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Analyzing the Physics in the Initial Collapse (continued)

o Between Figs C4 & C5 ("179" to "203") the distance $s_1\approx 45$ ft and $t_1=0.75$ s, so $a_t \approx 160$ ft/s$^2$.
o Between Figs C4 & C6 ("179" to "211") the distance $s_2\approx 75$ ft and $t_1=1.0$ s, so $a_t \approx 150$ ft/s$^2$.
Comparing the resulting shift force $\vert\mathbf{F_s}\vert$ to that of the force of gravity $\mathbf{F_g} = m_t \mathbf{g}$ yields for both cases:
\begin{displaymath}
\vert\mathbf{F_s}\vert/\vert\mathbf{F_g}\vert = a_t/g\approx 5
\end{displaymath} (4)

where $g = \vert\mathbf{g}\vert = 32$ ft/s$^2$ is the gravitational acceleration. Thus $\mathbf{F_s}$ is 5 times as large as Fg, whereas the $\mathbf{F_b}$ is as large if not larger (probably considerably so) than than the shift force. That is because breaking two segments of the Tower apart should be harder than moving the top one once they are broken. Thus Eqs (1)-(4) lead to an inescapable conclusion:

$\mathbf{F_T}$ is about an order of magnitude larger than the force of gravity. It could be even larger depending on how large the force is $\mathbf{F_b}$ that breaks the 2 segments of the building apart is.


Crockett Grabbe 2009-02-01