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Old 29th October 2006, 11:37 AM   #281
R.Mackey
Philosopher
 
Join Date: Apr 2006
Posts: 7,854
Originally Posted by TruthSeeker1234 View Post
Huh? Walk me through this Mackey.
Glad to. Thank you for entering an actual discussion. This way, we can both learn something.

Originally Posted by TruthSeeker1234 View Post
First, free-fall time in a vacuum is 9.2 sec, but air resistance adds to that, in relation to the ratio of surface area to mass.
Air resistance adds very little to that. As I have noted here dozens of times, the tower is not falling in a free-stream of still air. The only air drag on falling objects is on the sides.

Even if it was, air drag creates a drag force proportional to the square of the falling object's velocity. Because this is a non-linear relationship, the drag will be a minor correction until the velocity becomes reasonably close to the terminal velocity of the object falling. A steel girder will have a terminal velocity in excess of 110 meters per second. Free-fall in vacuum for 9.2 seconds only gets you to 90 meters per second. So even at worst, air drag is minor.

But remember that we are concerned with an object that falls on itself and accelerates, not one that falls at "free-fall" speeds. If we assume the top of the tower hits ground in 15 seconds, and accelerates at a constant rate, then its speed at impact is only 56 meters per second. Again, even if it fell in a free stream of air which it didn't, this means the drag force is at most only a quarter that of gravity. And remember, this is for the very top which moves the fastest. The overwhelming majority of the tower never gets to those speeds. When we also take into account the fact that it didn't fall in a free-stream, we may safely neglect drag entirely.

Originally Posted by TruthSeeker1234 View Post
You have this backwards. If free-fall is 66% of actual fall time, then 33% is left for deformation, not 66%. If you adjust your free fall time to be 12 seconds (more reasonable considering air), then you have 3/15 or 1/5 or 20% of PE available.
No, I don't. You see, the fact that it slows down 33% means that 1 - (0.66)2 = 54% is left for deformation.

Likewise, slowing to 12 seconds (a 25% slow down), not supported by the video but let's do it anyway, leaves 1 - (0.75)2 = 43% available for deformation. Plenty.

Think of it this way. How long does it take you to stop your car when you're driving 50 kph? Now try it from 100 kph. Is the stopping distance the same, or longer? Why is this? (It's because energy scales with the square of velocity.)


Originally Posted by TruthSeeker1234 View Post
This is imagining that the entire PE of the building is going to be directed toward the work. Thus you are imagining an entire tower on top of the actual tower, the "trash compactor" model of LARED, debunked by Wood.

http://www.democraticunderground.com...&mesg_id=50155
Wood is severely out of her depth.

The "lost" energy is all going towards deformation. Where else can it go?

Last edited by R.Mackey; 29th October 2006 at 12:08 PM. Reason: Took on the "12 Second" hypothesis.
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