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Is this just a coincidence or something more?

themohawkninja
Posts: 816
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10/25/2013 8:18:51 PM
Posted: 3 years ago
In my algebra class today, my teacher was putting up real life examples of variable relations to show the application of the subject (the subject being the relationships between variables), and she was geeking out as she explained how to different equations in physics, that explain to different things use the same relationships.

These being:

F=(kqQ)/d^2
and
F=(GMm)/r^2

As I stated earlier, she was geeking out over the fact that (constant values aside) these were basically the exact same equation, so what I am wondering is: Is this just a neat coincidence, or is there a real reason for this? Being both force equations, I have a feeling that you can "simplify" them to F=MA, but I wouldn't know how.
"Morals are simply a limit to man's potential."~Myself

Political correctness is like saying you can't have a steak, because a baby can't eat one ~Unknown
themohawkninja
Posts: 816
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10/25/2013 8:26:46 PM
Posted: 3 years ago
I used the wrong "to"... I really need to get into the habit of manually checking my spelling, instead of just relying on red squiggly lines.
"Morals are simply a limit to man's potential."~Myself

Political correctness is like saying you can't have a steak, because a baby can't eat one ~Unknown
Poetaster
Posts: 587
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10/25/2013 9:04:05 PM
Posted: 3 years ago
The classical electromagnetic and gravitational fields are both vector fields which spherically radiate from an ideal point source (a point charge in the former case; a point mass in the latter). Similar regions of area on two spheres are in the same proportion as their squared radii, so the magnitude of a spherically radiated vector field will drop off according to the squared distance (the "radius") from the source. In other words, it decreases with the inverse square of distance (1/d^2).

Many other phenomena can be modeled by an inverse square law; the brightness of an ideal light source drops off according to the inverse square of the distance from the light source.
"The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker
Poetaster
Posts: 587
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10/25/2013 9:08:08 PM
Posted: 3 years ago
There are more concise reasons for this equation parallelism between gravity and electricity, but these might be less helpful here; I would just recommend looking into the idea of an "inverse square law" for the most explanatory generality.
"The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker