I Help manipulating a Physics equation

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The discussion centers on manipulating the physics equation mg - m(g/(1+M/2m)) = T to arrive at T = mg/(1+2m/M). Participants suggest making a single fraction and dividing both the numerator and denominator by M/(2m) to simplify the equation. One user successfully combines terms and cancels out variables, ultimately confirming the manipulation leads to the desired result. The importance of proper parentheses placement in the equation is also highlighted for clarity. Overall, the algebraic approach is deemed straightforward and correct.
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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