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[Phys-L] conservation 101



On 01/30/2014 10:48 AM, Richard Tarara wondered:
how a 5-year old could possibly comprehend Energy and charge
conservation

Here's how my father explained it. It started with a
vintage hand-cranked grindstone. It was red, like this:

http://www.bob-easton.com/blog/wp-content/uploads/2009/11/grinder.jpg

When I was about five years old, he clamped the thing
to the headboard of my bed, so he could use it as part
of a bed-time story. The thing had a tremendous mechanical
advantage from crank to stone, tremendously well-cut gears,
and good bearings. If you gave it a good crank, it would
spin and spin and spin.

He pointed out that the mechanics also worked in
reverse. Starting from the non-spinning state, if I
grabbed the stone I could turn it, and this would make
the crank turn ever so slowly. The crank would turn
*even if my father opposed it* with all his strength.
Now my father was huge and strong by absolute standards,
even more so compared to my 5-year-old self, so the idea
that I could overpower him under any conditions made a
treeeeemendous impression.

He carefully pointed out that I had to move the stone
through a very long distance to move the crank a small
distance, and ...... drum roll ...... the product of
force times distance was the same on both ends.

If you want to get fussy, this was conservation of work,
not conservation of energy in general, but it was a
starting point, and it wasn't wrong.

He reinforced this with levers, e.g. a highly asymmetric
teeter totter made of a ladder laid out on the ground
with a fulcrum near one end. He stood on the short end
while I climbed onto the long end. The idea that I could
lift him, even a little bit, was impressive. Again the
product of force*distance was the same at both ends.

Next came a block and tackle. At this point he didn't
even need to explain. I could just look at the thing
and see that a big motion on the fall translated to a
small motion of the block. I tied one end to a sling
and the other end to a branch high in a tree and used
it to lift myself, so I had a very direct appreciation
for the forces and distances involved. It was all fun
and games until I was waaaay up in the air and the ropes
got tangled so I couldn't get down. I learned early
that there's a downside to being a mad scientist.

Conservation of charge is related to continuity of
current. One day when my brother and I were walking
home from school, we came to a place where workers
had been installing power lines. They had thrown
scraps of wire all over the place, pieces of 2-gauge
solid copper wire, a few feet long. Not being entirely
stupid, we grabbed them and carried them home. My
father was a wiz at building stuff out of bailing wire,
and he could not resist building stuff out of the
wire scraps. In particular, he built flashlights for
us. Each one had a coil of wire to hold the batteries,
and a crimp to hold the bulb. The nice thing was that
unlike an off-the-shelf flashlight, it was super-easy
to trace the path of the current.

My father was largely self-taught. He hated school, due
to too many bad experiences with teachers telling him
stuff that couldn't possibly be true. He read books.
Among other things, he was convinced that electric charge
was an abstraction. There was only one type of electric
charge, not two. The amount of charge could be positive
or negative, but this was just a point on a number line,
and there was only one number line, not two number lines.
You did not need to keep track of the amount of positive
charge on one number line and negative charge on a different
number line. He was right about this. Ben Franklin was
right about this.
In contrast, vast parts of today's PER literature
are dead wrong about this. The Arons book for
example makes a big fuss about this, which makes
for a depressing object lesson in the /opposite/
of critical reasoning.

Positive charge flowing to the left is the same as
negative charge flowing to the right. The two situations
are different as to chemistry, but that is the answer
to a different question. They are the same as to charge.
Charge is an abstraction, separate from the chemistry.

He illustrated this by building an apparatus to make
hydrogen and oxygen by electrolysis of water. It took
him several tries to come up with an apparatus that
worked properly, because the usual textbook instructions
are wrong. I didn't know it at the time, but watching
him struggle with it and make successive refinements
was an incredibly valuable lesson unto itself, a lesson
in how science is /really/ done, so very very unlike how
it is described on posters and in some "modern" physics
books.
http://www.av8n.com/physics/scientific-methods.htm#sec-poster

Again: Charge is an abstraction, separate from the chemistry.

In the same way, energy is an abstraction, as you can
see in a wave on a rope. The energy in the wave moves
along, even though the rope is in the same place before
and after. The energy is an abstraction, separate from
the rope.

I know there are people on this list who insist that
their students are organically incapable of dealing with
abstraction, symbolism, representation, and/or imagination.
I just don't believe it. Very young kids play with dolls,
using their imagination. They know full well that the
baby doll is not a real baby; it's just a symbol, an
abstract representation of a baby.

Of course there are always a few special-ed students
who are so impaired that they are unable to play with
dolls. However, that's not what we are talking about
here. Those students shouldn't be signing up for high-
school physics, and they certainly shouldn't be dictating
the content and pace of the course.

References:
http://www.av8n.com/physics/reality-reductionism.htm
http://www.av8n.com/physics/one-kind-of-charge.htm