psikeyhackr, why oh why did you have to get back to this before
we completed the discussion of failure energy in the Crush Models thread? I really believe you could come to understand this concept via the back door with a discussion of failure. But, since you brought it up now, I'm going to do what I said I would the next time someone brought it up:
OneWhiteEye wrote:Future incidents of unbridled pseudoscience will be directed to this announcement and may be followed with warning at moderator discretion. Threads may be split to the discard area without explanation other than linking to this announcement.
That announcement references Major_Tom's post above. This brings around full circle to here. After all the times and ways trying to explain this very simple idea, there is still no progress and yet I'm going to try one more time.
Potential energy is just that, it's not counted UNTIL it's lost. When a mass loses elevation in a gravitational field, it loses potential energy. If there's something holding it up, it doesn't lose elevation and therefore doesn't lose potential energy. Doesn't matter why it would lose elevation, it only matters that it does or not. If the Balzac-Vitry had instead been laced with thousands of charges to destroy all structural integrity in advance of the upper block, the change in total PE would be the same as it was. Intact building / Rubble pile. Initial PE / Final PE.
If the distance between the two points is full of mass that cannot be moved then what is the point of the mathematical calculation?
"...full of mass..."
The example you gave, Mt. Everest, is indeed full of well-compacted mass. The towers, even including office contents, were not full of mass and that is a crucial difference but still not the deciding factor in collapse. If Mt. Everest were to be sectioned to the same freestanding aspect ratio as a tower, I'm not sure how long it would take to collapse, but it would eventually. No, upper would not fall through lower, it's full of mass!!!
"...that cannot be moved... "
Unlike Mt. Everest, the towers were mostly air. If any level does fail, by assistance or otherwise, it no longer supports the load above and the load moves down, by definition. Whether it drops straight down or tips depends on the degree of uniformity of the failure across the footprint, but it will lose elevation in either case and therefore lose PE. How far and how fast depends on what the supporting force is, but it's defined to be less than the weight at the time of failure. The amount of potential energy loss depends only on the distance dropped and is the same no matter whether it drops slowly (slow failure near mg capacity) or in freefall (all capacity lost suddenly).
PE comes into calculations because, when a block has dropped
, it has lost PE. Before then, it's only potential energy, hence the name. Once some of it lost, it must be accounted for! Force dictates whether the block remains static or drops and what the instantaneous acceleration (therefore v and y) is over time. Energy is not force, but the two are related: work (energy) is force applied through a distance. Potential energy is the source for the work done in crushing because
the force derived from gravitional potential is weight!
If there is no failure (i.e., defect) there will be no motion, no PE loss. If there is a fail and downward movement occurs, there will be PE loss. Small displacement, small PE loss.
Capacity always greater than load
=> No motion -> no PE change -> no energy for work available -> no crushing
Capacity less than load at any point
=> some motion -> some PE change -> some energy available for work -> some crushing
Capacity always zero
=> free fall motion -> PE change (at maximal time rate - power) -> tons of energy available to do work
- and yet -
=> no work done in crushing
Your simulator is stuck in the last context, with magic supports added otherwise it would be simultaneous freefall of all floors. By this magic, you can invoke the inelastic collisions that also have to take place but it still leaves no resistive force due to supports, which take energy to fail.
I felt you'd finally come around on the PE thing once understanding how fail energy is incorporated into your simulation. You're doing F=ma and F is currently only mg so g = a. You want to include a force that's derived from the energy dissipated in failure of supports, and this force acts in opposition to gravity to slow the descent. You already have the dreaded PE loss implicit (force due to gravity) in your equation of motion, but don't know it! Major_Tom explained it above. You need a force derived from energy to counteract the force derived from loss of PE!
Do you see the irony?
psikeyhackr, we've been having this nice conversation in the Crush Model thread. I've been preparing some stupid pictures to help explain how to incorporate a resistive force into your simulator. I'm going to post over there when I have time. Can you trust me until then that the way PE enters the mechanics is quite sound? You're already doing it, that plus momentum is all you're doing, there's nothing wrong with it except you want it to be more realistic by adding some resistance. You don't realize that you're complaining that your simulation incorrectly calculates freefall between collisions! That's what all this is about...