Applying Newton's Laws and solving multiple object system question

[Allen93]

Homework Statement

A 3.00-KG mass and a 10.0-KG mass are attached to opposite ends of a massless cord which is strung over a frictinoless pulley.
a) What is the acceleration of the two-mass system?
b) What is the tension in the cord?

Homework Equations

F = net forces
Fg = force due to gravity
a = acceleration
m = mass
* = times (multiply)
g = gravity

Fg = m*g
F = ma

The Attempt at a Solution

I tried to draw a free body diagram of the two objects as one system, subtracting the least massive object from the most massive object (10 kg minus 3 kg). I then found the Fg of the system and used it to find the acceleration, then found the tension force using the acceleration found. According to the answer key, I am off, could anyone please show me the light?

 

[Sourabh N]

Once you draw the free body diagram, write down force equation (net force = mass*acceleration) for each of the bodies, separately. Then you can solve for acceleration.

 

[cupid.callin]

Welcome to PF

please can you post your FBD's?

just a rough drawing will work

 

[Sourabh N]

The setup is called an atwood machine. Fairly standard. Here's an http://www.staff.amu.edu.pl/~romangoc/graphics/M3/7-atwood-machine/M3-7-fig1.gif" off google.

 

[cupid.callin]

i know what is atwood machine and i understood he ques.

i just want to make sure that is FBD's are right

 

[Sourabh N]

Ahh I'm sorry, I thought it's the OP asking for FBD. :zzz:

 

[Allen93]

Welcome to PF

please can you post your FBD's?

just a rough drawing will work

I apologize for replying so late but here's the FBD.

 

[Allen93]

Once you draw the free body diagram, write down force equation (net force = mass*acceleration) for each of the bodies, separately. Then you can solve for acceleration.

Thank you!
I reworked the problem and set it up your way and I found the correct solution.
Thank you guys, it was really helpful.