Why is my Atwood's Machine homework solution incorrect?

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SUMMARY

The discussion centers on the incorrect solution to an Atwood's Machine problem involving three blocks with masses of 4 kg (m3), 2 kg (m2), and 1 kg (m1). The user calculated the acceleration (a) as 2.5 m/s² using the formula a = (Fg3 - Fg2 - Fg1)/m3, leading to a tension force (Ft3) of -49 N for the 4 kg block. However, the user expressed uncertainty about the tension force (Ft1) for the 1 kg block, calculated as 12 N. The calculations need verification for accuracy in the context of Newton's second law.

PREREQUISITES
  • Understanding of Newton's laws of motion, particularly Sigma F = ma.
  • Familiarity with gravitational force calculations, Fg = mg.
  • Basic knowledge of Atwood's Machine mechanics.
  • Ability to manipulate algebraic equations for solving physics problems.
NEXT STEPS
  • Review the principles of Atwood's Machine dynamics.
  • Study the application of Newton's second law in multi-body systems.
  • Learn how to derive tension forces in pulley systems.
  • Practice similar problems involving different mass configurations in Atwood's Machines.
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Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators looking for examples of common mistakes in solving Atwood's Machine problems.

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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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