Redwood
Graduate Poster
- Joined
- May 9, 2012
- Messages
- 1,557
Originally Posted by Redwood
But that's not what we're discussing! A falling brick is under constant acceleration due to gravity and when it (or any other weighty object) strikes something as insubstantial as tissue paper, the paper can't even slow it down, (i.e. make dv/dt negative)it can merely briefly reduce the acceleration to less than g (i.e. da/dt becomes negative) Something more substantial, like a pane of glass, will reduce the velocity (dv/dt becomes negative).
Why are you contradicting yourself? You claim I'm right, but then you say the paper can't even slow the brick down. You are playing the semantics game. You admit that the rice paper will reduce the acceleration at the instant of impact. Why does it matter if the velocity won't substantially change? What are you trying to prove?
There is no contradiction. The apparent contradiction results from the confusion in your own mind. You cannot understand the difference between reduced acceleration and reduced velocity. And, no, I'm not playing a "semantics game". I used elementary differential calculus to avoid semantics. (That's why real scientists and engineers use mathematics; it's not just for doing calculations.)
I'll make one last try to help you understand. Let's take a case where there are no impacts at all with solid objects:
Let's do a Galileo and drop a cannon ball from the top of the Tower of Pisa. Neglecting air resistance, it will hit the ground in ~8.5 seconds at a velocity of ~83 m/sec. It will be accelerating throughout the drop, that is dv/dt will always be positive.
However, it will not hit the ground exactly on time. Collisions with air molecules on the way down will reduce its acceleration just a tiny bit. So tiny that it can be neglected for all practical reasons. But it's there. A high-speed camera with a rate of 106 fps could detect the loss of acceleration, but it's doubtful that even a high-resolution 30 fps camera could.
Which means that for the entire drop:
dv/dt will always be positive. dv/dt2 will always be negative. If you think about it, since air resistance increases with velocity, this means that the loss of acceleration will be greater at the end of the drop than at the start. Meaning: dv/dt3 will always be negative, too!
Think about this, FF. Contemplate it. Run it through your mind as you prepare for bed. Someday, you may understand. It's possible, in principle.
SO: Falling objects can experience either a reduction or increase in velocity, a decrease in the increase of velocity, and even an increase in the rate of decrease of the increase of velocity, depending on what they fall through.
So now the money question: What does this have to do with the progressive collapses of the Twin Towers? The answer is, ABSOLUTELY NOTHING!
A progressive collapse can proceed with either an actual decrease in velocity at each floor, or a mere reduction in the acceleration. Which means that Newton's Laws of Motion are useless for studying the WHY of a progressive collapse! Resort must be taken to other physical laws.
Newton's Law of Gravitation DOES get star-billing and enters the stage at the very beginning, but then exits and is off-stage for the rest of the play. The rest of the play involves other physical laws.