Calculating the Fourth Mass: A Rope and Four Masses

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SUMMARY

The discussion focuses on calculating the fourth mass (m4) in a system of four masses suspended by a rope. The derived formula for m4 is expressed as m4 = [m1T2/(T1 − T2)] − m2 − m3, utilizing the principles of force and tension. The participants emphasize the importance of visual aids, such as diagrams, for solving physics problems effectively. The conversation highlights the relationship between tension and mass in static equilibrium scenarios.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Knowledge of tension in ropes and static equilibrium
  • Familiarity with algebraic manipulation of equations
  • Ability to interpret and analyze physics diagrams
NEXT STEPS
  • Study the principles of static equilibrium in physics
  • Learn about tension forces in multi-mass systems
  • Explore algebraic techniques for solving equations involving multiple variables
  • Review examples of similar physics problems involving mass and tension
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Students studying physics, particularly those focusing on mechanics, as well as educators seeking to clarify concepts related to tension and mass calculations.

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Homework Statement


2. There are four masses hanging by a rope from the
ceiling, as shown in the figure. Two of the tensions
and three of the masses have been measured.
Show that the fourth mass can be expressed as
m4 =[m1T2/(T1 − T2)]− m2 − m3.



Homework Equations


F=ma, F1=-F2, T=ma


The Attempt at a Solution


I think that (m1+m2+m3+m4)g=T1 and (m2+m3+m4)g=T2
I tried solving for g and substituting and try and solve for m4 but I just find it impssible to do.
 
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We can't help you unless we see the figure that goes with this question.
 
I tried copying and pasting from a pdf file but it didn't work but it's really easy actually I already figured it out, :). Thanks anyways.
 

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