Spreadsheet adjusted for average floor height of 3.79 meters or approximately 12 feet. Time to ground impact: 13.573 seconds now. Again, we're totally neglecting the minimal mass lost to pulverization that escapes vertical descent due to air compression (the dust you see) and aerodynamic drag, and of course the nugatory time associated with Did you think that adding .79 meters per floor would increase the collapse time by roughly 27%??? Nope. The increased space between floors gives the falling mass more time to accelerate unimpeded without having to transfer momentum. Hence the difference amounted to about 1.6 seconds total. About a 13% difference from my rough dimensions in the original model.
Oh, in the original, I did have a 7th column but didn't copy it. It was a dummy column for outputs of an iterative logic loop to ensure the distance traveled was 3.79 meters (within .02 meters). I used this instead of a quadratic to plug in time intervals that would satisfy the distance equation of motion.
The sheet below shows in 1: mass 2: velocity the instant before impact 3: (duh) 4: velocity after impact 5: Delta V 6: Time between successive impacts 7: Total time elapsed. If you want the iterative column and the code to satisfy some morbid curiosity, I can of course provide them as well.
As for the energy loss due to buckling, shearing, etc...since energy is conserved, as Cornelius mentioned, it becomes heat and acoustic energy (primarily heat of course.)
Edit, just perused the amateur paper linked. The assumption of flow is erroneous first off. Even if flow happened very briefly, and a portion of a lower floor failed, the failure would propagate in short order to catastrophic total failure in extremely short order due to the nature of the supports. The redundancies in velocity calculations are also completely amateurish. As stated earlier...reputable sources. Some kids who clearly haven't made it out of undergrad vs say...scholars from Northwestern, one of the most reputable schools in the nation (who's findings WERE reviewed)...would not be considered credible...ever. Just because it looks good to you, does not mean that it is. That paper looks like my sophomore year lab reports (only I would have obtained the right results.) Yah, I'd bet on the team from Northwestern.
Mass Velocity (initial) m/s g new velocity Velocity Dif time/floor total time
3 8.62 9.8 6.47 2.16 0.880 0.880
4 10.78 9.8 8.62 2.16 0.440 1.320
5 12.19 9.8 10.16 2.03 0.364 1.684
6 13.32 9.8 11.42 1.9 0.323 2.007
7 14.3 9.8 12.51 1.79 0.294 2.301
8 15.2 9.8 13.51 1.69 0.274 2.575
9 16.03 9.8 14.43 1.6 0.257 2.832
10 16.8 9.8 15.27 1.53 0.242 3.074
11 17.53 9.8 16.07 1.46 0.231 3.305
12 18.24 9.8 16.84 1.4 0.221 3.526
13 18.91 9.8 17.56 1.35 0.212 3.738
14 19.56 9.8 18.26 1.3 0.204 3.942
15 20.19 9.8 18.93 1.26 0.197 4.139
16 20.8 9.8 19.58 1.22 0.191 4.330
17 21.39 9.8 20.2 1.19 0.185 4.515
18 21.96 9.8 20.81 1.16 0.180 4.695
19 22.52 9.8 21.4 1.13 0.175 4.870
20 23.07 9.8 21.97 1.1 0.171 5.041
21 23.6 9.8 22.53 1.07 0.166 5.207
22 24.13 9.8 23.08 1.05 0.163 5.370
23 24.63 9.8 23.61 1.03 0.159 5.529
24 25.13 9.8 24.12 1.01 0.155 5.684
25 25.61 9.8 24.63 0.99 0.152 5.836
26 26.1 9.8 25.13 0.97 0.150 5.986
27 26.57 9.8 25.62 0.95 0.147 6.133
28 27.03 9.8 26.1 0.93 0.144 6.277
29 27.48 9.8 26.57 0.92 0.141 6.418
30 27.93 9.8 27.03 0.9 0.139 6.557
31 28.37 9.8 27.48 0.89 0.137 6.694
32 28.81 9.8 27.93 0.87 0.135 6.829
33 29.24 9.8 28.38 0.86 0.133 6.962
34 29.66 9.8 28.81 0.85 0.131 7.093
35 30.08 9.8 29.24 0.84 0.129 7.222
36 30.49 9.8 29.66 0.82 0.127 7.349
37 30.89 9.8 30.08 0.81 0.125 7.474
38 31.29 9.8 30.49 0.8 0.124 7.598
39 31.68 9.8 30.89 0.79 0.122 7.720
40 32.07 9.8 31.29 0.78 0.120 7.840
41 32.45 9.8 31.68 0.77 0.119 7.959
42 32.84 9.8 32.07 0.76 0.118 8.077
43 33.21 9.8 32.45 0.75 0.116 8.193
44 33.58 9.8 32.83 0.75 0.115 8.308
45 33.94 9.8 33.2 0.74 0.113 8.421
46 34.31 9.8 33.58 0.73 0.113 8.534
47 34.67 9.8 33.95 0.72 0.111 8.645
48 35.02 9.8 34.31 0.71 0.110 8.755
49 35.38 9.8 34.67 0.71 0.109 8.864
50 35.73 9.8 35.03 0.7 0.108 8.972
51 36.08 9.8 35.38 0.69 0.107 9.079
52 36.42 9.8 35.74 0.69 0.106 9.185
53 36.75 9.8 36.07 0.68 0.104 9.289
54 37.09 9.8 36.42 0.67 0.104 9.393
55 37.43 9.8 36.76 0.67 0.103 9.496
56 37.76 9.8 37.1 0.66 0.102 9.598
57 38.09 9.8 37.43 0.66 0.101 9.699
58 38.41 9.8 37.76 0.65 0.100 9.799
59 38.73 9.8 38.08 0.65 0.099 9.898
60 39.04 9.8 38.4 0.64 0.098 9.996
61 39.36 9.8 38.73 0.63 0.098 10.094
62 39.68 9.8 39.05 0.63 0.097 10.191
63 39.99 9.8 39.37 0.62 0.096 10.287
64 40.3 9.8 39.68 0.62 0.095 10.382
65 40.61 9.8 39.99 0.62 0.095 10.477
66 40.91 9.8 40.3 0.61 0.094 10.571
67 41.21 9.8 40.61 0.61 0.093 10.664
68 41.51 9.8 40.91 0.6 0.092 10.756
69 41.81 9.8 41.21 0.6 0.092 10.848
70 42.1 9.8 41.51 0.59 0.091 10.939
71 42.39 9.8 41.8 0.59 0.090 11.029
72 42.69 9.8 42.1 0.58 0.090 11.119
73 42.97 9.8 42.39 0.58 0.089 11.208
74 43.27 9.8 42.69 0.58 0.089 11.297
75 43.55 9.8 42.98 0.57 0.088 11.385
76 43.83 9.8 43.26 0.57 0.087 11.472
77 44.11 9.8 43.55 0.57 0.087 11.559
78 44.39 9.8 43.83 0.56 0.086 11.645
79 44.67 9.8 44.11 0.56 0.086 11.731
80 44.95 9.8 44.39 0.55 0.085 11.816
81 45.23 9.8 44.67 0.55 0.085 11.901
82 45.5 9.8 44.95 0.55 0.084 11.985
83 45.77 9.8 45.23 0.54 0.084 12.069
84 46.04 9.8 45.5 0.54 0.083 12.152
85 46.31 9.8 45.77 0.54 0.083 12.235
86 46.58 9.8 46.04 0.54 0.082 12.317
87 46.85 9.8 46.31 0.53 0.082 12.399
88 47.11 9.8 46.58 0.53 0.081 12.480
89 47.37 9.8 46.84 0.53 0.081 12.561
90 47.63 9.8 47.11 0.52 0.080 12.641
91 47.89 9.8 47.37 0.52 0.080 12.721
92 48.14 9.8 47.63 0.52 0.079 12.800
93 48.4 9.8 47.88 0.51 0.079 12.879
94 48.66 9.8 48.15 0.51 0.079 12.958
95 48.91 9.8 48.4 0.51 0.078 13.036
96 49.17 9.8 48.66 0.51 0.078 13.114
97 49.41 9.8 48.91 0.5 0.077 13.191
98 49.66 9.8 49.16 0.5 0.077 13.268
99 49.92 9.8 49.42 0.5 0.077 13.345
100 50.16 9.8 49.67 0.5 0.076 13.421
101 50.41 9.8 49.92 0.49 0.076 13.497
102 50.66 9.8 50.17 0.49 0.076
13.573
Edited by jimv, 09 June 2011 - 05:16 PM.
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