By potential energy, I assume Dan is talking about gravitational potential energy. This is the total amount of possible “falling” energy if you drop something from any given height.
For the uninitiated/casual observer, the likely thrust of Dan’s question is to steer the conversation to the
debunked “pulverized concrete” theory , as the idiot who put that abomination of science/logic out into the interwebs started with potential energy, and tried to prove that the towers fell “too quickly” by assuming that all the concrete in the twin towers was powdered.
PE=mgh
m= mass
g= gravity, i.e. gravitational acceleration or 9.8 m/s
h= height
G is a constant, 9.8 m/s/s
H is a height of 80 stories of 3.65 meters or almost exactly 292 meters. Remember we will assume that the top thirty stories of a 110 story building start falling. 110-30=80
So now that we have g and h, we can plug them in thusly:
PE=m(9.8)(292) or PE=m2861 (rounding decimal down)
This means that, any object, if dropped from 292 meters and ignoring air friction, will hit the ground with a force of roughly 2800 times the mass.
Here is an important point. What is mass? What is weight?
Weight is a force. It is the amount of force required to hold an object of a certain mass stationary against the pull of gravity. (
see Newtons third law) When you climb on a scale you are really measuring the amount of force required to hold you at equilibrium (motionless) against gravity.
Think about what this means. This means that an object falling from 292 meters will seem to strike the ground with a force or “weight” of 2800 times what it weighed when it was held stationary, 292 meters above the ground.
The ground will then absorb the falling energy and then hold the body at equilibrium again after that energy has been absorbed to hold that mass at equilibrium/rest.
Let’s do a quickie, common sense thought experiment to help understand what the “controlled demolition” theory is trying to say.
The controlled demolition theory rests on the following assumption: “the building was too strong to have collapsed from simple gravity”
Put another way “the building could easily absorb the energy of the falling section and not fully collapse”
Does this pass the common sense muster?
Let’s take an average guy off the street. He can hold a 100 pound bag over his head for a few minutes. Say he is balancing it on his head to make things simple. In terms of physics this means he is providing a force equal to gravity in order to hold this bag motionless.
This is what the lower 80 stories did for the upper 30 stories for 30 years before 9-11.
Now, one story is about 12.32 feet. The thirty floors started falling through the damaged sections, and at least one damaged, weakened floor gave way.
Take that bag away from our average guy and hold it 12.32 feet over his head. Now drop it on his head. What happens?
Ouch is right.
Let’s see how many pounds of force will be applied by that bag to the guy’s head.
KE is measured in joules. KE= ½* mass * velocity *velocity
First let’s convert to metric for ease of calculation.
Mass=45.36 kg
http://manuelsweb.com/kg_lbs.htm
H = 12.32 feet = 3.65 meters
http://www.saudia-online.com/conversion%20Table.htm
Ending velocity of bag= 8.45 meters/s
http://tutor4physics.com/calculators.htm
KE= ½(45.36)(8.45)(8.45) = 1619 joules
Convert 1619 Joules back to food/pounds force a.k.a. weight = 598
http://www.cleavebooks.co.uk/scol/ccenrgy.htm
For the controlled demolition theory to be correct the guy’s head must be able to apply almost 598 foot/pounds of force to stop the bag after such a fall.
Is this reasonable? I think we can safely, and without the possibility of jail time for seriously injuring some poor test subject, conclude that it is not.
Maybe “Galileo” would like to put this theory’s primary assumption to the test with a 100 bag of bull ?
The original Galileo was actually instrumental in noting that the rate of falling objects is not dependant on mass
http://www-istp.gsfc.nasa.gov/stargaze/Smass.htm . Perhaps our modern, more re ed, version of the real scientist can contribute something to science and prove that his head can hold, even for a split second, an eleven hundred pound object.
Dan, or anyone else, please feel free to recheck my calculations here. I might have deliberately made a mistake just to see if you are really following along…
