Help manipulating a Physics equation

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In summary, the conversation discusses a physics textbook example where an equation is manipulated to equal a different form. The approach involves making a single fraction and dividing both numerator and denominator by a factor, resulting in the equation T=mg/(1+2m/M). The conversation also addresses the importance of using brackets in the correct places.
  • #1
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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  • #2
The approach is good so far. Make a single fraction out of it, then divide both numerator and denominator by M/(2m).
 
  • #3
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?
 
  • #4
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?
 
  • #5
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.
 
  • #6
Looks fine.
Brackets around 2m denominatiors would have been more important than the other brackets by the way.
 

FAQ: Help manipulating a Physics equation

How do I rearrange a physics equation?

Rearranging a physics equation is done by manipulating the variables and constants on both sides of the equation. The goal is to isolate the variable that you are solving for on one side of the equation. This can be done by using algebraic operations such as addition, subtraction, multiplication, and division.

What is the purpose of manipulating a physics equation?

The purpose of manipulating a physics equation is to solve for a specific variable or to simplify the equation for easier understanding and analysis. Rearranging an equation can also help in making predictions or determining the relationship between different variables.

Are there any rules for manipulating a physics equation?

Yes, there are rules that must be followed when manipulating a physics equation. These include keeping the equation balanced by performing the same operation on both sides, using the correct order of operations, and being careful with negative signs and exponents.

How can I check if my manipulated equation is correct?

You can check the accuracy of your manipulated equation by plugging in values for the variables and seeing if the equation holds true. Another method is to compare your manipulated equation with the original equation and make sure they are equivalent.

Are there any tips for effectively manipulating a physics equation?

One tip for effectively manipulating a physics equation is to clearly define the variable you are solving for and to keep track of the operations you perform on both sides of the equation. Another tip is to practice and familiarize yourself with common algebraic operations and equations in physics. Using a systematic approach can also help in avoiding mistakes and making the process smoother.

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