Re: [Phys-l] Figuring Physics in the March TPT The Physics Teacher

[John Mallinckrodt <ajm@csupomona.edu>]

Several updates to my previous post:

First, and most important of all, I now see that John Clement was  
referring to Hewitt's "Figuring Physics," not Korsunsky's "Physics  
Challenges" to which my comments were addressed.  Assuming the latter  
and not yet having received my March issue of TPT, I went to the TPT  
web site and found the recently posted solution to the December  
"Physics Challenge."  Because it was of recent vintage and did indeed  
suffer from a mistaken analysis, I assumed I was addressing Clement's  
question.  I can well imagine that he and a few others have been  
scratching their heads over my response.

Second, assuming there is anyone who still cares (!)

a) The December "Physics Challenge" is available at

  http://scitation.aip.org/getpdf/servlet/GetPDFServlet? 
filetype=pdf&id=PHTEAH000046000009000556000001&idtype=cvips

b) Its published solution is available at

  http://scitation.aip.org/journals/doc/PHTEAH-home/challenges/ 
dec2008.pdf

c) and the AJP papers that I referred to in discussing the correct  
solution are

  Armstrong, "The Oscillating Spring and Weight--An Experiment Often  
Misinterpreted," AJP, 37, 447-449, 1969
  Sears, "A Demonstration of the Spring Mass-Correction," AJP, 37,  
645-648, (1969)
  Fox and Manhanty, "The Effective Mass of an Oscillating Spring,"  
AJP, 38, 98-100, (1970)

Finally, and of bare consequence, I see that the author of the  
published solution to the December Challenge is actually Renault who  
*teaches* at Tyler, not "Renault and Tyler."

My bads,

John

On Feb 18, 2009, at 3:27 PM, John Mallinckrodt wrote:

> On Feb 18, 2009, at 1:50 PM, John Clement wrote:
>
> > It has part of the analysis of the problem wrong.  Can anyone spot  
> > it!
>
> Renault and Tyler go astray by assuming that the potential energy is
> given by 1/2 kx^2, which is incorrect because the stretching isn't
> linear.  They effectively rederive the standard "add 1/3 of the mass
> of the spring" result, which is a good approximation for small spring
> masses precisely because, in that case, the stretching *is*  almost
> linear, but begins to fail for large spring masses as in this
> problem.  A proper solution must correctly account for the fact that
> the spring is an elastic medium which can support numerous modes of
> oscillation, only one of which is the usual fundamental mode.
>
> My own solution to the problem is available at
>
>    http://www.csupomona.edu/~ajm/special/Dec08TPT.pdf
>
> The difference between the correct solution and Renault and Tyler's
> "add 1/3 of the mass of the spring" approximation is less than a
> percent as my solution shows.
>
> It also turns out that this problem was discussed at length in the
> pages of AJP some forty years ago.
>
> A. JOHN "Slo" MALLINCKRODT
> Lead Guitarist, Out-Laws of Physics
>       http://outlawsofphysics.com
> Professor Emeritus of Physics, Cal Poly Pomona
>       http://www.csupomona.edu/~ajm
> Consulting Editor, AMERICAN JOURNAL of PHYSICS
>       http://www.kzoo.edu/ajp