Recently, thanks to my friend Martin I learned of a fascinating video, the author of which performed some model experiments to prove that 9/11 was an inside job.
I strongly recommend you to watch that video, too!
The author has modeled World Trade Center floors using cement boards attached to a supporting structure. Then, he has dropped a steel weight on the boards to show that the weight decelerated—while the footage of the twin towers collapse shows some acceleration! From that, he concluded that the “gravity collapse” theory must be wrong.
Frankly, there are some assumptions that I tend to oppose. In particular, the author claims that any theory is good only when it’s proven by experiment. True. But the science concerning twin towers collapse has been firmly established since sir Isaac Newton’s times. We don’t have to prove that classical mechanics works! Granted, such attempts make for a good pastime, but it’s very and very unlikely that there’s any revolutionary science that way.
In that regards, the author’s work can and should be checked against some simple physical models to see if he has possibly missed anything important.
Let’s introduce our model.
We have n planks each of mass m, the 1st plank is the topmost one, the nth plank is the bottommost one, and each successive pair of planks is separated by a height h. At the height H above the 1st plank, there’s a weight M.
Each plank is attached to some supporting structure, so they don’t fall. Now there’s an important condition — it takes energy A to break any plank from the supporting structure. That energy can be delivered through impact; if a plank is successfully detached from the supporting structure by the falling mass, it starts to fall down, too, otherwise it remains still.
The weigth M starts to fall. On its way down, it might break some planks from the supporting structure, increasing the mass that falls down, but losing parts of the energy it gained through the fall.
It becomes complicated, so let’s write down some equations. I’m lazy, so let’s do it the simple way. Consider all impacts to be inelastic. Let’s just figure out the speed of the falling mass immediately after each impact. That way, let’s define v_i to be the speed of the falling mass immediately after impact with i-th plank. And, let’s calculate the values of v_i for each i = 1…n.
We won’t get a continuous function of speed vs time that way, but we will still get the essential information — will the falling mass decelerate upon each successive impact and eventually stop, or will it actually accelerate.
How do we figure that out? Easy! Let’s just write down the law of conservation of energy.
Assume that after the first impact, the weight M keeps moving together with the 1st plank. Comparing the energy of the system with the initial state, we have
I would just remind you that A is the energy required to liberate a plank from its supporting structure, so that it becomes a free falling mass. In the important case when the right side of the equation is negative, the plank remains attached to the supporting structure, and any movement stops, so v_1 = 0.
Let’s just keep going, and write the law of conservation of energy for the two states: immediately after impact with (i+1)-th plank, and immediately after the impact with i-th plank.
In case the right side of the equation is negative, any movement stops and v_(i+1) becomes zero. Of course, it doesn’t follow from this equation, it’s just an additional condition. In case the movement stops, the work spent on unsuccessfully breaking the (i+1)-th plank free will be somewhat less than A, and you would have to amend the equation respectfully. Also, if we follow that logic and just look at the value of v_(i+1), we don’t distinguish the cases where the (i+1)-th plank is partially broken free, and the movement stops, and when the plank is fully liberated and the movement continues with zero initial speed. But the latter case is an oddity that would be fairly hard to achieve in practice, so let’s just treat the value of v_(i+1) as the stop condition: if it’s positive, the movement continues, if it’s zero, any movement stops forever.
Looking at the equation above, one can feel that A is the important parameter. If the value of A is big, the movement will stop soon. If it’s low, the falling mass will keep accelerating…
It’s time to write some code (it’s Matlab, but you can try to run it in Octave, with minor amendments) and look at the results of the simulation!
In the first test, let’s use the following parameters: M = 10 kg, H = 2 m, m = 5 kg, h = 0.1 m, A = 60 J. Sixty joules is a good punch, for a beginner. So, we get this:
As we can see, the weight M acquires some energy during its free fall before the first impact, so it keeps moving, persistently decelerating before it stops, unable to break the fifth plank free.
It’s fully consistent with the experiments run by the author of the video!
If we just stop here, we could claim that the official version of the 9/11 is a lie, and the twin towers could not have collapsed via the gravity force alone.
Instead, let’s just play a little bit with our simulation. What happens, if we lower the value of A, so that A = 40 J?
Voila! After hitting several planks and losing some energy, the mass of the stuff falling down becomes sufficiently high to break any successive plank free. It becomes unstoppable like a snowfall. More importantly, there’s a clear acceleration as more and more planks are broken free and contribute to the falling mass.
You can play with the simulation yourself, to see which conditions better represent the twin towers collapse. Or, if you have a plenty of free time, you can do some experiments. But stay safe! Playing with lower values of A means that the supporting structure will be necessarily quite flimsy, and prone to accidentally collapsing. There are some real dangers associated with that sort of experiments, so better avoid them.
To conclude, we can’t credit the author of the video with successfully modeling the twin towers collapse. He has overengineered the support system, resulting in excessively high values of A. On the other hand, we can clearly praise the author of the video for staying safe while running some physical experiments. It would have been a much sadder story, if the author of the video succeeded in creating an “artificial snowfall” with cement boards, but injured himself or died in the process.