Conservation of Momentum. As floors fell they gained mass of the floors above them The impact of a fueled Boeing 767 for a transcontinental flight: American 11 – Boeing 767-223ER http://en.wikipedia.org/wiki/Boeing_767#... Fuel: 24,100 gallons (91.000 L) Mass: 179,170 kg Speed: Full Power, dive ~ 915 kmh 915,000 m /hr / 3600 s/hr = 254.2 m/s KE = 0.5 * 179,170 kg * (254.2 m/s)^2 KE = 5.79 * 10^9 J 1 lb TNT = 4.7 *10^6 J 5.79 * 10^9 / 4.7 * 10^6 = 1231 pounds TNT Compare to US Military MK-84 Bomb loaded with H6 explosive 945 lbs TNT * 1.36 to convert to H6 = 1,285 lbs TNT http://en.wikipedia.org/wiki/Mark_84_bom... http://en.wikipedia.org/wiki/Composition... American 11 hit WTC1 (North Tower) with the kinetic energy of a US Air Force MK-84 bomb. That is more than enough to bring down a high rise, curtain wall, steel frame commercial office building….
Or the US Air Force needs bigger bombs. Add to that 24,000 gallons of burning Jet A Fuel running down the stairwells, elevator shafts, and utility conduits. It is amazing the building stood as long as it did.
Not, that it failed. 24,000 gallons is over 200 US Military Mark 77 Incendiary Bombs.
I'm not 100% familiar with which exact floor collapsed first, but let's take your example at face value since it is close enough and exact accuracy is not relevant due to the design of the building (or any skyscraper for that matter). Say you have the 93 story tall WTC tower. The 82nd floor columns suddenly collapse, sending the 83rd-93rd floors crashing down on the 81st.
Keep in mind, as you said, the top 11 floors are still all "stuck" together and intact. The entire weight of those floors are hitting the floor supports and columns of the 81st floor. They are absolutely not designed in anyway to support that much weight, much less the energy involved in them falling approximately 15 feet.
The way a column fails when a sudden high force impact hits it straight on is called buckling. It will instantaneously fail and essentially turn into a hinge. That is, it just bends as if it were a thin wire.
Now you have 12 floors coming down at the 80th floor. The mass of floors moving downward will actually have almost 2x as much energy as when it hit the higher floor because the majority of it has now dropped 30 feet. The same thing happens.
Instant failure. Now 13 floors. So on... This is why they collapsed at "near free-fall".
The amount of force that each floor was able to resist is almost negligible compared to the weight and kinetic energy the mass of floors had. It "progressively" snowballed, gained more and more energy with each floor it took down. Relating it back to your Newton's Law #3: Every action there is equal and opposite reaction.
Our "action" is the mass of floors falling straight down at the acceleration of gravity (32.2 ft/s2). Our force is the mass of those floors (HUGE) multiplied by that. The "reaction" is the strength those columns have to "push" up against that huge mass of floors.
As you can imagine, it was infinitely smaller than the energy that was transferred into them. This may be counter intuitive to some without an engineering degree, as those columns are holding up the ENTIRE building! Surely they could have slowed down the collapse or at least held it for a period of time right?
NO! When the building is stationary (prior to collapse) you have a FORCE that the weight is putting on the columns. There is NO kinetic energy.
Once you basically "drop" that huge mass onto the columns, you now have a HUGE amount of energy being transferred into the columns that is significantly higher than the column's strength, thus it fails, and it fails instantly. Think about it like this. 4 two-by-fours can easily hold up a heavy SUV.
Now imagine dropping that SUV 15 feet onto those two-by-fours. They will fail, and it will not slow it down hardly at all.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.