[qimg]http://www.science27.com/images/img_17.jpg[/qimg]
Apologies for treating you like a student but:
I am an examiner for mathematics and physics
'Explain' means explain. You cannot cut and paste a graph. That explains nothing.
It may demonstrate or show visually a principle, but in itself, to a layman, it is not an explanation.
As I said before you are deliberately avoiding discussing the maths itself, I suspect (and forgive me if I am wrong), because you do not understand it.
For a proportionality like
the weight is proportional to the thing to the power of 4
I would explain it thusly
this means that if you double the thing, the weight will increase by a factor of 2 to the power of 4
i.e. if you double the thing the weight will be 16 times bigger
if you triple the thing (multiply it by 3), then the weight will increase by a factor of 3 to the power of 4
i.e. if you triple the thing the weight will be 81 times bigger
if you quadraple the thing (times by 4), then the weight will increase by a factor of 4 to the power of 4
i.e. if you quadraple the thing, the weight will be 256 times bigger
Then perhaps I would explore the issue with some actual values, then perhaps plot these on a graph, then look at the shape of the graph and notice how astoundingly steep it gets very quickly
i.e. the weight is quite sensitive to changes in the thing
This may prove very useful for you to try....
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Your mistake is in this:
You look at this line
i.e. if you double the thing the weight will be 16 times bigger
and then conclude that because 16 is 8 x 2 there must be a scale factor of 8
(or a ratio of 2:16 which is 1:8)
BUT BUT BUT
If you try the same with this
i.e. if you triple the thing the weight will be 81 times bigger
You would end up saying that there is a ratio of 3:81 (or 1:27)
and here
i.e. if you quadraple the thing, the weight will be 256 times bigger
4:256 or 1: 64
This is our point.
YOu look at the first example, conclude it is a ratio of 1:8 and use that to describe
the whole relationship or the whole proportionality
which is plainly false....
you dont
notice this because your example has a power of 2 not 4
thus
2x2
2+2
are being confused in your head without realising it.
In my example
2x4
2^4
2+4
are quite different and the mistake stands out a bit more...
THIS is what I mean when I was saying do you understand the maths.. forget this "reality" and "gravity"... just concentrate on the purely mathematical relationship you are trying to use
You either do not understand it or you are using completely the wrong terminology to describe it.