11 Jun
2010
11 Jun
'10
12:18 p.m.
Tony Duell [ard at p850ug1.demon.co.uk] wrote:
That is exactly my point. The system is oversimplified so you can solve
it. But the simplified system is useless in the real world (air
resistance most certainly does matter for projectile motion). It is just
a game to get you to solve certain equations.
While I have no objection with learning how to solve equations, dressing
them up as being applciaable to a real world problem when they are not
doesn't help anyone.
Oh, it was wore thsn that. The projectile motion
always invovled a
parabolic trajectory. This assumes not only zero air
resistance, but also
uniform gravity acting vertically downwards -- in other words a flat
earth. Which I don't believe in.
Air resistance is ignored because otherwise the equations become too
complex. In any particular real world example that may or may not
lead to unacceptable errors.
The constant approximation is far less of a problem. The Earth's
radius is what ~6Mm, so even if your height changes by say 60m then
that's less than 1%.
Not if the projectile happens to be a satellite :-)
Which birngs me on to my next moan. All too often the subject is
'compartmentalised'. 'This is how to solve a projectile questio. This is
how to solve a planet orbiting the earth. This is how to solbe...' When
really the same laws (Newton's laws of motions _are_ a sufficiently good
apperoxiamation IMHO) apply in all the cases. Understand the fundamental
laws ansd you can solve just about any problem, even pone you've not been
taught.
The point is to teach you the simple case so that you understand it
and can move on to the complications later. There won't be a "later"
in A-level maths because there isn't enough time (you have to fit in
the rest of the course and the remaining A-levels).
I am probably strange, but I've read books that support this view. Namely
that for every subject there is a 'toy version' And actually it's much
easier to learn the real subject properly than the toy version. It may
appear to ne more complciated, but it isn't.
An example : Some years ago I was interested in how telephone exchanges
work -- the old step-by-step Strowger ones. I read a few simple books and
couldn't understnad them at all. I actually thought it was beyond me. And
then I bought the 2-volume set of 'Telephony' in a second hand bookshop.
I didn't realise it at the time, but this was a book used by the
telephone company (GPO) over here. Yes, iy's heavy going. Yes, it took mw
several weeks to work through it. ut it made sense. The reason is that
_every last relay_ is expaliend. There are complete schematics of
telephone exchanges. There's nothing missed out. And that made sense to me.
Just as the operation of a processor made sense to me when I battled
through the P850 and PDP11/45 manuals and understood what every last gate
did.
I don't recall whether I started solving stuff
numerically at A-level
or at degree-level, I suspect the latter. However, I do recall that the
Nor do I, bercuase I taught myself the 'interesting stuff' long before I
whould have known about it.
I could complain that the basic electronics on my
engineering science
course was pretty rudimentary and that the practicals were (in my view)
pretty basic. But there was a lot packed into the course and it
provided a foundation for many different areas. I don't think I could
be trusted to build a bridge now, but if I'd been that way inclined
I would have had enough of a grounding to get my foot in the door
somewhere.
Sure, you need a 'gorunding', but it has to be a good grounding. One
fundamental rule is that you should never learn something that you have
to unlearn later. And that the gorunding should be logical and as
complete as it can be, not a hotchpotch of unrelated stuff.
Alas the pretend 'education' I got at school failed in all respects.
Fortunately I had enough books to read up on the real version.
-tony