Let's see:
KE = 1/2mv^2
The mass of the towers was about 450 million kg, according to this. Four sources, he has. I think that's pretty definitive. So now we can take the KE of the top floor, and divide by two- that will be the average of the top and bottom floors. Then we'll compare that to the KE of a floor in the middle, and if they're comparable, then we're good to go- take the KE of the top floor and divide by two and multiply by 110 stories. We'll also assume that the mass is evenly divided among the floors, and that they were loaded to perhaps half of their load rating of 100lbs/sqft. That would be
208ft x 208ft = 43,264sqft
50lbs/sqft * 43264sqft = 2,163,200lbs = 981,211kg
additional weight per floor. So the top floor would be
450,000,000 kg / 110 floors = 4,090,909 kg/floor
so the total mass would be
4,090,909 kg + 981,211 kg = 5,072,120 kg/floor
Now, the velocity at impact we figured above was
90.4m/s
so our
KE = (5,072,120kg x (90.4m/s)^2)/2 = 20,725,088,521J
So, divide by 2 and we get
10,362,544,260J
OK, now let's try a floor halfway up:
t = (2d/a)^1/2 = (417/9.8)^1/2 = 6.52s
v = at = 9.8*6.52 = 63.93m/s
KE = (mv^2)/2 = (5,072,120kg x (63.93m/s)^2)/2 = 10,363,863,011J
Hey, look at that! They're almost equal! That means we can just multiply that 10 billion Joules of energy by 110 floors and get the total, to a very good approximation. Let's see now, that's
110 floors * 10,362,544,260J (see, I'm being conservative, took the lower value)
= 1,139,879,868,600J
OK, now how much is 1.1 trillion joules in tons of TNT-equivalent? Let's see, now, a ton of TNT is 4,184,000,000J. So how many tons of TNT is 1,139,879,868,600J?
1,139,879,868,600J / 4,184,000,000J/t = 272t
Now, that's 272 tons of TNT, more or less; five hundred forty one-thousand-pound blockbuster bombs, more or less. That's over a quarter kiloton. We're talking about as much energy as a small nuclear weapon- and we've only calculated the kinetic energy of the falling building. We haven't added in the burning fuel, or the burning paper and cloth and wood and plastic, or the kinetic energy of impact of the plane (which, by the way, would have substantially turned to heat, and been put into the tower by the plane debris, that's another small nuclear weapon-equivalent) and we've got enough heat to melt the entire whole thing.