Pavlovian Dogcatcher wrote:
OneWhiteEye wrote:As I say below, calculations for step-wise model collisions do not even involve PE.
You were talking about calculations of PE here:
I was talking about PE but I wasn't talking about collisions! I then separately answered psikeyhackr's question which concerned collisions, but not loss of PE except that's why the collision occurs in the first place:
OneWhiteEye wrote:Things collided before hitting the ground.
You brought collisions and PE together:
Pavlovian Dogcatcher wrote:Most definitely, yet that is ignored when one abstracts the situation into to calculating PE as if describing a ball dangling from a rope.
Anyway, sure Psikeyhackr's simulator effectively accounts for what you describe, but have you seen any attempts to calculate "the PE of the towers" which rightly do?
Mine, Greening's, femr2's and others - that's why they all pretty much agree with psikeyhackr's calculations. Mackey's analysis ignores collisions specifically but is nonetheless correct within the scope of what he attempts to do.
See appendix B here
, where the mass of a tower and it's center of mass are estimated to supposedly calculate the PE of the tower by abstracting it into a ball suspended from that height; resulting in the value of 4.09 x 10^11 Joules.
Point to you for finding such an analysis, but that's all you get. I never read his paper, so I didn't know he did this and it's the first time I've seen such a calculation simply involving total energy budget over the entire collapse. Nonetheless, the analysis appears correct, and the method most certainly is. While inelastic collision is not called out, nothing specific is - all known and unknown energy sinks are rolled into one big sink, which INCLUDES collisions.
He does a 'what if' table calculating how the overall collapse time differs when kinetic energy (gained from PE loss) is diminished due to loss to any and all sinks. Momentum-only collision is near the top of the list, probably between 39% and 48% dissipation fraction. Add more sinks if you like, it just goes lower in the table and longer on the collapse time.
There are continuum models, step-wise discrete models, and there is an aggregate calculation like what Mackey did. It's only step-wise if you consider one step to be a step-wise calculation. It doesn't specify motion over time, just total time and is appropriate only for that. Mackey's one step has boundary conditions at the beginning and end of collapse, story-wise computations like mine are just that, by story. femr2 and psikeyhackr both use timesteps, not story steps. Mackey cannot accurately test for arrest, he can only say what the net energy dissipated by the structure is if it collapses to completion and show the times for fraction dissipated. Even his model 'arrests' when the total dissipation equals total PE lost, the only case in which it will.
You assume because collision is not mentioned in Mackey's paper that energy lost to it is overlooked in the calculations, which is not so. It's not necessary to specify what the energy goes towards to calculate collapse time from net energy balance.
As for your question on the relationship between force and work done by a force; best I can tell, I understand it far better than you do.
Your response dodges giving the answer to a very simple question, so I don't think so. There's still the opportunity to go find a wiki page to link to, and copy and paste.