Why is my Atwood's Machine homework solution incorrect?

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The discussion centers on a student's Atwood's Machine homework solution, where they analyze the forces acting on three blocks of different masses. The student calculates the acceleration of the system using the net force equation and derives a value of 2.5 m/s². They also attempt to find the tension forces acting on the blocks, concluding with a tension of -49 N for one block and 12 N for another. Despite their calculations, the student expresses uncertainty about the correctness of their solution. The thread highlights the complexities of applying Newton's laws in multi-block systems.
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Homework Statement



ok here's the problem in a picture

h t t p : / / i m g 1 9 2 . i m a g e s h a c k . u s / i m g 1 9 2 / 4 5 0 0 / c a p t u r e x x w . j p g



Homework Equations



Sigma F = ma
Fg = mg

The Attempt at a Solution



ok I called the 4 kg block m3 and the 2 kg block m2 and the 1 kg block m1

I don't see what is wrong with my work

a. net force on m3 = m3 a = Fg3 - Fg2 - Fg1

divide by m3 to get a

a = (Fg3 - Fg2 - Fg1)/m3

made it look nice

a = (m3 g - m2 g - m1 g)/m3
= g - (m2g)/m3 - (m1 g)/m3
= g(1 - m2/m3 - m1/m3)
=9.8(1 - 2/4 - 1/4) = 2.5 m/s^2

b. net force on m3 = m3 a = Fg3 - Ft3
solved for the force of tension
Ft3 = -m3(a+g) = -4.0(2.5+9.8)= - 49 N

c. Net force m1 = m1 a = -Fg1 + Ft1
solved for Ft1
Ft1 = m1 (a+g) = 1.0(2.5 + 9.8) = 12 N
 
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i think i got it nevermind
 
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