Circumventing Newton's third law through Euler Inertial Forces

[Ghideon]

2 hours ago, John2020 said:

You are right, my mistake.

Thanks. Now that we agree on the basics I'll try to abstract away unnecessary stuff and make a drawing so we can check the forces involved.
 

Note: There may be some overlap with the analyse done by @swansont and I think that is a good thing. We may be able to use similarities and differences to find the exact place where the misunderstanding of Newton's laws comes from in Fig 1 in first post.

Edited October 14, 2020 by Ghideon
clarified

[John2020]

3 hours ago, swansont said:

The axial component of N₁ remains, and is the reason the nut accelerates.

I think N1 is enough to present the argument. However, what you write about the axial component of N1 cannot apply because you assume rectilinear motion for the nut from the moment there is none (there is no rectilinear real motion along the axis of rotation).

52 minutes ago, Ghideon said:

Now that we agree on the basics I'll try to abstract away unnecessary stuff and make a drawing so we can check the forces involved.

OK

Edited October 14, 2020 by John2020

[swansont]

41 minutes ago, John2020 said:

I think N1 is enough to present the argument. However, what you write about the axial component of N1 cannot apply because you assume rectilinear motion for the nut from the moment there is none (there is no rectilinear real motion along the axis of rotation).

In your diagram you say the velocity is not zero, so there is motion along the axis of rotation. Why are you all of the sudden claiming there is none?

[John2020]

1 hour ago, swansont said:

In your diagram you say the velocity is not zero, so there is motion along the axis of rotation. Why are you all of the sudden claiming there is none?

I am not addressing the velocity as value but the trajectory of the nut. The nut does not develop a velocity along the axis of rotation since it ascribes a helix (in our case the screw. removing the guiding bars then when you give a torque upon the nut, it will ascribe a helix, thus no axial real rectilinear velocity. Consequently, there is no real force along the axis of rotation.) 

[Ghideon]

Here is a first image @John2020
The bolt is vertical and free to rotate, there is a ideal friction-free bearing between the blue box and the bolt. The nut is friction free as well and initially placed at the top of the bolt. There is no engine or guide rod. Question: Is this a good starting point or would you want to add more details initially? Idea is that if we agree on the behaviour, forces, laws of conservation etc in this simple case we then move on to add more to the device until we find the spot where non-mainstream claims are introduced.

[John2020]

17 minutes ago, Ghideon said:

Idea is that if we agree on the behaviour, forces, laws of conservation etc in this simple case we then move on to add more to the device until we find the spot where non-mainstream claims are introduced.

The blue box and the screw is one system, right? If so then proceed. I am not sure because we have an external field now already that of gravity (I assume you are going to introduce a nut acceleration due to earth's gravitational field). Anyway, let us see what comes next.

Edited October 14, 2020 by John2020

[Ghideon]

39 minutes ago, John2020 said:

The blue box and the screw is one system, right?

Good point regarding system boundaries! That needs to be address, let's define the system as the bolt and the nut only. The blue box is not part of the system, it just serves as a holder so that the bolt is free to rotate. Ok?

And yes, if the above seems fine we may release the nut at the top of the bolt. Question: Which forces are most relevant to the concepts you try to introduce? Action/reaction pairs in the bolt/nut? other? Just so that the analysis stays focused and does not move into unnecessary parts. Another possibility is compare the conservation of momentum in this system and your setup.

Also, just to avoid confusion; we agreed after some initial discussion that the nut, pulled by gravity, will accelerate in the initial vertical bold example I posted. The fact that we now agree about the acceleration, how would an edited version of the bold part the look? We now know both cases are accelerated displacement so the difference, as stated does not hold:

21 hours ago, John2020 said:

I am aware about this analogy. Well this is not exactly the same as in my apparatus. The nut is being affected by a constant external gravitational force that implies constant evolution of nut around the screw that means constant displayment speed.

In my case is accelerated displacement. The displacement force is not rectilinear (as we see with real contact forces) and that was the reason I called it fictitious and more accurately an artificial fictitious force because of the translation screw construction that implies an helix trajectory is at play (not rectilinear motion).

However, the question remains: Where appear the normal forces pair (action-reaction) in your analogy and what is their angle in regards to the rotation axis or the evolution axis (your case).

(emphasis mine)

Edited October 14, 2020 by Ghideon
clarifications

[John2020]

23 minutes ago, Ghideon said:

We now know both cases are accelerated displacement so the difference, as stated does not hold:

Something is missing. In order your proposal to start working as you envisioned, it will require an initial torque, otherwise it will not start to accelerate. I think we should not orientate the construction vertically because we introduce an adfitional force due to gravity (it will complicate the analysis and will lead to wrong conclusions).

It would be better your construction to be placed in outer space horizontally and then to apply a couple (F_A and F_A') of non constant magnitude (increasing), permanently. That way it will start to accelerate just because of the applied torque (exactly as in my construction).

Edited October 14, 2020 by John2020

[Ghideon]

9 minutes ago, John2020 said:

Something is missing. In order your proposal to start working as you envisioned, it will require an initial torque, otherwise it will not start to accelerate.

Here we disagree. Why? Note that friction is not an issue. What is it, that according to you is holding back the nut? Why is it not starting to rotate?

 

(There are plenty of easy and useful analogies but I'll try not to post more analogies)

Edited October 14, 2020 by Ghideon

[John2020]

2 minutes ago, Ghideon said:

Here we disagree. Why? Note that friction is not an issue. What is holding back the nut?

Because the nut follows a helix trajectory and not a real rectilinear motion therefore it will require an initial torque. It is not the same conditions as in my construction because gravity comes into play (normally when the construction is 100% in parallel with gravity then it shouldn't be influence by it. However, in real conditions it will be difficult to be 100% in parallel in any location across the globe).

[Ghideon]

7 minutes ago, John2020 said:

Because the nut follows a helix trajectory and not a real rectilinear motion therefore it will require an initial torque. It is not the same conditions as in my construction because gravity comes into play (normally when the construction is 100% in parallel with gravity then it shouldn't be influence by it. However, in real conditions it will be difficult to be 100% in parallel in any location across the globe).

We seem to begin getting close to the issue. What force is holding the nut back? If it helps, imagine the treads on the bolt is much steeper.

 

"Because the nut follows a helix trajectory and not a real rectilinear motion therefore it will require an initial torque." That is not an explanation, that is a claim.

 

 

[John2020]

4 minutes ago, Ghideon said:

That is not an explanation, that is a claim.

We like it or not the nut follows a helix trajectory and not a rectilinear motion. Otherwise, it is like we are addressing Fig.1-Lower (unthreaded rod and nut's rectilinear motion). This is exactly the point of misunderstanding from your part meaning that you (and not only you) ignore this very crucial detail. We have a helix trajectory in Fig.1-Upper.

Edited October 14, 2020 by John2020

[Ghideon]

4 minutes ago, John2020 said:

We like it or not the nut follows a helix trajectory and not a rectilinear motion.

Initially the nut is at rest, the nut does not follow a helix trajectory until it is moving. So what force is keeping the nut from initially moving. Why does the nut have to be pushed? 

 

Edited October 14, 2020 by Ghideon

[John2020]

4 minutes ago, Ghideon said:

So what force is keeping the nut from initially moving. Why does the nut have to be pushed? 

The nut is not being pushed. The torque initiates its motion. Initiating its motion by the torque and then removing the torque the nut will acquire a constant speed for the frictionless horizontal scenario.

[Ghideon]

1 minute ago, John2020 said:

The nut is not being pushed. The torque initiates its motion. Initiating its motion by the torque and then removing the torque the nut will acquire a constant speed for the frictionless horizontal scenario.

That means we have found the spot where you claim Newton is incorrect? We may continue to examine further by removing (or adding) more details!

Just curios; does your idea hold for a bolt with a steep angle of the threads? I mean a bolt where the nut is moving a large vertical distance for each rotation. 

[swansont]

4 hours ago, John2020 said:

I am not addressing the velocity as value but the trajectory of the nut. The nut does not develop a velocity along the axis of rotation since it ascribes a helix (in our case the screw. removing the guiding bars then when you give a torque upon the nut, it will ascribe a helix, thus no axial real rectilinear velocity. Consequently, there is no real force along the axis of rotation.) 

The guide bars prevent this, but in any event, this is baloney. A rotating object can have a linear velocity. In some cases, such as this one, the rotational speed is related to the linear speed.

[John2020]

7 hours ago, swansont said:

In some cases, such as this one, the rotational speed is related to the linear speed.

As projecton but not as mechanism description. Here is a helping comparison:

-Cranksaft: Converts linear to rotational motion and vice versa through real forces. Here your analysis would be correct 

-Leadscrew with nut: Converts rotational motion (real force) to mass transfer (Inertial force). No real force is pushing along the axis since there is none. However, there is a real force that pushes the nut along the helix trajectory.

If you can see clearly the difference here then I will disclose you the rest which is a little bit tricky, actually.

I am almost in my workplace. See you later at the evening.

10 hours ago, Ghideon said:

That means we have found the spot where you claim Newton is incorrect?

See my reply to swansont, above. Nobody, said Newton is incorrect but incomplete in terms of an additional interpretation. If you take the total derivative of the change in momentum, reveals two terms, where the second one has today two interpretations (acrettion of mass, and ejection of mass). There could be a third interpretation for the same term.

[Ghideon]

58 minutes ago, John2020 said:

Nobody, said Newton is incorrect but incomplete in terms of an additional interpretation. If you take the total derivative of the change in momentum, reveals two terms, where the second one has today two interpretations (acrettion of mass, and ejection of mass). There could be a third interpretation for the same term.

Again: What force is keeping the nut from being pulled by gravity? If the nut remains at rest until torques is applied there is some force that equals the pull from gravity. 

Again; How about a case with a bolt with steep angle** threads. Do you prefer a picture that clarifies?

(I guess we are making progress, lots of unnecessary details are now removed and we may be able to generalise)

A quick return to this just to clarity:

11 hours ago, John2020 said:

The nut is not being pushed. The torque initiates its motion. Initiating its motion by the torque and then removing the torque the nut will acquire a constant speed for the frictionless horizontal scenario.

Speed will not be constant. I thought we have agreed that the nut will accelerate. Please clarify.

 

 

*) I'm not aware of the correct english term.

[John2020]

16 minutes ago, Ghideon said:

Again: What force is keeping the nut from being pulled by gravity? If the nut remains at rest until torques is applied there is some force that equals the pull from gravity. 

The normal forces between the thread and the nut.

 

17 minutes ago, Ghideon said:

Again; How about a case with a bolt with steep angle** threads. Do you prefer a picture that clarifies?

I am not a specialist on threads. Let's continue with what we have shared up to now.

[Ghideon]

1 minute ago, John2020 said:

The normal forces between the thread and the nut.

We can make a picture with the forces later today. Your statement implies that a ball would need a push to start rolling downhill. 

6 minutes ago, John2020 said:

I am not a specialist on threads. Let's continue with what we have shared up to now.

Expertise not needed. Here is an example. Place the nut at the top end (or any way along the thread except for at the bottom end). You claim that a frictionless nut will not slide down but remain at rest until torque is applied. 

[John2020]

23 minutes ago, Ghideon said:

Speed will not be constant. I thought we have agreed that the nut will accelerate. Please clarify.

What I confirmed back then I take it back because it is wrong. A couple of days ago I was studying this situation and I can say now I have a better view of how all the forces are exerted upon the nut and what is really going on.

My intuition was right but just now I am able to justify how this mechanism may work. 

I have to update my paper this weekend in order to add all these details as forces upon the thread, and nut as also something to counteract the system countertorque in order to not rotate.

My pause time is finished. See later in the evening.

3 minutes ago, Ghideon said:

Your statement implies that a ball would need a push to start rolling downhill

No. In the case of the ball, gravity exerts a force rectilinear, where just the component along the hill will affect and start directly the ball motion without push. It is not the same situation with the translation screw.

I have to go now.

41 minutes ago, Ghideon said:

Speed will not be constant. I thought we have agreed that the nut will accelerate. Please clarify.

I think you are right about gravity but it is not for the reason you probably think (no force along the axis of rotation). I will explain later. Yes, gravity will start pushing the nut along the helix. Here is another consideration: When you make a pure theoretical analysis (not real world application), I will be correct since then the lead must have almost zero length that will require a continues torque to apply.

Go ahead. You are right with gravity but not by claiming force along the axis of rotation. See you later in the evening.

[joigus]

Rotational motion is converted into linear motion, as Swansont and Ghideon say.

I'm working on more additional explanations.

In terms of:

(1) Systems of particles (dynamics of rigid solids)

(2) Lagrangian constraints (parametrizing the positions of these rigid solids)

\[d\theta_{n}=k_{n}dx_{n}\]

\[d\theta_{s}=k_{s}dx_{s}\]

\[2\pi=k_{n}h\]

\[2\pi=k_{s}h\]

theta_n is the nut's angular variable

theta_s is the screw's angular variable

x_n is the nut's COM position

x_s is the screw's COM position

k_n = k_s because nut and screw fit together with the same h (the linear "step" of the thread)

Later.

[John2020]

The helix angle should be also included. It is very important, otherwise the analysis will lead to wrong conclusions. With all respect, motion occurs just along the helix (crucial detail) and not along the axis of rotation of the screw. I hope you agree with me.

[joigus]

Just now, John2020 said:

The helix angle should be also included. It is very important, otherwise the analysis will lead to wrong conclusions. With all respect, motion occurs just along the helix (crucial detail) and not along the axis of rotation of the screw. I hope you agree with me.

That is implied in h.

Don't you see it?

Bigger angle, bigger step h. As Guideon noted with his image.

I just hope the step is not changing with time!

Rotation translates into relative linear displacement of both pieces. I hope you agree with that.

You further have,

\[dx_{s}+dx_{n}=0\]

That's why your system stays in place as a whole. Sorry.

[John2020]

29 minutes ago, joigus said:

Rotation translates into relative linear displacement of both pieces. I hope you agree with that.

You further have,dxn=0

That's why your system stays in place as a whole. Sorry.

Here you miss something. I will explain later.