Re: [Phys-l] internal/externalconservative/nonconservative forces!?!?

["John Clement" <clement@hal-pc.org>]

Of course Mgh implies a system.  You have to have a reference, and that is
the other half of the system.  So the Earth plus the object are the system.
Mgh is certainly an approximation, but in the laboratory it is so exact,
that it does not look like one.  So you first start with the model that the
gravitational energy follows this equation.  But later on you generalize to
the NTN general equation.  You don't start with the general equation.

The concept of system is very important even for the terrestrial
applications, as it helps the student understand the concept.  So the energy
in a ball thrown up, is not in the ball, but in the system of the
Earth-ball, or if you will in the connection between them.  At first this
connection can be visualized by the student sort of like a rubber band that
always pulls with the same force.

The system concept is important for problem solving because it allows you to
often generate simple solutions from complicated looking systems.

As to cutting both ways, there is ample evidence from the research that
students have to use the concepts, or they end up just being equation
hunters.  I would recommend the article about the twins solving the twin
paradox in the latest Physics Teacher.  It shows how understanding concepts
makes students more expert like in their problem solving.

John M. Clement
Houston, TX

> On 12/14/2010 05:19 PM, William Robertson wrote:
> > I believe that the concept of system is given short shrift in
> > too many physics or other science texts. There exists research showing
> > that understanding or not understanding a choice of system can
> > dramatically affect one's problem solving ability in physics.
>
> Well, that cuts both ways.
>
> Yes, physics is about principles.  But physics is also about applications
> and approximations.
>
> In the physics course, I want students to learn the principles.  But
> just as importantly, I want them to learn how to make well-controlled
> approximations.
>
> If we are talking about the earth/moon system, the gravitational energy
> is clearly in the system, not "in" the moon.  The principles of the thing
> are clear, and the same principles apply -- in principle -- to every other
> gravitating system.
>
> On the other hand, in a very wide range of practical applications,
> including soccer balls, planes, trains, and automobiles, we find "m g h"
> is an exceedingly good approximation, and is significantly simpler than
> "G M m / r".  Treating the earth (and the earth's gravitational field)
> as imperturbable is an approximation.  Like all approximations, sometimes
> it is appropriate and sometimes it is not.
>
> Deciding what approximation to use in this-or-that situation requires
> judgment and skill.
>
> It is ultra-super-important that students understand we are not peeved
> about the approximation but rather about certain _inappropriate uses_
> of the approximation.
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