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Re: [Phys-L] just for fun



On 12/27/2013 9:46 PM, Bill Nettles wrote:


As an additional point: figuring stuff out without a calculator
can be fun, if you make a game of it. Understanding stuff is
more fun than mindless number-crunching. Like most things,
it's more fun after you build up some skill.
Understanding stuff IS the "hard work" to which I was referring. Many students don't have take the time (or have the proper instruction) to build up some skill, because building skill isn't always fun. Using skill IS fun.


Which is why I think you'll find that very few students will find the suggestions that have been given here 'fun'. I find Gauss' Law problems 'fun' but I like and am reasonably skilled with geometry---students find these problems very difficult!

One thing I do suggest with calculus-level students is to do some numerical methods problems/projects. What I've found to be true year after year is that these students can DO calculus problems, but they don't really understand what the calculus does. My project along these lines is a bowling ball that falls out of the (now defunct) space-shuttle moving straight upwards at some given speed at some fairly high altitude. Find how long it takes the ball to strike the ground and how fast it is moving when it does. a) Do the standard Algebra textbook problem ignoring air resistance. b) Adjust the acceleration of gravity with the distance from earth's center. c) Include an air resistance term that depends on the velocity but using a constant air density. d) Use a function for the air density as a function of altitude. All of the above done using spreadsheet calculations broken down with delta-t at 10, 1, or .1 seconds.

The final spreadsheet developed can then be adjusted to use a constant 'g' and constant 'rho' to find the theoretical speed of a foam ball dropped from given heights (up to 50 or so feet) and using some adjustable parameters (fundamentally the power applied to v) fit the theory to some experimentally obtained data.

The point of all this is to try and really get at how calculus can give us very precise solutions to problems where the variables are interdependent.

rwt

--
Richard Tarara
Professor of Physics
Saint Mary's College

free Physics educational software
www.saintmarys.edu/~rtarara/software.html