We must make it convenient for people to find the definition so they can judge if the conservation of momentum is relevant.

Fall of Physics

In my rarely humble opinion (LOL) many of the people who claim the WTC towers underwent gravitational collapse seem to exaggerate what gravity can do. This is a table showing the velocity and distance fallen by an object from a stationary start. In the first 1/10th of a second the mass moves less than 2 inches and is only traveling at 3.2 ft/sec. So a gravitational collapse of the WTC meant the falling top portion must have accelerated what it struck much more than gravity could have and also have broken whatever was supporting that intact portion of the building.

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. v == initial velocity

Time V = at + v D = 1/2 at^2 + vt

v = 0

00.1 3.2 ft/sec 0.16 ft 1.92 in.

00.2 6.4 ft/sec 0.64 ft 7.68 in.

00.3 9.6 ft/sec 1.44 ft 17.28 1n.

00.4 12.8 ft/sec 2.56 ft

00.5 16.0 ft/sec 4.00 ft

00.6 19.2 ft/sec 5.76 ft

00.7 22.4 ft/sec 7.84 ft

00.8 25.6 ft/sec 10.24 ft

00.9 28.8 ft/sec 12.96 ft

01.0 32.0 ft/sec 16.00 ft

01.1 35.2 ft/sec 19.36 ft

01.2 38.4 ft/sec 23.04 ft

01.3 41.6 ft/sec 27.04 ft

01.4 44.8 ft/sec 31.36 ft

01.5 48.0 ft/sec 36.00 ft

01.6 51.2 ft/sec 40.96 ft

01.7 54.4 ft/sec 46.24 ft

01.8 57.6 ft/sec 51.84 ft

01.9 60.8 ft/sec 57.76 ft

02.0 64.0 ft/sec 64.00 ft

No matter what brought the towers down the conservation of momentum cannot have been violated. This is the equation for an inelastic collision in which two masses stick together. If the second mass is stationary then v2 is zero.

Conservation of Momentum:

(m1 * v1) + (m2 * v2) = (m1 + m2) * v3

This means the ratio of the stationary mass to the impact mass greatly affects the resulting velocity. If the impact mass is smaller then it will be slowed considerably, but in the opposite case the velocity of the stationary mass will change a lot. But in a gravitational collapse there will be the additional effect of gravitational acceleration before and after impact.

So I have done the calculations for 3 "magical" cases. In each case four masses are magically suspended and when struck from above each mass is released with no resistance. In case #1 the 4 masses are are equal, 2.5 tons each. In case #2 the masses are in the sequence 1, 2, 3 and 4 tons from top to bottom. Case #3 is the reverse sequence of 4, 3, 2 and 1 ton. When the masses are struck from above they begin moving on the basis of conservation of momentum and undergo gravitational acceleration until the next object is struck. Case #0 is just a 10 ton mass dropped from 64 feet with no impacts and is used as a reference case.

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. mass 1 mass 2 mass 3 mass 4

64 feet feet 48 feet 32 feet 16

Case 0 10 ton 0 0 0

speed 0 32 45.25 55.43 64 ft/sec

time 0 1 1.41 1.73 2 sec

Case 1 2.5 ton 2.5 2.5 2.5

speed 0 32 16 35.78 23.85 39.91 29.93 43.82 ft/sec

time 0 1 1.618 14% 2.12 23% 2.554 sec 28%

Case 2 1 ton 2 3 4

speed 0 32 10.67 33.74 16.87 36.17 21.70 38.66 ft/sec

time 0 1 1.721 22% 2.324 34% 2.854 sec 43%

Case 3 4 ton 3 2 1

speed 0 32 18.29 37.35 29.05 43.23 38.91 50.37 ft/sec

time 0 1 1.58 12% 2.023 17% 2.381 sec 19%

The Case line specifies the weight of mass at each of the 4 heights, 64, 48, 32 and 16 feet. These heights were chosen because they correspond to the "1/2 * 32 feet/sec^2" that is in the distance from acceleration equation thereby making calculations easier.

The speed line has the velocity of the net mass before and after impact based on conservation of momentum.

The time line has the time for the mass to fall to that point and the percentage difference from Case 0.

A body in freefall dropped from the top of the World Trade Center would have taken 9.2 seconds to reach the ground. The NIST says the tower that took longer to collapse did it in 11 seconds. So that is only 20% longer than the freefall time. But the WTC collapses required that the tens of thousands of tons of steel and concrete which had held up the buildings for 28 years be bent and broken and crushed. So how is it that only my absurd and miraculous collapse with inverted masses and disappearing supports comes down that fast in relation to freefall? A skyscraper must be bottom heavy and Case #2 using that distribution has double that percentage of time but it didn't require kinetic energy be used to break supports.

So what is the story with all of these people that claim there was a gravitational collapse but also pretend that knowing the TONS of STEEL and TONS of CONCRETE on every level isn't necessary? I have demonstrated that changing the distribution of mass alters the collapse time regardless of the strength of the material involved and how much kinetic energy would be required to break it.

Time and velocity calculations after impacts:

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. After Impact #1:

Case 1: 16 = 16t^2 + 16t 1 = t^2 + t t = 0.618 19.78+16

Case 2: 16 = 16t^2 + 10.67t 1 = t^2 + 0.666875t t = 0.721 23.07+10.67

Case 3: 16 = 16t^2 + 18.29t 1 = t^2 + 1.143125t t = 0.58 18.56+18.79

After Impact #2:

Case 1: 16 = 16t^2 + 23.85t 1 = t^2 + 1.490625t t = 0.502 16.06+23.85

Case 2: 16 = 16t^2 + 16.87t 1 = t^2 + 1.054375t t = 0.603 19.30+16.87

Case 3: 16 = 16t^2 + 29.05t 1 = t^2 + 1.815625t t = 0.443 14.18+29.05

After Impact #3:

Case 1: 16 = 16t^2 + 29.93t 1 = t^2 + 1.870781t t = 0.434 13.89+29.93

Case 2: 16 = 16t^2 + 21.70t 1 = t^2 + 1.35625t t = 0.53 16.96+21.70

Case 3: 16 = 16t^2 + 38.91t 1 = t^2 + 2.431875t t = 0.358 11.46+38.91

http://www.centerforinquiry.net/forums/viewreply/52039/
The "aim" here is to answer "Do you believe the World Trade Center was taken down by controlled demolition?"

in the context of "World Trade Center? What Really Happened?"

Physics isn't about believing. Physics is about understanding. One would think a structural engineer could understand that. :funny:

psik