9/11 Conspiracy post in progress, and it's not working

One of the many reasons offered to back the claim that 9/11 was a conspiracy is that the buildings fell at or near to a free-fall speed. I suspect the answer is here:

"The buildings did fall quickly - almost (but not exactly) at the same speed as if there was no resistance. Shouldn't the floors below have slowed it down? The huge dynamic loads due to the very large momentum of the upper floors falling were so great that they smashed through the lower floors very quickly. The columns were not designed to carry these huge loads and they provided little resistance."

It would be better to do this mathematically, though.

So we've got:

"A kilogram force,
for instance, is the force exerted by gravity on a mass of 1 kg.

1 kgf = (1 kg)(9.8 m/s^2) = 9.8 Newtons"

And kinetic energy from a falling object:

KE = (mass x velocity2)/2 or 1/2 mv2 (KE measured in joules)

And:

newtons multiplied by meters equal joules

So if I divide the KE by the distance the object has fallen in meters, I should get the dynamic load in newtons exerted by the object on the thing it hit, which I could then compare the static load exerted by the object on the support? Seems like it should work, but what do I know.

So using simplified numbers, let's pretend that stories 99-110 of the World Trade Center weighed 1 kilogram (don't like that? okay, we're just discussing failure of a tiny vertical cross section weighing a total of one kilo). A plane hits floor 98, impact blows away fire insulation, fire weakens (doesn't melt) steel, steel buckles, floor collapses, and now floors 98-110 collapse and fall 3 meters to floor 97. Floor 98 collapsed when its strength diminished below the force exerted by 1 kilo, or 9.8 newtons. What's the force that will be exerted by slightly over 1 kilo after a 3 meter fall?

I need to know the velocity, dammit. Now I'm tired of this. Found a calculator, here. It says the KE is 29.4 joules. Divide by 3 and you get 9.8 newtons. Dammit again, I'm defeated by the conservation of energy - I must be just measuring transfer between potential energy and kinetic energy. So how do you derive and compare static versus dynamic loads?

UPDATE: People in the comments are doing a much better job with this than I did.