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Re: [Phys-l] teaching energy

I'm curious about how you come up with the expression for the potential
energy of the stretched rubber bands (in the context of your course).

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Dan MacIsaac
Sent: Tuesday, October 03, 2006 12:12 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] teaching energy

Actually, for the past four semesters I've been teaching an energy-
centric highly nontraditional intro mechanics course from Fred
Goldberg's text "Physics for Elementary Teachers" or "PET"
<http://petproject.sdsu.edu/>
<http://www.its-about-time.com/htmls/pet/pet.html>

The curriculum starts with describing speed changes (speed-time, not
velocity-time graphs) then introduces kinetic energy as an energy of
motion: "The faster an object is moving, the more kinetic energy it
possesses" p1-23. Energy interaction diagrams are then introduced
and used throughout the course (force comes a cycle -or major
section- later than energy).

Then things get really cool. For instance the curricular route to
gravitational field energy starts with kinetic energy, then moves to
stored elastic potential energy in stretched rubber bands with carts
on tracks (concrete visible deformation), then moves to stored
magnetic field energy (carts on tracks interacting via magnets; an
invisibly stored deformation energy), then rotates through 90degrees
to become stored gravitational field energy in another invisible
field linking objects to the earth. Very nifty series of hands-on
activity based extensions indeed. Algebra and vector free fields.

A very nice algebra-free hands-on curriculum for elementary
teachers. It's interesting how the pre-service elementary teacher
college courses get some of the most sophisticated and revolutionary
rewrites.

Dan M

Dan MacIsaac, Associate Professor of Physics, SUNY-Buffalo State College
222SciBldg BSC, 1300 Elmwood Ave, Buffalo NY 14222 USA 716-878-3802
<macisadl@buffalostate.edu> <http://PhysicsEd.BuffaloState.edu>

On Oct 3, 2006, at 10:47 AM, John Denker wrote:

I think this is quite a nifty discussion. It is hard to imagine
a more appropriate topic for phys-l.


On 10/03/2006 09:48 AM, Robert Cohen wrote:
I've been skimming through the posts and I think there are three
points
of view:

1. Energy is associated with fields.
2. Energy is associated with objects.
3. Energy is associated with systems of objects.

I agree.

All three viewpoints are valid, and can be considered a chain of
successive approximations, in the order (1), (3), (2).

Item (1) i.e. fields is the modern, mainstream, deluxe model. It
is a model, not carved in stone, and not without dubious elements
if you look closely enough. The crucial disadvantage is that it
is complicated, waaay too complicated for an introductory class.
The advantage is that it is consistent with ideas of /local/
conservation of energy.

Item (3) i.e. the energy of the /system/ is the canonical Newtonian
approach. This was the state of the art from 1666 to 1915, and is
still good enough for any terrestrial practical application AFAIK.

It can be consistent with local conservation of energy, in the weak
sense of the term "consistent", if we restrict it to situations
where the length scales are short, the time scales are long, and the
velocities are small compared to c. (In more general situations it
would not be consistent with local conservation.)

This sort of conditional consistency is the rule (not the exception)
in introductory physics. A familiar example is KE = .5 m v^2, which
is not consistent with relativity, except in the low-velocity limit.

Item (2) is an approximation to item (3), useful when we take every
system of interest to be a two-body system, with one body being
the earth. We then call the other body "the object". We treat
the earth as infinitely massive in comparison. As a consequence
of these assumptions:
-- the earth is considered immovable;
-- the reduced mass of the system is equal to the mass of "the
object"
so we blur the distinction between mass and reduced mass;
-- the earth is the dominant contributor to creating the
gravitational
field; and
-- we use "the object" as the eponym of the full two-body system.

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Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l