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Unread 02-03-2006, 17:09
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Richard Wallace Richard Wallace is offline
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Re: Physics: ball launch using gravity

Quote:
Originally Posted by JoeXIII'007
Thanks again, and any ideas on how to get the ball just a wee bit higher would be really great.

-Joe
This may be a bit late in your project and a bit too abstract to be useful, but..

Neglecting friction, the problem of finding the curve of steepest descent rate (which would maximize velocity at the bottom) is called the brachistochrone problem. The solution is a cycloid curve.

The problem can be generalized using calculus of variations to include friction, rotational KE, etc.

The descending section of your Hot Wheels track appears to be very close to a cycloid.
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Richard Wallace

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I believe in intuition and inspiration. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.
(Cosmic Religion : With Other Opinions and Aphorisms (1931) by Albert Einstein, p. 97)
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