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Re: Swartz letter in AJP (work-energy theorem)

Brian Whatcott wrote:

At 02:55 PM 9/1/2004, you wrote:

>> /// I am reminded
>> of a somewhat similar confusing item in the high school text,
>> _Foundations of Physics_,
>> 2nd ed, by Lehrman and Swartz. On p.45 of the _Teacher's Guide_
for that
>> text, one finds
>> "The cavalier way in which we treat the difference in definition of
>> speed and velocity is
>> very deliberate. It is a reaction to certain situations in our own
>> experience where knowledge
>> of the defined difference became the essential feature of motion
study
>> to be tested with
>> true-false questions."


>> Hugh Logan
>> Retired physics teacher
>
>
> I can see why the quoted use of "cavalier" led to student difficulty.
> It means quite the opposite of the writer's intended value, where
> cavalier is "off-hand, curt, supercilious" [COD]

However, I thought Lehrman and Swartz's usage might fit in with one of
the M-W (online) dictionary entries for "cavalier" used as an adjective:
"marked by or given to offhand and often disdainful dismissal of
important matters" -- perhaps with the emphasis on "offhand" rather than
"disdainful." The reader of the text (not the _Teacher's Guide_ in which
the intent is "deliberate") might think the important matter of the
distinction between speed and velocity has been dismissed in an offhand
manner. In 1970, I could only think of a gentleman on a horse, perhaps
disdainful of those beneath him. I remained silent rather than display
further ignorance. In the AJP article, Cliff Swartz wrote, "You don't
plug friction into the wall socket or feed it gasoline or steak.
Certainly it cannot do negative work, a concept that can only bewilder
the innocent." Is Swartz being "cavalier" in his dismissal of negative
work, while admitting that
(if I interpret him correctly) juniors might use it?

Hugh Logan
Retired physics teacher



It seems to me that the L&S text in question treated the difference
between speed and velocity carefully.

I think they are emphasizing the cases where they are the same -- in the
context of one-dimensional
motion. And they are emphasizing speed rather than velocity. After
noting velocity is a vector, they state (p. 61), "In technical matters,
we use the word _speed_ to mean just the _magnitude_ of velocity.
Therefore it is a scalar. In this chapter, for example, we will be
describing speed instead of velocity, since we will deal only with
motion along a line. Where there is no reason to make the distinction,
the words are often used interchangeably." As noted in a previous post,
they define velocity as the time rate of position. They give several
examples of graphs of motion with d (position) vs. t (time) graphs.
These, to start, are made up of one or more straight line segments --
with positive slope, horizontal, and with negative slope. They denote
change of position as (delta d), where d is position. However, they say
that one way of determining d is with an odometer, describing it as
distance from the origin. None of their graphs show a negative value of
d, but (delta d) is negative if the slope is negative. They calculate
average speed by dividing (delta d) by (delta t) and then define it with
the formula v-bar=(delta d)/(delta t). Note that v is speed, not
velocity. Let us hope there is no change of direction during time
interval (delta t). It doesn't change in any of the examples. When they
get to the segment of the graph with negative slope, they state, "During
that time [the last two seconds] the object has _decreased_ its distance
from the origin, from 6 meters to 4 meters. Its speed is therefore
(2m)/(2s)=1 m/sec. Strictly speaking, however, (delta d) is _negative_ 2
meters, and the slope of the graph is also negative. Clearly, the
negative sign indicates that the object is traveling in the opposite
direction. While no one can deny that the speed is 1 m/sec, it is also
correct to state that the _velocity_ is -1 m/sec. The question of
direction has been introduced, although it is still limited to a single
line." Still, their formula for average speed would give -1 m/sec.

Other texts would define average velocity as v-bar=(delta x)/(delta t),
x being position. It seems like
L&S are using the definition of velocity for speed, but calling it
velocity if it comes out negative, then taking the absolute value to get
speed, or , as in the example, finding the distance instead of the
change of position before dividing -- tacking on the _negative_ if they
want the velocity. I know what they mean, but it gives me the willies,
and, strictly speaking, I don't think it is correct.

They (L&S) go on to instantaneous speed v=limit (delta d)/(delta t) as
delta t ---->0. This is demonstrated to be the slope of a d vs. t graph
(labeled _displacement vs time_). According to my take on "cavalier" as
they use it, this is an example - offhandedly discarding the distinction
between position and displacement. Their graph is of an S-shaped
monotonically increasing function. The slope is always positive, so that
both the instantaneous velocity and the speed are positive. But we would
have the same problem as before if the graph sloped downwards in some
region.

L&S is in many ways a good book, but the sections on kinematics in Chap.
3 bother me. Cliff Swartz wrote a similar book, _Phenomenal Physics_,
with no co-author. That might give a better idea of Swartz's approach to
this matter. Unfortunately, my copy was swiped before I retired, so I
can't refer to it. I recall that Dr. Lehrman was a biologist.


(Does the sub-conscious register "cavalier" as "carefully-er"?)

I don't think so. Whose sub-conscious? Not mine. I don't know if the
above has convinced you. The word "cavalier" appeared only in the
_Teacher's Guide_, but applied to the expected reaction of the reader
(most likely the teacher) of the text.


I have not read it, true: but almost every physics text makes a big
deal of the difference.

L&S makes a big deal of the sameness in the cases where they are the same.


(Nevertheless, physics teachers almost always want to use the
term 'velocity' where speed is in fact the term in question.)

I do that, although I am not unaware of it -- just too lazy to make the
distinction. I don't think I do it
when the velocity is negative and the speed is wanted. I think of "v" as
"velocity," not speed.

Then there is the question whether or not to use the full vector
notation for motion along a straight line.
I believe some are recommending this, although I don't ordinarily do so.
The signed velocity is just the component of the velocity along the line
once a positive direction has been defined, say with a unit vector along
that direction.


You quote Swartz in this way: "You don't plug friction into
the wall socket or feed it gasoline or steak...."
This is a standard argument against "reification" of the kind that
Jim Green champions, from time to time.
I take a different view: I see all physics, perhaps all science as a
kind of reification of model entities: cost, value, interest, work,
energy, entropy, enthalpy, friction and so on.
I do not rebel at the naming of defined concepts - I take it that
this concretion is what enables students to grasp the models in
question - it allows the physical manipulation of terms.

I would tend to agree with you.


About negative work: in the world of the accounts clerk, a debit
in one column is the credit in the other with an opposite sign.
I fancy the student has a more concrete conception of coinage,
for example.
You have 'em or you don't.
Owing money as an example of negative coins, has a conceptual
precipice for them, at times, I think.

The experts on Piaget's cognitive theory might have some ideas about this.

Thanks for all the comments.

Hugh Logan