Dr. G wrote:Einsteen and T. Sz:
I think we must be very careful about using the word decelerate when we really mean less acceleration! Indeed, many physics textbooks advise never to use the word "decelerate" but recommend instead using "negative acceleration" to avoid the ambiguity inherent in the word "decelerate".
In the example of the French building I posted yesterday, which no one has tried to calculate, (too bad, because it's very instructive), you have a good example of decreasing acceleration accompanied by a velocity increase. Thus if the upper block descends the first 7 meters in 1.22 seconds and the first 14 meters in 1.78 seconds, the drop from 7 to 14 meters obviously took 0.56 seconds. This implies that the acceleration changed from 9.4 m/s^2 to 3.69 m/s^2 at the 1.22 second mark. However it's simple to show that the velocity would have been 11.5 m/s at 1.22 seconds and 13.53 m/s at 1.78 seconds, so we should not say the upper block decelerated, because the velocity was always increasing, but rather there was a reduction in the acceleration.
And, by the way, this example nicely illustrates how precise the video measurements must be to detect these effects! After 1.22 seconds, or 7 meters of "near free fall" at 9.4 m/s^2, the block is moving at 11.5 m/s. It turns out that there is a change by a factor of two in the acceleration if the time to drop the 2nd 7 meters changes by a mere 0.04 seconds! It follows that in order to detect a jolt at 1.22 seconds (in my example!), the drop data must be recorded with a precision of better than 0.1 meters which implies a sampling rate of 10 milliseconds. I seriously doubt this level of precision is possible with any of the videos we are discussing.
It isn't just reduced acceleration in the abc tower, although that does occur after the first two story fall probably due to the loose debris of the demolished floors, there was a real 15 to 20% velocity loss
after the third story of the fall. This would have been when the upper block impacted the intact lower block. In the terms you would like to use, that means there was negative acceleration
. It is quite unambiguous also, as it takes time for the velocity to recover and the velocity drop can be detected with more than one data point. Measure it and see for yourself.
In WTC 1 the energy requirements to buckle the columns on the 97th and 99th floors would have drained 85% of the pre-impact velocity and conservation of momentum in picking up the 98th floor slab would have reduced it further. It would have been a dramatic velocity loss if there was an impulse after a 12 foot drop. There would then have been about a 1000 millisecond window to detect the velocity loss while it was recovering to pre-impact levels. But we don't see this velocity loss in WTC 1, therefore there was no negative acceleration, which means no force amplification and no natural mechanism for collapse. There is no way around that and that is why Dr. Bazant thought there had to be an impact and velocity loss or negative acceleration.