[Halc]

That's quite a handgun!  I'd expect that speed only from a rifle.  Irrelevant. We'll work with those numbers.

The bullet in the breech is obviously travelling at 100km/h and I now pull the trigger and the bullet flies off at 700m/s. The bullet continues it's travel in the direction of the train at 100km/h but now has a speed of 2520km/h.

Exactly, so the force on the bullet cannot always have been perpendicular to its motion.

The force is applied over say 100 usec (a 10th of a msec) which would yield ~700 m/sec over the length of a handgun barrel. We'll assume for simplicity that the force is constant for those 100 usec and zero before and after.

At time 0 the force becomes nonzero, and applied perpendicular to the bullet's initial 28 m/sec motion. After 0.1 usec (a thousanth of the total acceleration time), the bullet has accelerated 0.7 m/sec to the side. Total speed is 28.009 m/sec, which is pretty much the same speed as before because the force is mostly being applied perpendicular to the motion.

But now the bullet is already moving at 0.7 m/sec to the side and any continued force in that direction is now partially behind it, not perpendicular. The speed relative to the tracks begins to climb significantly.

After 10 usec (10th of the time under acceleration, 1/100th of the distance down the barrel, the bullet is now moving at 70 m/sec left and 28 m/sec forward which is 75.4 m/sec total, and now the trajectory is already mostly to the side, so about 0.9 of the force (sin(70 deg))being applied to the bullet contributes to increasing its speed. So the vast majority of the acceleration is pretty much directly in line with the motion of the bullet, not perpendicular with it. Only at first (a nanosecond or so) is the force perpendicular.

Since the direction of the bullet motion changes and the force direction doesn't, the force does not remain perpendicular.
With orbits, as the trajectory changes direction, the force does in lockstep, so it is perpendicular at all times.

It's all the same with the balls, with about 100 usec of acceleration time, perpendicular only at first and not the rest of the time.

[paul cotter]

Thank you Halc, all is now clear. The force is momentarily perpendicular but subsequently almost entirely inline.

[Momentus (OP)]

This is the quote from Principia

by a single but large impulse the centripetal force acts,

This is a quote from @Origin

A momentary impulse is not what Newton is talking about 

i
Perpendicular force does not change the magnitude component of velocity. it changes the direction and only the direction.
This is true, and Newton would agree.  I agree that some of the posters do not agree with this.

Your force is not being applied perpendicular to the motion of the body in question. This has been repeatedly pointed out, and repeatedly ignored. So the conclusion that the speed doesn't change is false since it is based on a false assumption.

Isaac NEWTON: Philosophiae Naturalis Principia Mathematica. 3rd Ed.
Book I Section II.
Translated and Annotated by Ian Bruce. Page 95
SECTION II. On the finding of centripetal forces.
PROPOSITION I. THEOREM I.

Truly, when the body comes to B, by a single but large impulse the centripetal force acts, and brings about that the body deflects from the line Bc and goes along in the line BC

How is that not clear to you? The speed does not change when Newton says he applies an impulse perpendicular to the motion. Why should the speed change when, in my diagram, I apply an impulse perpendicular to the force?

Is your argument that a perpendicular force cannot be produced, that there is no way to reproduce Newton?s experiment? Or is is just my experiment?

Working from first principles Newton says that a perpendicular impulse, which incidentally he is happy to define as a centripetal force, Alters velocity by changing direction and not changing speed.
I am merely echoing what he said.

[paul cotter]

You are echoing your own errors in your own echo chamber, impervious to reason and correction. I was incorrect in some of my statements but I am happy to have Halc correct them. You appear oblivious to the help that has been offered. In my case I did study mechanics while at college but my entire career has been in electrical engineering and as such I had little need for collisions and centripetal force details. Any study of mechanics was 50 years ago and I was bound to be rusty.

[Momentus (OP)]

You are echoing your own errors in your own echo chamber, impervious to reason and correction.

Which part of my echoing Newton is in need of correction?

[Origin]

I am merely echoing what he said.

Newton did not say a collision is a centripetal force.

[Origin]

Which part of my echoing Newton is in need of correction?

The part where you say the x component of the blue balls velocity drops from 4 m/s to 2.6 m/s without a force causing it.  Newton says that's impossible.
The other glaring error in your example is that it violates the conservation of energy.
These 2 errors shows beyond a shadow of a doubt that your analysis is wrong.

[Bored chemist]

Which part of my echoing Newton is in need of correction?

Your insistence that movement in a straight line is the same as movement in a circle.
You say that.
Newton did not say that.
So, you are not, in fact, echoing Newton.

[Origin]

I would really like to see your explanation for why the x component of the blue balls velocity decreased.
Likewise I would like to see your explanation of why the conversation of energy doesn't apply to your example.
Hopefully you will stop dodging these questions.

[Momentus (OP)]

Newton did not say a collision is a centripetal force.

No said the same as I keep on saying. A perpendicular force. In my drawing I apply a perpendicular force. In his drawing he applies a perpendicular force. You are using collision as a debating point, it is irrelevant. Newton applied an impulse to a mass moving in a straight line. I apply the same impulse to a mass moving in a straight line

Newton says that's impossible.

Do you have a source or did you just put words in Newton?s mouth?

Your insistence that movement in a straight line is the same as movement in a circle.

  Yes of course I did. Over and over and over. Quote me.

I would really like to see your explanation for why the x component of the blue balls velocity decreased.

I have posted that the motion along the x axis is the vector of the blue ball moving at the same speed, in a new direction. Just as Newton shows in his drawing.

Likewise I would like to see your explanation of why the conversation of energy doesn't apply to your example.

Back to your straw man. Newton?s drawing shows what happens. Start there. Prove Newton wrong.

How is that not clear to you? The speed does not change when Newton says he applies an impulse perpendicular to the motion. Why should the speed change when, in my diagram, I apply an impulse perpendicular to the force?

Is your argument that a perpendicular force cannot be produced, that there is no way to reproduce Newton?s experiment? Or is is just my experiment?

Working from first principles Newton says that a perpendicular impulse, which incidentally he is happy to define as a centripetal force, Alters velocity by changing direction and not changing speed.
I am merely echoing what he said.

I can see that trying to illustrate Dark Motion with a snooker ball example has caused confusion. My apologies. Look at Newtons example instead.

[Origin]

I have posted that the motion along the x axis is the vector of the blue ball moving at the same speed, in a new direction.

That means the x component of the speed has changed from 4 m/s to ~2.6 m/s without any force in the x direction.  That is not possible according to Newtons first law. 
Your example shows the red balls impulse causes the blue ball to move in the Y direction.  100% of the energy / momentum of the red ball was transferred to the blue ball in the Y direction.  This is obvious since the masses of the balls are the same and before the collision the velocity of the red ball was 3 m/s in the y direction and the blue balls velocity was 0 m/s in the y direction and after the collision the blue balls velocity was 3 m/s in the y direction and the red balls velocity was 0 m/s in the y direction.  So where is the force that slows the x component of the blue balls velocity coming from?  It can't be coming from the red ball since 100% of the red balls energy was transferred to the blue ball.
Arm waving is not the answer I am looking for.  What is the physical reason the ball slowed down?  Where is the force that causes the blue ball to slow down in the x direction, or are you claiming there is no need for a force to slow the ball?
 

Back to your straw man.

Your problem is an elastic collision between 2 balls and my calculations are showing an elastic collision between the 2 balls.  That is not a strawman.  So you are either lying, you don't know what a strawman is, or are so woefully ignorant of physics that you can't follow my calculations.  Which is it?

I think it is time to close this thread.  The OP refuses to listen any help provided and refuses to answer questions in good faith.  He just keep repeating his misconceptions.

[Origin]

I can see that trying to illustrate Dark Motion with a snooker ball example has caused confusion. My apologies. Look at Newtons example instead.

Why would we look at Newtonian mechanics?  You said your "dark motion" is something that Newton missed, so Newtons laws and mechanics will be of little help.  That is unless "dark motion" does use Newtonian mechanics, in which case why not call dark motion - just motion?

[paul cotter]

Hi Origin, this is futile and I agree that the thread should be locked. The OP is plainly in a "black is white" mode.

[Momentus (OP)]

Why would we look at Newtonian mechanics?  You said your "dark motion" is something that Newton missed, so Newtons laws and mechanics will be of little help. 

Are you being deliberately dense?

Philosophiae Naturalis Principia Mathematica.
SECTION II. On the finding of centripetal forces.

Newton?s first step is to show a simple action of force on a moving mass.
A trivial thing, he gives few words to the action. Simple and straightforward.

The action he describes is not reversible.

All the clever postings about rifles and gnats, revolvers and trains, Golf clubs and toys, kinetics and collisions, do not have any effect on Newton?s simple action, which he uses as a prelude to his complex centripetal force.

The action that Newton describes in his Finding of centripetal forces is not reversable. It is not symetrical.

Those are the facts.

My contribution is to identify this action and give it a name.
Dark Motion.

So go ahead and close the thread. I am tired of talking to obdurate assho

Brian Morris.

[paul cotter]

Nasty remarks like that only serve to demean he who delivers them. I have a suggestion for you: take your ideas to the physics department of your nearest accredited university and see how well it is received and then report back to the forum.

[Origin]

Those are the facts.

The facts are that the collision problem as you describe it violates the conservation of momentum, the conservation of energy and Newtons first law of motion.  In other words your description must be wrong.  So that means you must be  misunderstanding Philosophiae Naturalis Principia Mathematica.  I'm not surprised since it is very hard to follow the language in the paper as it is 350 years old.  Maybe you could look at a more recent text book on physics.
 

[Origin]

This is a discovery I made many years ago. I think you will find it a challenge to your beliefs. It is not a theory, it does not violate Newton's basic axioms too much and of course you can replicate the experiment very easily.

First you say that you have made a discovery that violates Newtonian mechanics (a little).

The action that Newton describes in his Finding of centripetal forces is not reversable. It is not symetrical.

My contribution is to identify this action and give it a name.
Dark Motion.

Now you say you have discovered nothing, you are just giving a name to part of Newtons explanation of centripetal force.

Which is it?

[paul cotter]

Origin, your suggestion of an updated physics book is a great idea but alas it will not work with this poster. He is not open to anything that challenges his great discovery, as he sees it.

[Halc]

Nasty remarks like that only serve to demean he who delivers them.

Momentus has earned a 10 day vacation for that remark, before which this topic will be closed, so no more posts here from him.
There will be a more careful watch on posts in other topics.

He is not open to anything that challenges his great discovery, as he sees it.

Totally agree that logic, mathematics, and reason fall on deaf ears with this guy. He is here for the conflict, not to learn anything.
I suspect the ban will be permanent before too long.

Thanks to both of you for your efforts, which are noticed by the non-participating reader if not the OP.