WORLD TRADE CENTER COLLAPSE AS INELASTIC COLLISION, AND THE “VARIABLE MASS” PROBLEMS IN PHYSICS. WHY- WITHOUT A CONTROLLED DEMOLITION OF BASEMENT – WTC1 COLLAPSE WOULD HAVE STOPPED 15 STORIES BENEATH. Alberto Miatello Abstract In these years since September 11, 2001, many remarkable studies and specialists have correctly criticized and challenged the “official” version and hypothesis that just a “gravity-driven” collapse of top buildings, after structural weakening by airliners crashes and fires, could have possessed energy enough to totally crushing down both Twin Towers, (and especially WTC1, whose top damaged and falling 12 stories were only 10% of total building) and also WTC7(which suffered neither an airliner crash nor big fires!). However, no alternative study – as far as known – proposed yet a physical/mathematical model explaining why, how and where the collapse of top WTC1 alone would have stopped long before the total destruction of building. Therefore, this paper is the first trying to set out and modellize the problem of WTC1(and WTC2) collapse as an inelastic collision in the frame of “variable-mass” problems of physics, in which a variable initial mass (Mi) - here the top 12 falling stories - with a known accretion/ablation factor, under two contrary forces (here gravity (g) against structural resistance () of steel beams, concrete flooring, etc. ) and thereby receiving a constant “thrust”, gets turned into a final mass (Mf). How powerful and correct this model is, can be evaluated just thinking that the “variable mass” approach in physics and engineering was many times used, since the beginning of XX century, to precisely calculate the energy to send rockets to space and to the Moon (it is also known as the “rocket equation”). Hence, just the many times suggested hypothesis of a controlled demolition, i.e. the demolition of Twin Towers mainly through blasting charges at the basement, can explain their total and quick collapse. whereas the “gravity -driven” total demolition of Twin Towers by the collapse of top buildings alone is an impossible mechanism in physics. This model can also explain what really happens, in physical/mathematical terms, both when a controlled demolition succeeds in totally destroying a building, and when it fails with just a resulting partial destruction. “A problem well put is a problem half-solved” John Dewey Introduction: why “super-experts” sometimes fail. Let us start this paper with a digression, and a bit ironical memory. In 1993 an Italian film, “Caro Diario”, winner of 1994 Cannes Filmfestival [1] described the misadventures of the protagonist, Nanni Moretti (who was also the movie director and producer), when he was diagnosed a Hodgkin disease, a form of cancer of lymphatic system. At the beginning his first symptom was just a persistent itching of skin, particularly during night hours. Moretti therefore thought he was affected by a skin disease, and consulted several dermatologists, even the most renowned and expensive, and he was diagnosed in different ways, and prescribed a lot of medicines for skin diseases. However, as his health conditions were not improving at all, and he was also losing weight, at the end he consulted a medical internist and radiologist, who soon diagnosed Moretti’s actual disease, and directed him toward an effective therapy, rescuing him. Now the question is: why those “super -specialists” and dermatologists failed, whereas the medical internist found the correct diagnosis? Probably because those dermatologists were too much – surely for professional tendency – focusing on a “particular”, i.e. skin, rather than correctly thinking to put that symptom in the “general” framework of patient’s body. Something very similar happened with the scientific analysis of WTC collapse. Prof. Bazant, a renowned specialist in civil engineering whose analysis are almost totally in agreement with the official conclusion by NIST, wrote [2] : “…When the next buckle with its group of plastic hinges forms, the upper part has already traveled many floors down and has acquired a much higher kinetic energy” (??). Sadly for Bazant, but the mechanism he described is a blatant violation of the main laws of Physics! Actually, it is simply impossible that a mass A which impacts a mass B in rest could acquire more kinetic energy. On the contrary – as any textbook of Physics can tell you and we shall see – the final energy after impact will always and mathematically be lower than before! An error such as that is so big that all the following analysis becomes fatally spoiled.