Finding rope tension and acceleration between two objects

[Curtis]

Homework Statement

"Block A has mass m_a=4.0kg, and block B has mass m_b=2.0kg. The coefficient of kinetic friction between block B and the horizontal plane is μ_k=0.50. The inclined plane is frictionless and at angle θ=30°. The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass. Find (a) the tension in the cord and (b) the magnitude of the acceleration of the blocks.

Rough drawing:

Homework Equations

F_N=mgcosθ
f_k=μ_kF_n
T=mg+ma
F_N=mg+ma_y
-f_k=ma_x

The Attempt at a Solution

Well, the first thing I did was find the force acting on the pulley from the 4kg block, which I found to be 33.948N. Then, I found the kinetic friction force of the flat surface underneath the 2kg block, for which I got 9.8N. After this, I'm just completely stuck. Everything I've read about tension requires acceleration. Anyway, I tried both adding and subtracting the kinetic friction from the 4kg block's force, then dividing by 2kg. I checked the answer in the back of the book, which turned out to be 13N and 1.6m/s² for (b), neither of which I reached through any combination of equations.

I figured that the tension is supposed to be found first though, given the order of the problems. I did mess around trying to find the acceleration a little, using -f_k=ma_x, but I didn't get further than that (if that even is in the right direction).

I really just had no idea what to do with this. I've read through the chapter and browsed the internet for no less than three hours trying to figure out something and my brain's to the point of feeling like jelly. Any help would be greatly appreciated, even just a push in the right direction.

 

[PhanthomJay]

Homework Statement

"Block A has mass m_a=4.0kg, and block B has mass m_b=2.0kg. The coefficient of kinetic friction between block B and the horizontal plane is μ_k=0.50. The inclined plane is frictionless and at angle θ=30°. The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass. Find (a) the tension in the cord and (b) the magnitude of the acceleration.

Homework Equations

F_N=mgcosθ

For block A

f_k=μ_kF_n

For block B

T=mg+ma

where did this come from?

-f_k=ma_x

.No,

The Attempt at a Solution

Well, the first thing I did was find the force acting on the pulley from the 4kg block, which I found to be 33.948N. Then, I found the kinetic friction force of the flat surface underneath the 2kg block, for which I got 9.8N. After this, I'm just completely stuck. Everything I've read about tension requires acceleration. Anyway, I tried both adding and subtracting the kinetic friction from the 4kg block's force, then dividing by 2kg. I checked the answer in the back of the book, which turned out to be 13N and 1.6m/s² for (b), neither of which I reached through any combination of equations.

I figured that the tension is supposed to be found first though, given the order of the problems. I did mess around trying to find the acceleration a little, using -f_k=ma_x, but I didn't get further than that (if that even is in the

You must use free body diagrams for each block when solving these problems. Isolate each block and show the forces acting on them. For block A , for example, the component of its weight acts down the plane, and the tension force acts up the plane. Write tthe equstion that comes from Newtons 2nd law. Do the same for the other block . You get 2 equations and 2 unknowns which you can solve.
.

 

[Simon Bridge]

What he said.
I just want to add that the first thing you do is draw a free-body diagram for each block separately. You appear to be trying to think about the interactions between components - don't.