the "archimedes post" the other day, got me thinking about the leaning tower of pizza...i believe the math for that post can be used to crunch the numbers that structure is experiencing, here goes--
the skinny--
tower weight, + angle of lean( derive angle from height/distance off-center), % 2, = pounds of force in the direction of the lean, minus 1 = foot-pounds in the direction of the lean...
the numbers--
32,000,000 pounds + 3.9984 degrees = 32,000,003.9984
32,000,003.9984 % 2 = 16,000,001.9992 pounds of force in the direction of the lean
16,000,001.9992 - 1 = 16,000,000.9992 foot-pounds of force in the direction the structure is leaning--
so, that's the news, the leaning tower of pizza has 16,000,000.9992 foot-pounds of force trying to knock it over...
the other side( trailing-side of tilt)--
on the other side( the trailing-side of the tilt), different math is needed, if the tower were exactly straight, there would be 16,000,000 pounds, or 15,999,999 foot-pounds( of force), pushing away from the center of the tower, in all directions, however, once the tower begins to tilt, the weight shifts, to the tilting side, from all the other directions, until there is no weight on any sides, but the tilting side--
calc for trailing side--
the trailing side has -3.9985 pounds( -3.9984 foot-pounds) pushing away from the lean, and + 3.9985 pounds( or, +3.9984 foot-pounds) pushing in the direction of the lean--
cumulative lateral tork calc--
by combining the totals( 16,000,000.9992 foot-pounds + 3.9984 foot-pounds), pushing in the direction of the lean, from both sides, we get 16,000,004.9976 foot-pounds of "lateral tork", trying to tip the structure over--
ciao, john kruschke--
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