
$F_e=-k \Delta x$

FIRST PICTURE
I have some doubts here because of the spring... I'll tell you what forces I've drawn. For $A$, I drew the weight and the force applied by $B$ (the normal force) on the vertical axis; and the elastic force pointing to the right on the horizontal axis.
For $B$, I drew the weight, the normal force and the force applied by $A$ on the vertical axis; on the horizontal axis I drew the force $F$ showed in the picture.
Is this correct? Because I don't know if the spring applies a force on $B$, and in that case, I don't know what its direction would be.

SECOND PICTURE
For $A$, if I take a coordinate system where the normal force is aligned with the vertical axis, I have the normal force and vertical component of the weight in the $Y$ axis and the horizontal component of the weight on the $X$ axis.
For $B$, we have the normal force and the weight on the vertical axis; and the elastic force on the horizontal axis.

But I don't know what should I do with the data from $B$, the spring doesn't affect $A$, does it? Also, if there is no friction, shouldn't $B$ be moving to the left?

 

[rmwhitehill7918]

I believe that your thinking for the first picture is correct. Obviously, gravity must be acting upon both of the objects, and likewise, since both $A$ and $B$ are resting on surfaces, they must be experiencing some normal force. Now, we know from the figure that $F$ is applied to $B$, which causes a spring force on $A$. Now, from Newton's Third Law, we know that if the spring pushes on $A$ then $A$ must push back on the spring, and since the spring is attached to $B$, the spring must exert a force onto it.

For the second problem, since $B$ exerts a normal force on $A$, then $A$ must exert an equal and opposite force on $B$, so the deformation of the spring due to the force of $B$ is related to the force that $A$ exerts on $B$. So if you include this new force in your equations, you should be able to use the data provided to calculate the desired values with those new equations.