Help manipulating a Physics equation

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Discussion Overview

The discussion revolves around manipulating a physics equation related to tension (T) in a system involving mass (m) and another mass (M). Participants are attempting to derive a specific form of the equation from a given expression, focusing on algebraic manipulation and simplification techniques.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents an equation and expresses uncertainty about how to manipulate it to reach the desired form.
  • Another participant suggests making a single fraction and dividing both the numerator and denominator by M/(2m) as a potential approach.
  • A participant acknowledges missing parentheses in their initial attempt and revises the equation, questioning whether this changes the approach needed.
  • One participant describes their process of combining fractions and simplifying, asking for confirmation on the correctness of their steps.
  • Another participant comments on the simplicity of the algebra involved, suggesting it is not particularly challenging.
  • A later reply notes the importance of proper bracket placement in the equation for clarity.

Areas of Agreement / Disagreement

Participants generally agree on the algebraic approach to manipulating the equation, but there are variations in the specific steps taken and some uncertainty about the correctness of those steps. No consensus is reached on a definitive solution.

Contextual Notes

Some participants mention missing parentheses and the importance of proper bracket placement, indicating potential ambiguities in the expressions used. The discussion does not resolve these issues.

Michael Barilla
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I'm reading my physics textbook and the example has an equation of...

mg-m(g/(1+M/2m)) = T

manipulated so that it equals...

T = mg/(1+2m/M)

I'm not sure how to get this I tried to distribute the m to get...

mg - mg/(1+M/2m)

and multiplying mg by ((1+M/2m)/(1+M/2m)) but could not get the result the book got.
 
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The approach is good so far. Make a single fraction out of it, then divide both numerator and denominator by M/(2m).
 
It seems i missed some parentheses; it should be...

mg - m(g/(1+(M/2m))) = T*

T = mg/(1+(2m/M))*

And...

mg - mg/(1+(M/2m))

respectively

Does that change the approach?
 
mfb said:
The approach is good so far. Make a single fraction out of it, then divide both numerator and denominator by M/(2m).

I made into one single fraction of...

(mg + (Mmg/2m) - mg)/(1+(M/2m))

canceled out the mg's and multiplied the top by the reciprocal of the bottom...

Mmg/2m x 1/(1+(M/2m)) = Mmg/(2m +2Mm/2m)

Took out M from the denominator...

Mmg/(M(2m/M+1)

Which is equal to...

mg/(1+(2m/M))

Did i do this correctly?
 
Michael Barilla said:
I'm reading my physics textbook and the example has an equation of...

mg-m(g/(1+M/2m)) = T

manipulated so that it equals...

T = mg/(1+2m/M)

I'm not sure how to get this I tried to distribute the m to get...

mg - mg/(1+M/2m)

and multiplying mg by ((1+M/2m)/(1+M/2m)) but could not get the result the book got.
Only looked briefly - did not read it;
Mere basic algebra. Nothing tough and nothing unusual.
 
Looks fine.
Brackets around 2m denominatiors would have been more important than the other brackets by the way.
 

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