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Re: Why work before energy in texts



Oh, Ludwik, you ask good questions. Let me mumble a bit more:

I am not always precise in my posts because I assume that listers can get
my point without my beating them over the head. I have said that I feel
awkward spelling out what I have as I assume everyone can do this stuff
better than I.

> There can be no change in the level of energy of a system
> without doing work on the system.

Level usually means elevation to me. Why not the "amount"
of energy?

Here the language may be beyond me -- others are welcome to help here. I
don't use "amount" because it might (and usually does) imply to the
student's mind that I have reified "energy". Giving even a hint that this
is what the instructor implies I consider to be a big mistake -- if not a
disaster. I don't think that "level' has hurt me in my presentations. How
about "magnitude"?

In either case the "what is energy?" question
must be addressed in the first physics course. You must
define new concepts when you introduce them. Right?

I tell them immediately what I mean by the word "energy": 0.5mv^2. The word
-- along with the concept -- was coined by Young as I recall. (Others can
comment), It is just a word after all -- not a discovery of some new
element like flubonium) The concept is just a property of the fligit --
like saying the fligit is blue or cubic. I grant you that this property
is usually a bit more useful than color, but it is just a property -- an
invented property at that.

Later the usage gets modified as KE, PE (and more specific formulations)
are introduced --
But I am careful to point out what is work and what is KE.

> Let's call 0.5mv^2 the energy of the fligit and the force
> times the distance the work I did on the fligit. Class after
> you take the calculus, you will understand how this is derived.

It is not necessary to say "the work I did", the "work done by
my force" would probably be better. A work done be a person
is often associated with "being tired", not with the physical
quantity we call work in physics. I agree, it is a nitpick.

Nitpicks are often valuable --- a sidebar at this point might be valuable
to distinguish between physical effort and the physics usage. I often have
students form a tug of war at the front of the class (My classes are
typically a bit physical and always Socratic). There is a discussion
about how much work is done and whether they are tired.

You do not need calculus to show that 0.5 is not an arbitrary
factor. This is not a nitpick.

OK

> Greater work; greater increase in the level of the
> energy. ie W==Fxd = deltaE -- always and necessarily

"Always and necessarily?" I would prefer to show that this is true
in one or two situations before generalizing. You probably had
this in mind, right?

Oh, my comment was meant as a comment to the list. Sorry . I lost my head.

> Now if I slide the book across the table slowly, there are again two
> forces acting -- my hand and friction -- and the work done by each force
> cancels. See the book does not continue to move -- the level of energy is
> not increased.

Another nitpick. The amount of energy associated with that book
would not necessarily change if the book continued to move. Think
of the constant velocity and of the horizontal path. Yes, I know
that you know this, Jim.

When I do this, the book stops -- so it begins from rest and ends at rest
-- I just hope that the students don't worry about thermo at this point; I
will get back to the demo at the appropriate time.

> What is the difference between gravity and friction? With gravity I
> can get a subsequent increase in the level of energy and with friction
> I can not. Let me call such forces conservative and non-conservative.
>
> Because the work done by conservative forces has the potential to increase
> the level of energy of the system, I will call this work, deltaPE. And I
> will call the first energy KE.

Are you saying that deltaPE = m*g*h BY DEFINITION or are you
referring to a hidden derivation?

It is not a derivation; it is a (temporary) definition -- to get amplified
as other examples arise.

> So Wnc + Wc== Wnc + deltaPE = deltaKE

In most textbbooks this is derived from F=m*a plus kinematics.
Are you leaning on this?

No. My assignment here was to teach a "bone head" class. I snuck the W/E
principle in at the first of this discussion. Everything gets
modified/amplified/clarified as the class goes along during the
semester. (I don't know what you mean by "plus kinematics")

> But things look better if I change signs and write
>
> Wnc=deltaKE + deltaPE

Algebraically, it must be - deltaPE. You probably meant

Wnc=deltaKE + something, where something=-deltaPE

Huh???

> And we have work and both PE(-Wc) and KE(E) all at
> the same time. And the students understand what is going
> on and why much better.

How does the "at the same time" promote better understanding?
This is not a nitpick.

I think that it has been established that coupled concepts are better
taught together. I leave this to PER types to confirm and to comment further.

Best wishes, Jim

Jim Green
mailto:JMGreen@sisna.com
http://users.sisna.com/jmgreen