Re: [Phys-l] accurate numerical solution of equations of motion

["Rick Tarara" <rtarara@saintmarys.edu>]

Let me just comment on the spreadsheet note--not the much more elegant 
programming ideas.

I do a 'simple' exercise with my intro-calc level class for chem, math, and 
engineering students.  I do this because they REALLY DON'T get this anywhere 
else early in their courses.

My exercise is to drop a bowling ball from 100 km up.  I want the time to 
hit the ground and the speed.

Level one:  Just worry about the variation in the acceleration due to 
gravity.

Level two:  Add in air resistance, using a constant coefficient but check v 
and v^2 dependencies.

Level three:  Break apart the air resistance coefficient and make the 
geometrical factor a variable and model the air density as non-constant.  We 
only get to a simple model there--linearly decreasing with altitude.  With 
more time, we could get more sophisticated there, but the point of the 
exercise is to show how to break down the complexities.

We take a simple numerical approach.  Calculate the acceleration from the 
current force.  Find the velocity as v_0 + a(delta)t, and find the position 
as y_0 + v(delta)t, with delta-t a variable.  Now recalculate the forces and 
acceleration and repeat.  In one two-hour session we get most of this done.

Next step is to use their spreadsheet to predict the behavior of a falling 
foam ball.  This they drop and time for distance up to 10-12 meters (drop 
off balconies in our library).  THEN display the data and the predictions on 
the same graph--again they haven't done this before--and search on the 
adjustable parameters for the best fit.

I try to emphasize, especially to the engineers, that this is probably the 
most useful and important lab exercise we will do all year!

So--pedagogically--I highly recommend using spreadsheet for numerical 
methods with science/engineering student.  I'm sure this is done in 'real' 
engineering programs, but here we only prepare students for engineering 
courses they take across the street at the University.

Rick

***************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN
rtarara@saintmarys.edu
******************************
Free Physics Software
PC & Mac
www.saintmarys.edu/~rtarara/software.html
*******************************

----- Original Message ----- 
From: "John Denker" <jsd@av8n.com>
> ================
>
> I know it is somewhat eccentric to use elegant old-school numerical
> techniques on a spreadsheet.  Many old-school numerical analysts
> despise spreadsheets.  But bear with me; I'm not as crazy as
> you might think.  There is a segment of the population that is
> intimidated by c++ and is not going to learn it anytime soon ...
> but is not intimidated by spreadsheets.  The folks in this segment
> are never going to read big fancy books on numerical methods ...
> but you can teach them a couple of good ideas, like using second-
> order Euler for part of the problem, and using stride=2 for the
> other part.  These ideas allow them to get really good results
> from their spreadsheets.
>
> Pedagogical remark:  Almost all real-world physics jobs involve
> a ton of computing.  IMHO there should be more of an effort to
> integrate computing into the physics curriculum at all levels.
> I'm not sure _how_ to do this, given how overcrowded the schedule
> already is ... but still it needs to be done somehow.  Otherwise
> the product will suffer.
>
> ==============================
>
> There's a lot more I could say about this if anybody is interested,
> but I'll stop here for now.
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