A very simple question concerning the algebra of physics

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Homework Help Overview

The discussion revolves around algebraic manipulations in physics, specifically involving expressions related to energy, mass, and momentum. The original poster presents a substitution involving the expression \(\frac{Ec^2}{mv}\) and explores its implications.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the validity of substituting expressions in physics, particularly focusing on the relationship between energy, mass, and momentum. There is a consideration of whether the original poster's approach aligns with established principles.

Discussion Status

The conversation appears to be progressing with participants affirming the original poster's substitution approach. Some express curiosity about the implications of the substitution, while others confirm that substituting equal expressions is generally acceptable.

Contextual Notes

There is a mention of a specific context involving particles at a close distance and their momentum, which may influence the discussion but is not fully explored. The original poster's example is noted as being somewhat trivial, indicating a focus on understanding rather than deriving complex results.

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Suppose I had an expression, for the sake of this post

[tex]\frac{Ec^2}{mv}[/tex]

we know that [tex]c^2 = \frac{E}{m}[/tex] so can the above expression be substituted as

[tex]c^2 \frac{c^2}{v}[/tex]

Yes, yes, I know this result is very uninteresting, I was just making a quick example. Thank you!
 
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I ask this because some work I am following states that if two particles are really close separated at a distance R then the momentum is large proportional to

[tex]\frac{\hbar}{R}[/tex]

Then it says that using a substitution then in E=pc

[tex]E= \frac{\hbar c}{R}[/tex]

so in this sense, if you can do it that way, you can also do it my way, the reversed way in the OP, right?
 
help1please said:
Suppose I had an expression, for the sake of this post

[tex]\frac{Ec^2}{mv}[/tex]

we know that [tex]c^2 = \frac{E}{m}[/tex] so can the above expression be substituted as

[tex]c^2 \frac{c^2}{v}[/tex]

Yes, yes, I know this result is very uninteresting, I was just making a quick example. Thank you!

So far so good. Is that the whole question? You can always substitute equal for equals.
 
Thank you, that is all I wanted to know! :)
 

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