Free-Body Diagrams: Several Objects and Newton's Third Law

AI Thread Summary
The discussion revolves around solving a physics problem involving a system of boxes connected by strings and pulleys. The main tasks are to find the acceleration of each box and the tension in the strings after the system is released. The user initially struggles with the equations of motion and the signs in the tension equations, particularly for T1. After some reflection, they realize that reversing the signs in their T1 equation might resolve their confusion regarding the direction of forces. The user seeks clarification on how to properly account for the weight directions of the masses to achieve the correct solution.
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Homework Statement


A box of mass m2=3.5 kg rests on a frictionless horizontal shelf and is attached by strings to bodes of masses m1 = 1.5 kg and m3 = 2.5kg. Both pulleys are frictionless and massless. The system is released from rest. After it is released, find (A) the acceleration of each of the boxes, and (B) the tension in each string.
T1=M1*g-M1*accel
T2=M2*g-M3g-M3*accel
Fn=M2*G
-T1+T2 = M3*accel

Homework Equations


Summation of Force in the x direction = m * acceleration. I set up three of these equations one for each object. I also set up the equation summation of force in the y direction = m * acceleration for m2 on a horizontal shelf.

The Attempt at a Solution


I have attempted to find ways of plugging the different equations into the other equations to produce the acceleration, but have failed to get the answer the textbook gets. Which is 1.3.
 
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I figured it out. My T1 equation has reversed signs! Silly me. Thanks!
 
Actually I cannot figure out where I went wrong on the T1 equation to mess up the signs. Do I need to acknowledge that M1 will be the weight going up and M3 will be in the downward direction? I think that will give me the correct signs for T1? I am a little confused I must admit.
 
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