Equilibrium Pulley Tension Problem

[livewire852]

Hello! I've been trying to understand this one for a while now, and think there might be a general mental block with regards to pulleys, tension etc.

Homework Statement

http://s3.photobucket.com/albums/y5...tions/?action=view&current=pulleyquestion.jpg
Question: "The system is in equilibrium and the pulleys are weightless and frictionless. The acceleration of gravity is 9.8 m/s^2. Find the tension T. Answer in units of N."

Homework Equations

w=mg?
Not really sure about these

The Attempt at a Solution

Right, so so far I've tried solving for T2 and T3 separately then solving the big T. Since the pulley on the right has only the 14N mass acting on it, then T2 should be 14N/2, or 7N right? Then for the second pulley on the left, I got
T3 + T2 - 19 = 0, which would make T3 = 12. Presumably this would make T = 24 N, but this isn't correct!
I imagine I am making some heinous oversight or massive assumption. Thanks in advance!

 

[PhanthomJay]

Hello! I've been trying to understand this one for a while now, and think there might be a general mental block with regards to pulleys, tension etc.

Homework Statement

http://s3.photobucket.com/albums/y5...tions/?action=view&current=pulleyquestion.jpg
Question: "The system is in equilibrium and the pulleys are weightless and frictionless. The acceleration of gravity is 9.8 m/s^2. Find the tension T. Answer in units of N."

Homework Equations

w=mg?
Not really sure about these

The Attempt at a Solution

Right, so so far I've tried solving for T2 and T3 separately then solving the big T. Since the pulley on the right has only the 14N mass acting on it, then T2 should be 14N/2, or 7N right?

right!

Then for the second pulley on the left, I got
T3 + T2 - 19 = 0, which would make T3 = 12. Presumably this would make T = 24 N, but this isn't correct!

Tension forces always pull away from the objects on which they act. Correct your error in signage.