What is the Symbolic Solution to the Acceleration Problem of Two Blocks?

[rey242]

Homework Statement

When force F(force is at an angle Theda) is not too large, box m1(smaller top box) moves with box m2(bigger bottom box) without sliding. Find the magnitude of the acceleration of the two blocks.(see attachment)

Homework Equations

F=ma

The Attempt at a Solution

This is from a test that I took and I just wanted to make sure to see if I really did this wrong. The test is all symbolic, by the way.
Fcos(x)-F(friction kinetic)=(m1+m2)a (this is the system equation for the right-left direction)
F(normal)-(m1+m2)g=0 (this is the system equation for the up-down direction)
F(friction kinetic)=F(normal)*(coefficient of kinetic friction)

In order to figure out the acceleration, I got acceleration by itself and plugged in the 3rd equation into F(friction) in the first equation.
Fcos(x)-F(normal)*(coeff.)=(m1+m2)a

Then I used the second equation and replace the force normal:

Fcos(x)-(m1+m2)g*(coeff)=(m1+m2)a

Then after some math, I got this:

Fcos(x)=(m1+m2)a+(m1+m2)g(coeff)
(Fcos(x)/(m1+m2))=a+g(coeff)
(Fcos(x)/(m1+m2))-g(coeff)=a

So can anyone double check this to see if this works out or if the professor is right and this is totally wrong?

 

[LowlyPion]

F(normal)-(m1+m2)g=0 (this is the system equation for the up-down direction)

This equation is not correct. If should be ...

F_n = (m1 + m2)*g + F*sinθ

Which means that

F_fr = μ_k*((m1 + m2)*g + F*sinθ)

etc.

 

[rey242]

oh wow that explains a lot thanks!