Sorry! Gravity only accelerates the object (with mass m). The contact is due to the fact that something else, another object, not gravity, is in the way of the moving object.
You are making a non-point. And you are still, seemingly purposly, ignoring an important aspect.
No impact is possible or could a kinetic force be applied from one object to another unless one of the objects is in motion in relation to the other object.
Gravity is what caused the motion of the upper section of the WTC to impact into the floors below it. Gravity gives and object potential energy due to it's position in a gravitational field in refrence to a specific point.
http://en.wikipedia.org/wiki/Potential_energy
Once the support gave out from under the upper section of the WTC, the upper section was free to go into motion. It's potential energy was converted into momentum.
Momentum is mass times velocity. (Or rather p=mv)
http://en.wikipedia.org/wiki/Momentum
Gravity provides the velocity and the mass times the velocity determins the kinetic energy the mass will impart into the object it comes into contact with.
http://en.wikipedia.org/wiki/Kinetic_energy
At contact the moving object applies a force F on the other object.
And guess where that force comes from. Guess what causes the object to move in the first place.
That force is the product of mass and the velocity which is provided by potential energy which is provided by gravity.
At contact, the other object applies a force on the moving object that happens to be -F. Newton has established that and everybody agrees today (except NIST, Bazant, Greening and other cl-wns).
Yes, equal and opposite reaction and all that.
The issue is can the structures involved survive the forces of the impacts. If the energies involved are greater than the load bearing or structural integrity of the objects they will fail. And if the structures fail they will not be able to arrest the movenment of the object in motion.
And in the case of WTC those structures that have failed and become disconnected from thier support structures will become part of the mass in motion since they 1. failed to arrest the moving mass and 2. Also have potential energy due to thier mass and position in a gravitational field. Not to mention and residual energy left over from the initial impact that caused thier failure. Gravity, in the form of potential energy, is constanly applying extra energy into the reaction as the failing structures become free to move on thier own.
That means that the moving mass has increased and is still in motion and would impart an even larger force to the structures below. If the first floor was not able to withstand the initial impact what the chances the floor below it would also be able to withstand the impacts?
If the moving object is fairly solid you may expect force -F to stop the moving object; it may, e.g. bounce. Like a ball!
Except that the WTC as an architectural structure is not solid. The individual components that make up the WTC make be considered solid object (i.e columns, beams, etc.)
If the moving object is a weak structure - like the upper part of WTC1; just columns spread around, some beams and thin concrete floors and plenty of air (95% of total volume) with total mass m - you should know that force -F will destroy the moving object when applied locally on its weakest parts, e.g. a thin floor.
You are forgetting that the moving upper section of the wtc is also applying a force on the lower section which is made up of the very same materials as the upper floors.
Remember the floors were connected to the columns so if any deformation takes place in the floor structures due to impacts, the displacement of the floor structures will cause stress to the columns and the loss of the integrity or support of the floor structures will weaken the column structure's integrity.
Bazant assumes that this is not the case. He assumes that the bottom floor of the moving object is SUPERSTRONG and can demolish anything it contacts (except the rubble on the ground)
Same thing is assumed in the videos - topic of this thread.
And you seem to be assuming that the lower section is super strong and can arrest any mass impacting upon it.
Remember the structural integrity of the upper floors may be destroyed but the aggregate mass of the materials that make up the upper section is still there and all that mass is still moving down due to gravity.
All those columns, floor sections and concrete and wall sections will continue to impact on the floors below.
And because the moving mass has volume all the energy of the entire upper section will not be expended all at once. The individual components of the upper section will cause a multitude of local failures. All those local failures will add up and some cases a local failure in a key location or support structure can lead to a progressive collapse. All it takes is a lucky impact in the right location.
But I am sorry to say that the bottom floor of the upper part of WTC1 was only designed to carry persons and furniture at a max capacity of 300 kgs/m² (or less). If you had dropped a grand piano on that floor, it (or its legs) would have made a hole in the floor.
As are the upper floors of the lower part of the WTC. The lower part of the WTC is made up of the same materials of the upper section. that would mean that the upper floor of the lower section is only designed to carry the same capacity of the lower floor of the upper section.
Imagine a million grand pianos all making holes in the upper floor of the lower section of the WTC.
Note that force -F is not applied to the total upper part with mass m. It is applied locally to a thin floor that has very little mass, and even less local strength and -F produces a very high pressure on the mowing objects floor. So -F destroys the first floor it contacts in the upper part. And then the second, and third ... and then probably the destruction stops.
You are over simplifying the interaction. The structural integrity of the entire building is compromised when the upper section became disconnected from the lower section.
Please review the architectural structure of the WTC towers. The building had a clolumn tube with in a tube structure. The upper section had what was called a hat truss structrure that connected the inner column structure to the outer column structure. Along with the floors this provided structural integrity to the building as a whole.
Once the upper section became detached the WTC lost a large part of its structural integrity.
http://911research.wtc7.net/wtc/arch/hattruss.html
Why does the local destruction stops. Simply because now, after destruction/arrest force -F = m*g is applied to the upper part via plenty of contact points, and -F happens to be the weight of the upper part. Equilibrium is reinstated.
Again you are oversimplifing the interaction. The collapse was a very chaotic event, there were many factors involved that you seem to be overlooking. You are applying tha math as if the upper and lower section were solid mass. They are not.
Once the materials become disarticulated from the structures you have many different individual interactions that can all cause local failures that can accumulate with the possibilty of progressive collapse depending on where and how structures were impacted.
The upper part, that tried to destroy the other object, now only applies F = m*g, on the other object. No big deal. Happens every time you drop something on something and when the action is arrested.
that is unless the forces involved are greater that the maximum structural stress of the objects involved. Which happens when you drop a glass bottle on another glass bottle.
Except according Bazant, of course! BUT then what you dropped must be rigid, SUPERSTRONG, and what was dropped on must be SUPERWEAK and that was not the case on 9/11. But that is what the authorities want you to believe - have FAITH son - and it terrorizes me.
And you are assuming the opposite that a super weak is being dropped on a super strong. I'd say it was more like a weak is being dropped on another weak.
Hints re the solution to the Match Box Experiment problem can be found above. It has nothing to do with scale.
Your matchbox experiment is completly missguided and has no relation to reality in refrence to the WTC.