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Akareyon at ATS wrote:"TBH, I read your ponderings "is momentum conserved, yes, no, a little, some more, a little less" and they somewhat scared me..."
I wrote:I totally understand why that might make you apprehensive, after all isn't it a physical law that momentum is always conserved? Yes, but only if the entire system is considered. Here, the entire system is the building+Earth and, at that scale, momentum is indeed conserved. When ignoring the planet, as we are, momentum is most assuredly NOT conserved. What was the momentum of the rubble pile? Zero. QED.
The tower is coupled to ground. As the upper section begins to descend, the lower section (despite experiencing overload conditions locally) experiences a time-averaged force less than the static load of the upper section. The lower section unloads. As a result, the Earth moves up to meet the falling upper block!
You really want to go there, or would you rather acquire confidence that I'm absolutely correct that momentum is not conserved in the system under study?
I wrote:In the last post, I confirmed that I agree with the basic tenets of classical mechanics by saying momentum is conserved globally but specified correctly that momentum is not conserved locally - at the scale of the tower.
Now, please allow me to tug you back the other way. I claim momentum IS conserved locally at a finer granularity, at least with respect to the slab models I was discussing in the writings which apparently disturbed you, and of the type we're discussing here. An abstraction is that collisions between slabs occur instantaneously, therefore no displacement occurs during collision and no work can be done against coupling to ground. Therefore, momentum IS conserved during collision. Good thing, too, because without some invariant, the mechanical problem cannot be solved.
Now, do you understand the back-and-forth? It wasn't waffling, it was analysis.
I wrote:If collapse goes to completion in a momentum-only (no supports) inelastic configuration, then the entire event can be considered a single inelastic collision in the sense that the final velocity of the debris pile just before hitting ground is that given by a collision between the upper block and the lower block as point masses - ignoring gravitational effects, of course. So, in a horizontal arrangement of inelastic slabs, a single impactor hitting a line of 99 masses has the collective debris zone speed reduced to 1/100th that at the final collision. Makes perfect sense.
OneWhiteEye wrote:ODE Toolkit... no tabular data...
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