Deriving Formula for m2 in Terms of m1, a, and g in a Two Mass System

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Homework Help Overview

The discussion revolves around deriving a formula for the mass m2 in terms of mass m1, acceleration a, and gravitational acceleration g in a two-mass system. The participants are exploring the dynamics of the system, which involves understanding the relationships between the masses and the forces acting on them.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to isolate variables in the equations presented, questioning the correctness of the equations and their algebraic manipulations. There are discussions about the roles of mass and weight, and how they relate to the forces in the system. Some participants are also clarifying the context of the problem, including the importance of diagrams and specific setups.

Discussion Status

The discussion is ongoing, with various interpretations of the problem being explored. Some participants have offered insights into the relationships between the variables, while others are still grappling with the algebraic steps needed to derive the formula. There is a recognition of the need for clarity regarding the equations and the physical setup.

Contextual Notes

Participants have noted the absence of a diagram that is crucial for understanding the problem. There are also mentions of specific homework constraints and the need to derive equations without numerical values, which adds to the complexity of the discussion.

  • #61
Oh, I was overcomplicating it again! We're literally just pulling it out of the equation, I let he subscript mess me up.

m2g-m2a=m1a
m2(g-a)=m1a

Better?
 
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  • #62
it is still not isolated (all by itself) ... it is still multiplying that difference ...
 
  • #63
Oh, right. Shoot. But was the step correct? Can I divide both sides by m2, yielding g-a=m1a/m2 ? Or would that not be considered solving for m2, since it's not on it's own side?
 
  • #64
collected it as common factor, good.
you want it on TOP, by itself ... not on bottom.
move the other factor, instead of m2 .
 
  • #65
Oh! Duh! m2=m1a/g-a ?
 
  • #66
keep the old parentheses, right? ok, done.

move on to the one with friction
 
  • #67
m2=m1a/(g-a)

Do you mean we're done here?
 
  • #68
well, look at 2 special cases first:
1) what m2 will make zero acceleration?
2) what m2 will make acceleration = 9.8 m/s² ?
 
  • #69
Lightgrav, I would really love to come back to these questions, but I have so many other problems this week that I can't justify spending the time on the extra questions that they deserve. Thanks so much for helping me with the problem! :smile: I will eventually come back to these if I have a moment.
 

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