8
   

Can an object be accelerating and yet -not- moving?

 
 
maxdancona
 
  1  
Reply Mon 25 Feb, 2013 02:17 pm
@dalehileman,
Quote:
let's move on to the real world where the upward motion of the ball produces a slight updraft which keeps that peak flat even for a microsecond. For all practical purposes of human intercourse the peak is flat


Huh???

dalehileman
 
  1  
Reply Mon 25 Feb, 2013 02:23 pm
@maxdancona,
Max I'm not sure huh which, but since you've bolded it I assume it's the latter. Intercourse also means communication, chat

Thus the Average Clod (me) would conclude it's flat even though a clever defense attorney might be able to acquit Don, that is, if every jury member were a theoretical physicist
0 Replies
 
DrewDad
 
  1  
Reply Mon 25 Feb, 2013 02:28 pm
@dalehileman,
Zero duration.

What is the width of a line?

What is the thickness of a plane?

What are the dimensions of the point where the x and y axises cross?
contrex
 
  1  
Reply Mon 25 Feb, 2013 02:29 pm
@dalehileman,
dalehileman wrote:
But then what is its duration


Its duration is "infinitesimal", that is, non-zero, but smaller than any positive number. See Newton's infinitesimal calculus. In ordinary language, "incalculably small".

0 Replies
 
dalehileman
 
  1  
Reply Mon 25 Feb, 2013 02:40 pm
@DrewDad,
Drew you perhaps misunderstand me. All those are the theoretical zero. But your delay between acceleration and motion, you said, has a theoretical duration

Okay, it's a different kind of zero, concerning rate not length, very technical, two different definitions of zero, one bigger than the other. There are all sorts of such mathematical abstractions but remember they aren't real, they're only circulation of electrical charges in the humanoid brain

See Con above, "In ordinary language, "incalculably small".

So okay, replies Intuition, still not zero. Conclusion: It's flat on top of the peak, the ball had actually stopped
contrex
 
  1  
Reply Mon 25 Feb, 2013 02:58 pm
@dalehileman,
dalehileman wrote:
So okay, replies Intuition, still not zero. Conclusion: It's flat on top of the peak, the ball had actually stopped


An object projected at an angle of 90 degrees from the horizontal, (i.e. vertically) no more "stops" at the highest point of its flight than one projected at a smaller angle.

This "intuition" thing is getting a bit old, now.


contrex
 
  1  
Reply Mon 25 Feb, 2013 03:00 pm
@dalehileman,
dalehileman wrote:
There are all sorts of such mathematical abstractions but remember they aren't real


This is a remarkably naive statement.
DrewDad
 
  1  
Reply Mon 25 Feb, 2013 03:31 pm
@dalehileman,
dalehileman wrote:
But your delay between acceleration and motion, you said, has a theoretical duration

No, I did not say that. If I did, I misspoke. There is no delay between acceleration and motion. There is a point in time where the speed is zero, and acceleration is non-zero.

dalehileman wrote:
Okay, it's a different kind of zero, concerning rate not length, very technical, two different definitions of zero, one bigger than the other.

That makes no sense.

dalehileman wrote:
There are all sorts of such mathematical abstractions but remember they aren't real, they're only circulation of electrical charges in the humanoid brain

What's your point?
contrex
 
  1  
Reply Mon 25 Feb, 2013 03:40 pm
@contrex,
contrex wrote:

dalehileman wrote:
There are all sorts of such mathematical abstractions but remember they aren't real


This is a remarkably naive statement.



Or remarkably profound...
0 Replies
 
dalehileman
 
  1  
Reply Mon 25 Feb, 2013 04:40 pm
@contrex,
Quote:
An object projected at an angle of 90 degrees from the horizontal, (i.e. vertically) no more "stops" at the highest point of its flight than one projected at a smaller angle.
My point was, that at the peak if acceleration precedes the instant of zero motion as Drew asserts, then the object must have stopped for an "infinitesimal" duration and therefore the peak is ever-so slightly flat during that time. Presto, it had stopped

Quote:
Or remarkably profound...
Why, thank you Con, I was sure you were dubious of my profundity

Quote:
This "intuition" thing is getting a bit old, now.
My most sincere apologies, I shall try to remember whenever I'm addressing you, Con
0 Replies
 
dalehileman
 
  1  
Reply Mon 25 Feb, 2013 04:55 pm
@DrewDad,
dalehileman wrote:
But your delay between acceleration and motion, you said, has a theoretical duration

Quote:
No, I did not say that. If I did, I misspoke. There is no delay between acceleration and motion.
If that's so, then, Con, I withdraw my above assertion that the ball is stopped at its peak

Quote:
There is a point in time where the speed is zero, and acceleration is non-zero.
Forgive me Drew, no offense, but this seems to contradict your last statement

dalehileman wrote:
Okay, it's a different kind of zero, concerning rate not length, very technical, two different definitions of zero, one bigger than the other.

Quote:
That makes no sense.
I agree it doesn't. I was merely paraphrasing Con to the effect that the acceleration preceded the movement, which statement he withdrew (misspoke); that is, before reinstating it above, leaving me in a state of utter consternation

dalehileman wrote:
There are all sorts of such mathematical abstractions but remember they aren't real, they're only circulation of electrical charges in the humanoid brain

Quote:
What's your point?
The idea that the ball didn't stop is purely abstract, metaphysical, semantical
georgeob1
 
  1  
Reply Mon 25 Feb, 2013 05:33 pm
@dalehileman,
There is very little detectable consistency in what you call "intuition". It is clear now that you treat instants of time, points on a line or path as intrinsically counterintuitive - never mind the fact that millions do not. Certainly anyone who has studied algebra or geometry has been exposed to this, and it is the core of elementary courses in calculus - not to mention all of modern science and engineering.

There is another matter here that is in my view, entirely compatable with experience and intuition, about which you also appear to be confused. That is that the motion of anything involves speed and direction. Changing either involves force and acceleration. Surely you have experienced the side force (or acceleration) associated with driving a car around a sharp curve at nearly constant speed. The fact is you are experiencing in inward acceleration, perpindicular to your direction of movement, and the centrfugal force you experience in the turn is merely the inertial reaction to it. Our intuition in this area is reinforced with hundread of everyday experiences, raanging from riding in a car to leaning a bicycle or motorbike into a turn, or simply digging+ in your leg and foot as you shift direction while playing soccer or football. In each the acceleration and reaction forces last a finite interval of time, and during that period the change in speed and direction is continuous. So that at every instant in the interval the object is subject to applied forces and acceleration and its motion (speed and direction) is continuously changing

What is it you find "counterintuitive" about that?
0 Replies
 
DrewDad
 
  1  
Reply Mon 25 Feb, 2013 05:40 pm
@dalehileman,
dalehileman wrote:

dalehileman wrote:
But your delay between acceleration and motion, you said, has a theoretical duration

Quote:
No, I did not say that. If I did, I misspoke. There is no delay between acceleration and motion.
If that's so, then, Con, I withdraw my above assertion that the ball is stopped at its peak

Quote:
There is a point in time where the speed is zero, and acceleration is non-zero.
Forgive me Drew, no offense, but this seems to contradict your last statement

Only because you apparently do not understand that a point has no length.

Duration is a measure of length. One second, ten seconds, etc. Therefore, you are asking me to measure the length of a point, which is a contradiction. The point in time has no duration. It just is.

I'm sorry that you are unable to grasp this fundamental idea. You seem to understand that a line has no width, and that a plane has no depth. What is the hang up understanding that a point has no length?
dalehileman
 
  1  
Reply Mon 25 Feb, 2013 06:47 pm
@DrewDad,
Quote:
Only because you apparently do not understand that a point has no length.
Oh no, Drew, I do

Quote:
Duration is a measure of length. One second, ten seconds, etc.
No kidding
(Sorry Drew, couldn't resist

Quote:
Therefore, you are asking me to measure the length of a point,
No not at all

Quote:
which is a contradiction.
Yes it would be wouldn't it

Quote:
The point in time has no duration. It just is.
I understand, that is, as those electrical charges running around in our minds, not something "real"

Quote:
I'm sorry that you are unable to grasp this fundamental idea.
I'm sorry you've adopted that notion

Quote:
You seem to understand that a line has no width, and that a plane has no depth.
I don't know why you say that

Quote:
What is the hang up understanding that a point has no length?
I don't remember asserting that it did. However I might have misspoke also, I do that too

There seems to have been some confusion about the idea that if acceleration precedes movement then there must be a duration of infinitesimal flat at the apex of the acceleration graph, implying that the ball has stopped. Understand, Drew, that was proposed by somebody who later withdrew it, before apparently reinstating it then denying the reinstatement. So I just don't know what to believe

But abandoning that consideration for a moment, how about the updraft in a practical situation which apparently does in fact cause the ball to stop for a very short time, also an interesting subject fraught with potential for conflict
0 Replies
 
DrewDad
 
  1  
Reply Mon 25 Feb, 2013 08:41 pm
@dalehileman,
dalehileman wrote:

Quote:
There is a point in time when your speed is still zero, but your acceleration is some amount greater than zero.
My immediate reaction is that (theoretically) they'd happen at the same instant. However if acceleration is defined as a change in velocity then your implication is, that moment isn't of zero duration

Very interesting

But then what is its duration

This is where you're asking me to measure the length of a point.

Unless you're just being a jackass.
0 Replies
 
MattDavis
 
  1  
Reply Mon 25 Feb, 2013 10:08 pm
@contrex,
contrex wrote:
This "intuition" thing is getting a bit old, now.

It has been old, as old as calculus.
You might find this article interesting:
Infinitesimals: Intuition and Rigor


Let's not lose sight of the fact that calculus is a model.
The model which assumes continuity, and disregards the discrete.
There is a bit of a conundrum however, in that continuity is meaningless without reference to the discrete.
A "real number" line is meaningless without reference to an "integer number" line.

If the basic structure of the universe is continuous... don't let go of calculus.
If the basic structure of the universe is discrete... maybe understand it is only an approximation.
Very Happy
contrex
 
  1  
Reply Tue 26 Feb, 2013 11:33 am
@dalehileman,
dalehileman wrote:

dalehileman wrote:
But your delay between acceleration and motion, you said, has a theoretical duration

Quote:
No, I did not say that. If I did, I misspoke. There is no delay between acceleration and motion.
If that's so, then, Con, I withdraw my above assertion that the ball is stopped at its peak


You have got your quotes mixed up. I am "Con", and I never wrote that. For a start, being a British English speaker I would never use "misspoke".
contrex
 
  1  
Reply Tue 26 Feb, 2013 11:35 am
dahileman wrote:
I was merely paraphrasing Con to the effect that the acceleration preceded the movement, which statement he withdrew (misspoke);


I never said that nor withdrew it either.
dalehileman
 
  1  
Reply Tue 26 Feb, 2013 01:01 pm
@contrex,
Quote:
I am "Con", and I never wrote that.
Forgive Con, an old fella with incipient Alz's and failing memory as well as laziness scrolling back
0 Replies
 
dalehileman
 
  1  
Reply Tue 26 Feb, 2013 01:06 pm
@MattDavis,
Quote:
There is a bit of a conundrum however, in that continuity is meaningless without reference to the discrete.
Yea, Matt, essentially why I maintain it's perfectly okay to say that in a practical situation the ball does indeed stop at the peak of its trajectory. Actually the graph is pretty nearly horizontal there, supposedly satisfying that condition for a point of zero duration. However in reality for a short time it looks pretty nearly parallel to that horizontal line, perhaps crossing over several times but averaging zero, thus stopped

Especially if there's a slight updraft
 

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