Tension problem, finding acceleration with kinetic friction

[p0ps1c1e]

Three blocks are connected as shown in the uploaded picture. The strings and friction-less pulleys have negligible masses, and the coefficient of kinetic friction between the 2.0 kg block and the table is 0.17. What is the acceleration of the 2.0 kg block?

Homework Equations

∑F = ma

The Attempt at a Solution

So i wrote 3 Newton equations:

-μ_k-T₁+T₂ = m₂a

T₁-m₁g = m₁a

T₂-m₃g = m₃a

Putting them together I got:

-μ_km₂g - m₁g + m₃g = a(m₂ + m₁ - m₃)


and then tried to solve for acceleration. Problem is every time I do it I end up with a 0 in the denominator so I don't know if I'm doing something wrong conceptually or if I am just messing up in my algebra. I'm also not sure if all three of the blocks have the same acceleration. I would think so since they are all on a string.

 

[Simon Bridge]

Your equation do not match your drawing... but I think I can figure it out.
m1=1kg, m2=2kg and m3=3kg right?

The first equation is incorrect - what is the equation governing friction?
The last equation is inconsistent with the first two - check the direction for positive acceleration.

 

[p0ps1c1e]

Oh derp... haha. Thanks.

I'm looking through my old exams and I'm finding so many little mistakes like that.