The Harmonic Overhang Effect in Stacked Books

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SUMMARY

The discussion centers on the "Harmonic Overhang Effect," which occurs when a stack of books is arranged in a staggered manner, creating a visual effect where the top book extends beyond the bottom book. This phenomenon is mathematically represented by the series 1/2 + 1/3 + 1/4 + 1/5, which describes the limit of the overhang as more books are added. The term "Harmonic Overhang" was confirmed by a user referencing a publication in Science magazine titled "The Joys of Longer Hangovers." This effect illustrates principles of balance and physics in a practical scenario.

PREREQUISITES
  • Understanding of basic physics concepts related to balance and center of mass.
  • Familiarity with mathematical series, particularly harmonic series.
  • Knowledge of visual representation techniques for physical phenomena.
  • Experience with practical applications of physics in everyday objects.
NEXT STEPS
  • Research the mathematical properties of harmonic series and their applications.
  • Explore the principles of balance and center of mass in physics.
  • Investigate visual representation techniques for demonstrating physical effects.
  • Read the article "The Joys of Longer Hangovers" published in Science magazine for deeper insights.
USEFUL FOR

This discussion is beneficial for physics enthusiasts, educators, and students interested in the practical applications of mathematical concepts in everyday scenarios, particularly those exploring balance and visual effects in physical objects.

Ulfsark
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Hello,
I'm curious as to the name of a particular "effect."

Imagine a stack of 10 books, uniform in weight and size, each 9 inches across. Now Imagine flaring them out in one inch intervals, forming a staircase. The topmost book is going to be one inch out from the bottom most book, and effectively "floating." What is the name of this? I know its not a keystone, but similar. I understand how it works, but i just don't know the name of it. Thank you :)

A picture of my own creation of the effect can be viewed here: http://i653.photobucket.com/albums/uu252/ulfsark9/StackedBooks.gif
 
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The standard solution limit is the series 1/2 plus 1/3 plus 1/4 plus 1/5 etc. But a better one was published in Science magazine under the title "The Joys of Longer Hangovers"
Bob S

See longer hangover here (see post #8):
https://www.physicsforums.com/showthread.php?t=305336
 
Last edited:
Harmonic Overhang! Thank you!
 

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