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

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SUMMARY

The discussion focuses on solving a physics problem involving three masses (m1 = 1.5 kg, m2 = 3.5 kg, m3 = 2.5 kg) connected by strings over frictionless pulleys. The main objectives are to determine the acceleration of the boxes and the tension in each string after the system is released from rest. The correct acceleration is established as 1.3 m/s², with the tension equations needing careful attention to sign conventions. The user identified an error in the T1 equation related to the direction of forces acting on the masses.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Familiarity with free-body diagrams
  • Knowledge of tension in strings and forces in equilibrium
  • Basic algebra for solving equations
NEXT STEPS
  • Review Newton's Second Law and its application in multi-body systems
  • Practice drawing and analyzing free-body diagrams for various configurations
  • Study the effects of frictionless surfaces on tension and acceleration
  • Explore common mistakes in sign conventions when applying force equations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators looking for examples of problem-solving techniques in multi-object systems.

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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.
 
Last edited:
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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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