The roof line of WTC1 (The North Tower) begins dropping with sudden onset and accelerates uniformly downward at about 64% of the acceleration of gravity (g) until it disappears into the dust. This means it is meeting resistance equal to about 36% of its weight. The implication of this, however, is that the force it is exerting on the lower section of the building is also only 36% of its weight. This is much less than the force it would exert if it were at rest.
The acceleration data thus prove that the falling top section of the building cannot be responsible for the destruction of the lower section of the building. A complete analysis has been published in the article entitled "Destruction of the World Trade Center North Tower and Fundamental Physics" Journal of 9/11 Studies, Vol 28, Feb 2010. (Some calculus and basic physics required.)
Downward Acceleration of the North Tower
This is the start of the collapse of World Trade Center, number One, also known as the North Tower.
We are here tracking the motion of the roof line at two-tenths second intervals through approximately 32 meters, or 8 stories. This graph shows the height of the roof line as a function of time.
First note that there is a sudden onset of collapse as the point we are tracking makes a sudden transition from being at rest to an approximately constant downward acceleration.
So far so good. But now turn it around. Newton's third law says interactions between objects work both ways. The forces two objects exert on each other are always equal and opposite. If the upward force acting on the falling block is 36% of the weight of the falling block, the downward force exerted by the falling block must be exactly the same, 36% of the weight of the falling block.
In other words, the top section of the building is exerting less force on the lower, stronger, undamaged structure than it would if it were simply sitting motionless. Therefore, as long as the top section of the building is in uniform, downward acceleration it cannot possibly be providing sufficient force to destroy the building.
This may seem counter-intuitive to you. You might think a falling block coming down on the lower section of the building would observe a greater force than a stationary block. But that is true only if the falling block actually impacts the lower block, which would cause the falling block to decelerate. The only way the falling block can continue to accelerate smoothly, as we see here, is for the lower section of the building to give way without significant resistance.
If this rate of acceleration continued all the way to the ground the building would fall about 11.5 seconds. This is close to the observed collapse time.
Given the fact that it is accelerating downward, the top section of the building, whatever its condition, cannot possibly be destroying the lower section of the building.
The destruction of the building must be caused by something else.
[I want to acknowledge the work of Graeme MacQueen and Tony Szamboti who made similar measurements by other means and have reached similar conclusions. Their paper is entitled "The Missing Jolt"]