Solving a 2-Mass System Connected by a Rope

[raptik]

Homework Statement

Two masses M₁ = .600kg and M₂ = 2.2kg connected by a cord of negligible mass and passes over a frictionless pulley of negligible mass. Assuming that y-axis has a positive upward direction, what is the tension in the cord?

Homework Equations

F = ma

W = mg

The Attempt at a Solution

I first tried to add up the F_g for both masses under the assumption that the opposing force would be the tension.

I then subtracted the larger F_g from the smaller F_g which was also wrong.

I then came upon https://www.physicsforums.com/showthread.php?t=201258" and tried to follow the process discussed there. I tried to solve for a based on the posts discussed in the other thread but was lost on posts 9 and 10 (NEwayz, back to what I did).

I found the equations of the two blocks to be T - m₁g = m₁a and m₂g - T = m₂a.
this makes T = m₁a + m₁g = m₂g - m₂a.
Plugging in the numbers gives 5.88N + .6a = 21.56N - 2.2a
solving for a gives a = 5.6ms^-2
Plugging this back into the T equation gives a T of 9.24N
I then double the T because there is T working on both ends of the rope and get 18.48N.
I turns out that this is an incorrect answer and I am now out of ideas. Please help.

 

[hage567]

You don't double T. The tension T is acting throughout the rope. It isn't T on one side and T on the other giving 2T total.