Err, would the ball from floor 110 need to strike the ball at 109 (to start 109's motion) if you're even trying to at all simulate the collapse; as the KE from floor/ball 110 is added to floor/ball 109 so floor/ball 109 accelerates faster (initially) than freefall? Or am I completely off base here?
Yes, you would need to consider that the balls get combined in order to simulate the collapse, which Judy didn't do. You would conserve momentum at the collision, not energy, and there would be energy leftover for things such as breaking the balls, and heat.
Here's something I just threw together in Excel. I'll try to explain a little what I did. In this billiard ball model, you can figure what speed it finishes at, based on the speed it started at, and the gravitational potential energy it acquires during its 12.3 foot fall. I apologize for the English units:
Vf = Sqrt( V0^2 + 2*g*h )
A close approximation of the time for each floor to fall would be the distance of 12.3 feet, divided by the average of the initial velocity and the ending velocity for that floor. This would be a little off for the first few floors, but would be pretty accurate through most of the fall. A good approximation for 110 floors.
The initial velocity for each floor would be the final velocity of the floor above it, adjusted down by the conservation of momentum of adding one more ball to the mass. For example, if 20 balls are falling at speed V from above, then by conservation of momentum the 21 balls should start their fall at V*20/21.
That's pretty much all you need to know, now just let Excel do the figuring floor-by-floor:
Code:
floor #balls V0 Vf Vavg time cuml. time
110 1 0.00 28.06 14.03 0.88 0.88
109 2 14.03 31.37 22.70 0.54 1.42
108 3 20.91 34.99 27.95 0.44 1.86
107 4 26.24 38.42 32.33 0.38 2.24
106 5 30.73 41.62 36.18 0.34 2.58
105 6 34.68 44.61 39.64 0.31 2.89
...
7 104 164.00 166.39 165.20 0.07 14.54
6 105 164.80 167.17 165.99 0.07 14.62
5 106 165.60 167.96 166.78 0.07 14.69
4 107 166.39 168.74 167.56 0.07 14.76
3 108 167.17 169.51 168.34 0.07 14.84
2 109 167.96 170.28 169.12 0.07 14.91
1 110 168.74 171.05 169.89 0.07 14.98
So by this model, the collapse should have taken 15 seconds, with plenty of energy left over for destroying the material. This kind of analysis is
not hard to do, but I guess beyond the grasp of a PhD in ME.