Solve Tension in Three Blocks of Mass: m1, m2, m3

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SUMMARY

The discussion focuses on solving for the tensions T1 and T3 in a system of three blocks with masses m1 = 4 kg, m2 = 5 kg, and m3 = 8 kg connected by strings over ideal pulleys. The correct acceleration of the system is determined to be 2.31 m/s². The user initially misapplied the formula for tension, T = m(g - a), by incorrectly subtracting acceleration from gravitational force instead of adding them. After correcting this mistake, the user successfully calculated T1 and T3, with T1 being 7.5 N and T3 being 8 N.

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I have a couple questions that I can't figure out regarding the following question. The picture pertains to the question.

http://img81.imageshack.us/img81/8229/physnd4.jpg

Three blocks of mass m1 = 4 kg, m2 = 5 kg and m3 = 8 kg are connected by strings which pass over two ideal pulleys as shown in the figure below.

What is T1, the magnitude of the tension in the string that is connected to the block of mass m1?

and

What is T3, the magnitude of the tension in the string that is connected to the block of mass m3?

I found acceleration to be 2.31m/s^2 (and it was correct). I know Fnet = ma, but for whatever reason I am setting something up wrong for Fnet. I thought Fnet would be the force of gravity acting on the block + the force being pulled up (in the case of m1) or the block going downward (as in m3).

Any help would be appreciated.
 
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Try making a Free Body Diagram for the block in the middle. That will really help.
 
Ok, I figured it out, thanks. Basically for T1 what I was doing wrong in the equation T = m (g-a) was taking 9.81-2.31 instead of adding them together. Then I was able to figure out that T3 was 8 (9.81-2.31).
 

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