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



On 12/08/2010 05:01 AM, Savinainen Antti wrote:

John D. pointed out some ideas presented in a site:

<http://www.physicsclassroom.com/class/energy/u5l2a.cfm>

First, John did not cite the site correctly when stating that

"the internal forces are «sometimes referred to as nonconservative
forces» while the others are «sometimes referred to as conservative
forces».

Good point, I got the wires crossed. Sorry.

The site stated these other way round which might make a bit more
sense. However, this is not John's point in his criticism.

We agree, that is not my main point. But I don't see how their
idea makes even one bit of sense either way. The idea that
Ftens is «external» while Fspring is «internal» -- or vice versa --
is insane either way. What if we have a spring under tension?

Also, I don't buy the idea that something like this could make a
little "bit" of sense. I am reminded of the old joke: a watch that
is completely broken tells the correct time twice a day. That does
not, however, mean that the watch is even one bit useful.

It seems
to me that the site is not careful at all in defining what "system"
means as without a well-defined system it is quite hard to see what
forces are internal and what are external.

Agreed.

For instance, a system
could be a falling ball. In that case the gravitational force is an
"external" force.

That is giving the site way too much credit. The site says
emphatically and categorically that Fgrav is an internal force.

I will stipulate that you can pretend the site makes sense if
you selectively assume what they meant is the opposite of what
they actually said.

On the other hand, if the system includes both the
ball and the Earth then the gravitational force is internal to the
system (this is ssumed in the example given by the site).

I don't think that's what they are assuming. Certainly that's
not what they actually say. A simpler hypothesis to explain
where they are coming from goes like this: If you assume the
gravitational energy is known as a function of the position of
the object, they consider it to be "intrinsic" to the object.
I will not quibble about the distinction between "intrinsic"
and "internal". This hypothesis is consistent with what
follows:

Another point to be made concerns the usage of conservative and
non-conservative forces.

Yes, this is a major point.

I don't think that it is a good idea to
equate an "internal" force and conservative force.

Indeed!

My hypothesis is that they used a "syllogism" like this:
a) They think gravity is always a conservative force-field, and
b) they think they can equate conservative with internal and
non-conservative with external. so therefore
c) gravity must be internal.

Given that (a) is wrong and (b) is wrong, we shouldn't be too
surprised to find that (c) is wrong. See item (3) below for
more on this.

However, I can see
the point the site is aiming at. A conservative force in physics
refers to "a force with the property that the work done in moving a
particle between two points is independent of the path taken"

Yes, that has been the conventional meaning for many decades.

(<http://en.wikipedia.org/wiki/Conservative_force>). In addition to
this Wikipedia makes a similar point to the site: "Informally, a
conservative force can be thought of as a force that conserves
mechanical energy."

That "informal" idea is just wrong.

And I could add that this
informal statement is about all you need to know about conservative
force in a usual HS mechanics course addressing energy.

I disagree.

And this is the idea the site *attempts* to
convey if I understand it correctly.

It attempts without succeeding. So we have a failed attempt at
a worthless goal.

Let's consider some examples.

1) Let's start with a very simple scenario: The object is a
just a mass. It dangles from a string. Its weight is supported
by tension in the string. The whole situation is static. There
is no friction or any kind of dissipation (to an exceedingly good
approximation).

Are you trying to tell me that in this situation, Fgrav is
conservative while Ftens is nonconservative? I hope not.
Yet that is what is being taught on the classroom.com web
site.

2) Now let's consider something more interesting, such as an
Atwood machine. Now our system is mass "A", which is attached
by a string to mass "B" which is not part of our system. As
mass A moves, tension does work on our system, changing its
mechanical energy.

Is this what they mean when they say that Ftens is external
and non-conservative?

For one thing, Ftens is no more external in this scenario than
it was in the previous scenario.

Much much much more importantly, the fact that the mechanical
energy of our system is changing does *not* mean that mechanical
energy is not being conserved.

I am making a point about the distinction between constancy and
conservation. These are not the same thing! This is important!
This point is not even hinted at on that site, yet is is more
important than any of the points that are made on that site.

Let's be clear: Any conservation law includes a contribution
from flow across the boundary. In scenario 2, mechanical
energy is conserved as it flows (via the string) across the
boundary of our system. Energy is conserved even though the
system energy is not constant.

Also, the focus on mechanical energy (and the disregard of total
energy) is profoundly misguided. The important thing about
conservation of energy is the fact that "the" energy (i.e. the
total energy) is actually conserved. The fact that some subset
of the energy (e.g. the mechanical energy) is sometimes not
separately conserved is on the list of subsidiary ideas. It
needs to be mentioned, but it doesn't need to be emphasized.
My point is that the tail should not be allowed to wag the
dog ... yet on this site, they emphasize the tail and have
entirely thrown away the rest of the dog.

3) It is worth emphasizing that a gravitational field does not
necessarily leave the mechanical energy of a system constant.
Let our "system" be a satellite in equatorial orbit around the
moon. We observe from an earth-centered nonrotating reference
frame.

Notation:
⊕ = earth
☽ = moon
• = satellite


Snapshot 1: v+V ↑ ↑
⊕ ☽ •



Snapshot 2: ↑
⊕ • ☽
v-V ↓


You can see that in the course of an orbit, the satellites KE
(and overall mechanical E) change dramatically, depending on
whether its orbital velocity V (around the moon) is "with" or
"against" the moon's orbital velocity v (around the earth).

The physics here is worth remembering: A force-field is conservative
if it is the gradient of some /static/ potential. If the potential
is moving, or is time-varying, then all bets are off.

From this we conclude that the scheme at classroom.com for
classifying forces is wrong coming and going. The things it
calls conservative are not necessarily so. The things it calls
nonconservative are not necessarily so. If this site were a
watch, it would tell the correct time twice a day.

So...to answer John's question: "Is there any possibility that this
is not as bad as it looks?" I would say that the approach taken by
the site *could* probably work in a HS level IF the notions of system
and conservative/non-conservative forces are developed carefully
enough.

That sounds nice, but in this case developing the ideas "carefully"
would require contradicting all the main points made by this
classroom.com web page.

The site is profoundly misguided about what /should/ be conserved.

The site is wrong about what is internal and what is external.

The site is wrong about what is conservative and what is nonconservative.

These topics are at the very core of what physics is.

And ... why go to all this trouble, when doing things right is so
very much easier?!!!! Tried-and-true explanations of what energy is
are readily available.

How wrong does something have to be before we give it a failing grade?