Is This the Solution? A Review of Dynamics Pushing Blocks with Visuals

[alingy1]

Please look at pictures.
Weirdly, my textbook does not give the answer to this question.

Can you check my answer? Sorry for the really bad writing. If you ask, I can more clearly write it.

 

[haruspex]

The handwriting is decipherable, but it's hard to follow what you are doing because it's not clear which equations relate to which FBD.
Please post your working by typing - it's not hard - making it clear which forces relate to which body.
Click on the Go Advanced button. You can pick ∑ off the quick symbols on the right and superscript and subscript from the X², X₂ icons along the top.

 

[alingy1]

Here goes nothing!
For m1:
∑Fy=N₁-m₁g-sin(30)F=0
∑Fx=-N₂₁-f_k+cos(30)F=m₁a

For m2:
∑Fx=-μ_km₂g+N₁₂=m₂a
∑Fy=N₂-m₂g=0

Add both ∑Fx equations:
-μ_km₁g-μ_km₂g+cos(30)F=(m₁+m₂)a

a=1.41 m/s^2
N₁₂=N₂₁=11.52N

That looks great! How about the physics?

 

[haruspex]

You've missed something out. Write out the equations relating N₁, F, f_k.

 

[alingy1]

I do not understand. Can you be more specific? What is it I am missing? I've been looking at the problem long enough that everything seems good.

 

[alingy1]

Got it. I mixed up the fk equation. I'm fixing it now and posting the new solution.

 

[alingy1]

Here goes nothing!
For m1:
∑Fy=N₁-m₁g-sin(30)F=0
∑Fx=-N₂₁-f_k+cos(30)F=m₁a

For m2:
∑Fx=-μ_km₂g+N₁₂=m₂a
∑Fy=N₂-m₂g=0

Add both ∑Fx equations:
-μ_km₁g-μ_km₂g+cos(30)F=(m₁+m₂)a

a=1.41 m/s^2
N₁₂=N₂₁=11.52N

That looks great! How about the physics?

Here is my new equation:

μ_k(sin(30)F+m₁g)-μ_km₂g+cos30F=(m₁+m₂)a

a=1.16 m/s^2
N₁₂=N₂₁=10.52 N

 

[Nathanael]

Here is my new equation:

μ_k(sin(30)F+m₁g)-μ_km₂g+cos30F=(m₁+m₂)a

a=1.16 m/s^2
N₁₂=N₂₁=10.52 N

Those answers are correct (and if they're not, we made the same mistakes hahah)

Except for the rounding, if you rounded a to 2 decimals it would actually go up to 1.17 but that's pedantic, your equation is correct.



edit: Actually, there should be a negative sign in very the beginning of your first equation, but you must have just forgotten to type that, because your answer is correct.

 

[alingy1]

Yes, I did forget the minus! I hope someone else confirms! At least we are two ;)

 

[haruspex]

I hope someone else confirms! At least we are two ;)

Make that three.