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A physics teacher saw the following in a student's work:

$f=\mu n$

$Pa=\frac{n}{m^2}$

$T=\frac{n}{am}$

The teacher realized the student's capitalization was correct. What are these equations used for?

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    $\begingroup$ Did you just turn this comment into a puzzle? :) $\endgroup$ – Riley Aug 4 '18 at 17:33
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    $\begingroup$ To show the importance of Bass's comment. $\endgroup$ – Tom Aug 4 '18 at 17:39
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    $\begingroup$ The last two are 'units' equations, with time in seconds given as $N/kgms^{-2}$. Not sure how friction, pressure and time are related though... $\endgroup$ – TheSimpliFire Aug 5 '18 at 9:21
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    $\begingroup$ All have "n". And the teacher said All Caps are OK $\endgroup$ – DEEM Aug 5 '18 at 10:10
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Thanks to Oehm for help formatting!

Very cool question!

Answer:

They are equations for unit prefixes

Line1:

$ f = \mu n$, $f$(femto), $\mu$(micro), $n$(nano),
$f = 10^{-15}$, $\mu = 10^{-6}$, $n = 10^{-9}$, $\mu n = 10^{-15}$ thus, $f = \mu n$

Line 2:

$Pa=\frac{n}{m^2}$, $P$(peta), $n$(nano), $m$(milli),
$Pa = 10^{15} 10^{-18} = 10^{-3}$, $\frac{n}{m^2} = \frac{10^{-9}}{(10^{-3})^2} = 10^{-3}$, thus $Pa=\frac{n}{m^2}$

Line 3:

$T=\frac{n}{am}$, $T$(tera), $n$(nano), $a$(atto), $m$(milli),
$T=10^{12}$, $\frac{n}{am} = \frac{10^{-9}}{10^{-18}10^{-3}} = 10^{12}$, thus $T=\frac{n}{am}$

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    $\begingroup$ Good find. Multi-line/-paragraph spoilers are a bit tricky. You have to prefix each line of the block with >! and you must introduce line breaks manually with the <br /> tag ior with two or more spaces at the end of a line. But I think that the current markup with a spoiler block for each formula is fine. $\endgroup$ – M Oehm Aug 5 '18 at 18:46
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Well, I guess it should be me to get things started with a partial answer identifying the more famous equations these are not:

$f=\mu n$ is not

$F=\mu N$, the formula for kinetic friction, where

$F$ is the magnitude of the force caused by friction
$\mu$ is the coefficient of friction, and
$N$ is the magnitude of the normal force.

$Pa=\frac{n}{m^2}$ is not

$Pa=\frac{N}{m^2}$, the definition of a pascal (the SI unit of pressure) as being one newton per square meter.

$T=\frac{n}{am}$ is not

$T=\frac{N}{Am}$, the definition of a tesla (the SI unit of magnetic flux density) as being one newton divided by an ampere-metre.

(In all of the above non-answers, notice how the puzzle topic has forced me to painstakingly write all the scientists' names without a capital letter, because that's how you are supposed to do it when those names are used as units.)

The actual purpose of the equations coming up as soon as I figure them out :-)
(Probably better not to start holding your breath though..)

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