2 blocks on top of each other, applied force, friction, and tension

[TFOrange]

Homework Statement

A 4.32 kg block is placed on top of a 9.16 kg
block. A horizontal force of F = 66.6 N is
applied to the 9.16 kg block, and the 4.32 kg
block is tied to the wall. The coefficient of
kinetic friction between all moving surfaces
is 0.169. There is friction both between the
masses and between the 9.16 kg block and the
ground.
The acceleration of gravity is 9.8 m/s^2.
Determine Tension of string in N

(see image)

Homework Equations

ƩF = ma
f_s = μ_k*F_N

The Attempt at a Solution

(see attachment for free body diagrams)
ƩF = ma
m = 4.32 kg
a_{top block} = 0
ƩF = F_applied - f_k - T
0 = (44.274) - (7.155) - T
T = 44.274 - 7.155
T = 37.119

Apparently I did something wrong somewhere, but I'm not sure where.

 

[Doc Al]

What forces act on the upper block? (I don't understand your FBDs.)

 

[TFOrange]

Well maybe it isn't supposed to be there, but I was thinking that since the bottom block has a force in that direction that is not completely canceled out by friction, it would cause the top block to have a force as well, which is equal to F_{applied (to the bottom block)} - f_k

 

[Doc Al]

Well maybe it isn't supposed to be there, but I was thinking that since the bottom block has a force in that direction that is not completely canceled out by friction, it would cause the top block to have a force as well, which is equal to F_{applied (to the bottom block)} - f_k

That applied force acts on the bottom block, not on the top block. So it doesn't belong in your analysis of the top block. The only influence that the bottom block exerts on the top block is through the normal force and friction.

 

[TFOrange]

Oh! so T = f
and so it's T = 7.155
Thanks!

 

[Doc Al]

Oh! so T = f
and so it's T = 7.155

Yep!