Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

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



After getting all my factors of 2 in the right spots, I agree with John. Three points are made b this exchange:
1. A valuable resource is Abramowitz and Stegun, <Handbook of Mathematical Functions> published by Dover.
2. Intuition needs to be checkede by calculation. Note that the curved path is more than 10% longer than the straight ramp.
3. Just because an answer is not available in terms of elementary functions is not a reason to avoid a calculation.
Regards,
Jack


On Fri, 27 Oct 2006, John Mallinckrodt wrote:

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>



_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l


--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley