Re: [Phys-l] Newton and Snell (was Global evolution as fact)

["Dr. Richard Tarara" <rtarara@saintmarys.edu>]

There are some advantages to working with the kinematics equations despite 
all the negatives given by Bob.

1)  Students have (often faulty) concepts of velocity and acceleration that 
may need serious work--even if you want to start with momentum and energy.

2)  The kinematics equations can be derived easily from basic definitions. 
Sometimes students get the idea that all our equations are just pulled from 
some body orifice!  ;-)

3)  The basic kinematics equations can be used to build complex solutions 
through numerical methods (spreadsheets) where key quantities ARE held 
constant over a short period of time to approximate the evolution of a 
system.  This can give insight into the ultimate meaning differential 
equations or at least why we like to write equations as such.  The problem 
we work on is a bowling ball falling from 100 km above the earth's surface 
(falls out of the shuttle on the way to orbit).  Finding the time to hit the 
ground and the speed at which it hits is the goal--starting with just the 
consideration of the changing 'g', then adding in a velocity dependent air 
resistance term, and finally modelling the air resistance with functional 
representation of air density with height.  Later we use that same 
spreadsheet--drop foam balls from various (and some quite large) heights, 
and fitting the data with the numerical model.   The heart of the 
spreadsheet is just that acceleration is a function of height and velocity, 
but for each short time period (.1 seconds typically) the velocity will 
change by acceleration x delta-t with the acceleration held constant and the 
height will change by v x delta-t, both relationships straight from the 
kinematics equations.

Even if you do work with momentum and energy first, I'm sure you run into 
the same problems of students not understanding 'CHANGE IN'.   No matter how 
simple it seems to us, that a changing velocity means the object sped up, 
slowed down,  and/or changed direction and a change in speed/kinetic energy 
means the object sped up or slowed down , these are very difficult ideas for 
many students.  Using the most common form of the work-energy theorem (Net 
Work = change in KE) a series of questions asking students to determine if 
the net work is positive, negative, or zero giving a whole list of actions 
(my favorites being parts of the motion of a vertically thrown ball) remain 
mysterious to many, many students.  Knowing that this is a major stumbling 
block, I personally like to work on velocity and acceleration separately, 
right at the start of the course, and keep working on these throughout the 
course.  While you might avoid the word acceleration in a momentum/energy 
first approach you still end up dealing with changes in velocity.

Bottom line--I don't see anything wrong with momentum/energy first, but I 
don't necessarily see a big advantage either.  I also feel there is (can be) 
considerable value in working with the kinematics equations (if nothing else 
as the gateway to 'PHYSICS' problem solving--and this is physics IMO, not 
just math.)

Rick

Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
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----- Original Message ----- 
From: "LaMontagne, Bob" <RLAMONT@providence.edu>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Wednesday, January 12, 2011 1:07 PM
Subject: Re: [Phys-l] Newton and Snell (was Global evolution as fact)


> John,
>
> I have no doubts that physics can teach these topics more effectively, 
> especially if there is some hands-on component to the teaching. My 
> question really goes to whether we should be teaching kinematics at all. 
> Most accelerations in practice are not constant. Most projectile motions 
> are not parabolic  (even in the flat earth approximation) because of air 
> resistance. There are many useful topics we choose to leave out of general 
> physics. I just hope we are not spending an inordinate amount of time on 
> idealized motions just to produce practice problems for F=ma. Most motion 
> problems can be done more easily using momentum and energy - and don't 
> require the artificial restriction of constant acceleration - although 
> that class of problems is easily included. Take the case of dropping a 
> ball---most of the interesting parameters of the motion come from energy 
> balance - the kinematic equations aren't actually used at all.
>
> Bob at PC
>
> ________________________________________
> From: phys-l-bounces@carnot.physics.buffalo.edu 
> [phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Clement 
> [clement@hal-pc.org]
> Sent: Wednesday, January 12, 2011 12:19 AM
> To: 'Forum for Physics Educators'
> Subject: Re: [Phys-l] Newton and Snell (was Global evolution as fact)
>
> The big reason for spending time on kinematics is that math does not teach
> them in a manner so as to generate understanding.  The research shows that
> students have to use multiple representations: pictorial (motion maps),
> graphs, descriptions, and lastly equations.  Unfortunately most 
> conventional
> physics courses also do not generate good understanding.
>
> The work of Jerry Epstein has shown that students come out of math courses
> with very low understanding, so we have to teach them the relevant math. 
> I
> can confirm this from what I have observed in the calculus based courses.
> Actually well over 30 years ago I taught a conceptual physics course at 
> Duke
> U where I stressed kinematic graphs, and a student who had taken calculus
> told me that it made her understand calculus.  In addition the students 
> did
> very well at relating velocity, position, and acceleration graphs.
>
> It has been stated that the sequence of starting with impulse momentum is
> superior to the conventional one.  I would say that this would need to be
> demonstrated by using conceptual tests such as the FCI/FMCE.  At present 
> the
> Modeling program has some classes that have achieved normalized gain as 
> high
> as 90%, so it would seem to be that the conventional sequence works very
> well provided research based instruction is used.  So I must take 
> exception
> to the claim that impulse-momentum is superior.  It has not been
> demonstrated.
>
> Actually the dividing line between math and physics is fairly broad, as 
> are
> all dividing lines between fields.  Kinematics is both math and physics.
>
> John M. Clement
> Houston, TX
>
> > May I also chime in with a preference for your outline of topics. We 
> > spend
> > too much time with the kinematic equations for constant acceleration -
> > mostly because we wish to apply F=ma at some point. These are really math
> > equations, not physics per se. It may be nice to know how long a runway
> > must be if an aircraft with a certain acceleration needs a certain take
> > off speed - but these are math problems. We probably only do them in our
> > courses because we spent time developing the kinematic equations. If we
> > covered other topics, and used impulse<-->momentum instead of F=ma, we
> > would probably find a whole new set of problems that we would feel are
> > important.
>
>
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