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

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SUMMARY

The discussion revolves around deriving a formula for mass m2 in terms of mass m1, acceleration a, and gravitational acceleration g in a two-mass system. Participants clarify the correct equations and concepts, emphasizing the need to isolate variables properly. The equation discussed is m1g = (m1 + m2)g - m2a, which leads to the conclusion that m2 can be expressed as m2 = (m1g - ma) / g. The importance of understanding forces and their directions in relation to mass and acceleration is highlighted throughout the conversation.

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  • Newton's Second Law of Motion (F=ma)
  • Understanding of gravitational force (weight = mg)
  • Basic algebra for isolating variables in equations
  • Concept of tension in a two-mass system
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  • #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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