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Old 25th August 2010, 12:17 PM   #72
R.Mackey
Philosopher
 
Join Date: Apr 2006
Posts: 7,854
Originally Posted by pgimeno View Post
Either I am in his ignore list, or the ignorance of my arguments is mere dishonesty. I explained why these were not "mistakes" in post #41.
It's the latter.

Originally Posted by alexi_drago View Post
This has come into my mind when thinking about this before and I have no idea if it's right so can someone explain why it's wrong.

The forces acting on the upper and lower blocks are equal but opposite, the force acting on the lower block does not accelerate the lower block downwards but the force on the upper block does accelerate the upper block upwards so there is more destructive force acting on the lower block.
This is not the only factor, but it too is partially correct.

Think of it in terms of impulse -- the total change of momentum at a particular impact. Impulse is equal and opposite, by conservation of momentum. Impulse is equal to F delta-T (force times the time over which the force is applied), or M delta-V (the raw change of momentum in its familiar definition P = m V).

When we look at the "upper block," it's delta-V is smaller than the delta-V experienced by the newly broken part of the lower block. As you say, the upper block decelerates by an average 1/3 g, while the lower block accelerates by an average 2/3 g. This is because the participating part of the lower block masses less than the participating part of the upper block -- it really is the compacted mass and upper block versus a small number of floors at a time, not the entire lower block.

The reason only part of the lower block participates at any given time is because the lower block is still a mostly intact sparse structure of braced columns. When it's hit, the columns lose bracing, get loaded eccentrically, shear their welds and bolts, and in some cases are totally overwhelmed and fracture entirely. These pieces break at a stress much too low to actually support the descending mass. This also has nothing to do with the strength of the perfectly intact building -- the descending rubble heap isn't contacting the lower structure at its strongest points, and it's introducing brand new failure modes, so the effective opposing strength of the lower structure is far lower than its ideal carrying capacity. Furthermore, where the lower structure does resist at or near its ideal strength, it can only do so for a very brief delta-T -- until reaching its failure strain, which takes only about ten milliseconds at the speeds of collapse -- and this is not enough to amount to all that much total impulse.

The upper chunk, in contrast, is cushioned by a thick layer of rubble. This is compacted about as far as it can, thus it doesn't have those complex failure modes and it doesn't suffer much more "damage" even at much higher stresses. So the rubble pile remains, and the lower structure gives way. This is for the same reason you don't sink into the ground, even though you can push your finger easily through a cupful of soil.

The "upper block," what remains of it, rides on top of this cushion of debris. It is supported pretty well. It also only decelerates at that lower rate, thanks to the much greater inertia of the upper block + debris. So the only real force it suffers is the inertial force, i.e. its own self-weight times its deceleration, again about 1/3 g. It can be expected to survive this deceleration. It's only when the rubble pile has nowhere else to go and the upper block has to suddenly stop, dissipating all of its momentum in mere milliseconds, that it totally fails.

Again, this is slightly idealized, but you get the point. Unless you're a Truther.

Last edited by R.Mackey; 25th August 2010 at 12:20 PM.
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