Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

[Phys-L] Re: Energy is primary and fundamental? (was RE: First Day Activities or Demos)



----- Original Message -----
From: "rlamont" <rlamont@POSTOFFICE.PROVIDENCE.EDU>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Thursday, August 11, 2005 10:17 AM
Subject: Re: Energy is primary and fundamental? (was RE: First Day
Activities or Demos)


So far all you've done is to criticized the Modeling approach
to handling the concept of energy. How about offering something
concrete as a superior alternative, and I'll see if I can pick some
holes in it?

As you can probably tell, I don't start my course by addressing
energy. But I do get to it in due time.

I do the same.

My opening exercise is to have the students whack at a bowling
ball with a soft foam waffle ball bat. One student strikes the
ball while calling out a steady rhythm of 1 and 2 and 3 and 4,
etc., striking the ball when each number is spoken. The other
students line the corridor. As the ball rolls by them, the
student nearest the ball when a 5, 10, 15, etc., is called out
places a coin on the floor where the ball was at that time. We
then record the number of tiles the ball has moved versus the
number of hits or "time". When the students can do this
reasonably well, we repeat the experiment, but this time the ball
is batted when both the numbers and the words "and" are spoken,
doubling the rate at which the batting force is applied.

The student now spend the rest of the class (and part of the next
one) analyzing the motion. I have the students plot the speed of
the ball (in tiles/hit).

I would hesitate to focus on the ratio of tiles per hit as being "speed", of
course, but I get the idea.

I give them no definitions of how to
calculate or plot the speed. This usually results in a lively
discussion amongst the work groups as to whether they should plot
the whole distance traveled versus the total number of hits, or
only the distance traveled in one 5 hit period versus a 5 hit
time interval. They invariably conclude that the 5 hit approach
makes more sense to them. I stay out of that argument.

I then have them come up with their own definition of
acceleration and then have them plot it versus time.

Since kids mostly confuse "speed" with "acceleration", there has to be more
going on than just, "Come up with a definition of acceleration"?

They usually
find that the acceleration is fairly constant - implying that a
constant force produces a constant acceleration. They also
analyze the case where the ball was batted twice as often. Very
nicely, they find that the acceleration doubles - hence Newton's
2nd Law of motion.

Does twice as often imply twice the force? If you were working from
momentum change being related to frequency of pushing, I'd be more
comfortable with this progression.

Later on in the course, we revisit the data. They find that the
value of v squared is twice as large at the end of the corridor
than it was half way down the corridor. They also find that the
value of v squared is twice as large for the case when the ball
was batted twice as often. This leads to the quantity v squared
being related to the product of force and distance.

Ok, how do you get to v squared as the variable of interest? What's the
significance of v squared as opposed to v or v cubed? Isn't pulling that
out of the air "voodoo"? Now it may be that you've emphasized (as Modeling
does) the importance of graphs that result in straight lines as fundamental
to expressing the relationship of plotted variables to one another, which
WOULD indicate why v squared is of special interest, but I don't know from
the little you've posted.

This introduces kinetic energy.

Ok, but how is relating this factor to "kinetic energy" not "voodoo"?

The usual free fall experiments then
naturally bring in the relation between falling distance and v
squared - and the whole potential, kinetic, and total energy
conservation thing.

So how does potential energy get defined? How do you know when you "have"
it? In what way is potential energy different from kinetic and how does one
"change" into the other? If a rope were being held by you, but was slipping
out of your hands so that the object falls, would the relationship still
hold? Why not?

It's all physical and "hands-on". Energy becomes a simple
bookkeeping system that easily allows making predictions about
the dynamics of a system without fussing with the details of
vectors, constraint forces, time variation of forces, etc.

Don't get me wrong, I like the approach itself, and I see what you're
getting at - Developing concepts from data, but it seems to me that there is
a potential limitation here in that, yes, you can show that for a
free-falling object (with a streamlined configuration), v squared is related
to distance fallen, but you still have to use the term "energy", and haven't
really given the kids anything more to hang their hats on than some of my
colleagues who talk about it early on. Why don't you get the same distance
to v squared relationship for an object sliding horizontally? At some
point, you have to employ the idea of "energy", don't you? At some point
you have to talk about work transferring energy, don't you?

The advantage of what you do is that you are developing concepts (or at
least ideas) from data. That's a good thing. In Modeling this is
developing an operational definition before employing the label, and is a
standard technique. I now see from whence your criticism of energy first
comes, but again, I think you overestimate the perceived "concern" that
students will have over the "voodooness" of energy. They've been using the
idea for most of their lives and feel (unjustifiably) confident in their
understanding of it. They are much more likely to be uncomfortable about
immediately delving into mathmatics and graphing, imo.