Moments Question (IWTSE.org) -- Three balances and two masses

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Homework Help Overview

The discussion revolves around a problem involving moments and balances, specifically focusing on the interaction between three balances and two masses. Participants are exploring the implications of mass assumptions and the application of the moments equation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the assumption of equal mass for the balances and whether to ignore their mass entirely. There are inquiries about calculating weights at different arms and the relevance of mechanical advantage. Some participants raise concerns about dimensional consistency in the expressions derived.

Discussion Status

The discussion is active, with participants providing guidance on assumptions regarding the mass of the beams and suggesting methods for checking dimensional consistency. There is no explicit consensus, but some productive directions have been offered regarding the approach to the problem.

Contextual Notes

Participants note the lack of information regarding the mass of the beams and the importance of including units in the calculations. There is an acknowledgment of potential algebraic errors in the original attempts.

TomK
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Homework Statement
Contraptions - Balances
Relevant Equations
Moments Equation
IWTSE (Contraptions, Balances).jpg
Balances Working 1.jpg
Balances Working 2.jpg


I think I have done this in an inefficient way. I assumed from the question that the three balances were of equal mass, though I'm not sure if I should have ignored their mass entirely. The correct answer is X = (62 + [2/9]) kg. Please help.
 
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Among the three balances, first think of the left one. How much weight is there at 1m arm for 10kg weight at 4m arm ? Then think of the right one how much weight is there at 3.5m arm for X kg weight at 3.5m arm ? With these two results think of the center balance.
 
TomK said:
Homework Statement:: Contraptions - Balances
Relevant Equations:: Moments Equation
I think I have done this in an inefficient way. I assumed from the question that the three balances were of equal mass, though I'm not sure if I should have ignored their mass entirely. The correct answer is X = (62 + [2/9]) kg. Please help.
Yes, you should take the beams as zero mass, otherwise you do not have enough information.
At the end you have an expression X(g-10/7). Because you have not included units throughout, I am not sure what this means, but it is dimensionally inconsistent. g is an acceleration; the 10/7 may or may not be dimensionless, but it is certainly not an acceleration.

Having arrived at clear proof of an algebraic error, I would apply 'binary chop': check an equation somewhere in the middle for dimensional consistency; if that is wrong, check one quarter of the way through, else check at the three quarters mark; etc.
 
For this specific problem, I would not bother with calculating the reaction forces at the three fulcrums.
Using mechanical advantage should be sufficient, if allowed.
 
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haruspex said:
Yes, you should take the beams as zero mass, otherwise you do not have enough information.
At the end you have an expression X(g-10/7). Because you have not included units throughout, I am not sure what this means, but it is dimensionally inconsistent. g is an acceleration; the 10/7 may or may not be dimensionless, but it is certainly not an acceleration.

Having arrived at clear proof of an algebraic error, I would apply 'binary chop': check an equation somewhere in the middle for dimensional consistency; if that is wrong, check one quarter of the way through, else check at the three quarters mark; etc.

Thank you for your advice. I redid the question, assuming the beams have zero mass, and I got the right answer.
 
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