Missing something obvious in this derivation

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In summary, the conversation discusses a derivation for converting the kinetic energy of a two-body problem to a reduced mass system. The speaker is confused about the absence of a $$\mu^2$$ term when plugging values into the formula. However, it is explained that the mass terms are squared in the process and cancel out, resulting in a simple formula of ##\frac{m_1m_2}{m_1+m_2}##. The conversation concludes by emphasizing the importance of working out the algebra instead of trying to imagine the solution.
  • #1
TheCanadian
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Hi,

I've attached a file displaying a derivation to make the kinetic energy of a two-body problem into a kinetic energy only involving the reduced mass. When plugging 8.3 into 8.1, I just don't quite see how this derivation makes sense. Shouldn't there be a $$ \mu^2$$ term? Since when squaring the absolute value of r1, aren't the mass terms also squared? If I'm not mistaken, it simply looks like the mass terms are not squared when plugging in 8.3 into 8.1.

I feel like I'm missing something painfully obvious here, so any help is appreciated!
 

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  • #2
TheCanadian said:
I feel like I'm missing something painfully obvious here,
Isn't it just a matter of dimensions? Why would you expect mass2 to come into the energy formula?
 
  • #3
There's a factor of ##m_1+m_2## that cancels against one of the factors in the denominator.
 
  • #4
TheCanadian said:
Since when squaring the absolute value of r1, aren't the mass terms also squared?
Yes, they are squared. But if you make the substitutions and work through the algebra, you just end up with ##\frac{m_1m_2}{m_1+m_2}##
 
  • #5
I agree with fzero.
 
  • #6
Right. Just put it down on paper, instead of imagining what will happen, and it comes out very easily.
 

FAQ: Missing something obvious in this derivation

Why did I miss something obvious in this derivation?

As a scientist, it is natural to overlook certain details or make mistakes in the process of conducting experiments and analyzing data. It is important to carefully review your work and have others review it as well to catch any potential errors or oversights.

How can I prevent myself from missing something obvious in future derivations?

To prevent missing something obvious, it is helpful to take breaks during the derivation process and come back to it with a fresh perspective. You can also try explaining your work to someone else to see if they can identify any mistakes or areas that need clarification.

Is it common for scientists to miss something obvious in their derivations?

Yes, it is common for scientists to make mistakes or overlook certain details in their derivations. This is why it is important to have a peer-review process and to constantly evaluate and improve upon your work.

How can I recognize if I have missed something obvious in my derivation?

If you have a feeling that something is not quite right or if your results do not match your expectations, it is possible that you have missed something obvious in your derivation. It is important to carefully check your work and seek feedback from others to identify any potential mistakes.

Will missing something obvious in this derivation affect the validity of my research?

It depends on the significance of the error or omission. If it is a minor detail, it may not greatly impact the overall validity of your research. However, if it is a major mistake, it is important to acknowledge and correct it in order to maintain the integrity of your work.

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