Re: [Phys-l] time to bottom of ramp

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

I tried the time to the bottom of a quarter-circle ramp problem using
the numerical method presented by Feynman in chapter 9 of the Feynman
Lectures Volume I.  The method lends itself well to an introductory
calculus-based physics course for which calculus is a co-requisite
rather than a pre-requisite but in which you still want students to be
able to solve first-semester problems that don't lend themselves to
unsophisticated analytical solutions.  Spreadsheet software makes the
method pretty easy to implement.  The ease with one can make graphs in
spreadsheets makes graphs useful for indicating whether or not the
method is working.  Constancy of mechanical energy in the problem at
hand makes for an easy check on the final angular velocity.  (I
arbitrarily chose to work with angular variables.)  The spreadsheet for
the quarter-circle ramp problem is at:
http://www.anselm.edu/internet/physics/phys-l/qtrCircleRamp.xls.zip 
It yields the same result that John M. and others got:  For a
quarter-circle ramp of radius 1 meter, the time on the circular ramp is
.5923 s whereas the time to travel from rest from the same start point
to the same end point along a straight ramp is .6388 s.  The former is
92.7% of the latter.

Jeff Schnick

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John
Mallinckrodt
Sent: Friday, October 27, 2006 7:13 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] time to bottom of ramp

On Oct 27, 2006, at 2:29 PM, Jack Uretsky wrote:

>  	For a frictionless quarter-circle arc of radius h, the time to
> travel the arc is (barring arithmetic errors) about 2.6 times to slide
> down an inclined ramp between the same 2 points.  The answer can be
> expressed as a beta-function.

Nah.  Doesn't make sense.  Here's my stab:  I get that the curved  
ramp takes 7.4% less time.  The ratio of curved ramp time to straight  
ramp time is

     B(1/4,1/2) / [4 sqrt(2)] = 0.927 ...

John Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://outlawsofphysics.com>



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