Could Fictitious forces accelerate and change the CoM through internal mass transfer?

[John2020]

Fig.1.Isolated System and Internal Fictitious Force 

\[\Delta \omega \neq 0 \Rightarrow \sum{F}_\mathrm{int} = {F}_\mathrm{Fictitious} \neq const. (varying) \]

\[\sum{F}_\mathrm{int} = \frac{m_\mathrm{T}  \cdot ({u}^{\prime}_{\mathrm{cm}}- {u}_\mathrm{{cm}})}{\Delta t} \neq 0 \] 

\[\frac{\Delta {p}}{\Delta t} = \frac{m \cdot ({u}^{\prime} - {u})}{\Delta t} = \frac{m_\mathrm{T}  \cdot ({u}^{\prime}_{\mathrm{cm}}- {u}_\mathrm{{cm}})}{\Delta t} \] 

\[{u}^{\prime} \neq {u} \Rightarrow {u}^{\prime}_{\mathrm{cm}} \neq {u}_{\mathrm{cm}} \Rightarrow {a} \neq 0.\]

 

 

Fig.2.Isolated System and Internal Collinear forces (Action-Reaction pair)

\[\sum{F}_\mathrm{int} = \left( {F}_\mathrm{A} + {F}_\mathrm{R} \right) = 0 \text{ (collinear)}\]

\[\frac{\Delta {p}}{\Delta t} = \sum{F}_\mathrm{int} = \frac{m \cdot ({u}^{\prime} - {u})}{\Delta t} = 0 \]

\[\frac{m \cdot ({u}^{\prime} - {u})}{\Delta t} = \frac{m_\mathrm{T}  \cdot ({u}^{\prime}_{\mathrm{cm}}- {u}_\mathrm{{cm}})}{\Delta t}\]

\[{u}^{\prime} = {u} \Rightarrow {u}^{\prime}_{\mathrm{cm}} = {u}_{\mathrm{cm}} \Rightarrow {a} = 0.\]

Could someone help me on these questions:

a) In Fig.1. is what is shown a Fictitious force?

b) IF (a) is true, is there any reaction force being exerted on rest of system?

 

Edited October 1, 2020 by John2020

[pzkpfw]

Just a note, "Fictitious" is not a synonym for "magic".

[John2020]

1 minute ago, pzkpfw said:

Just a note, "Fictitious" is not a synonym for "magic"

Of course not. A better name is "Inertial".

[swansont]

A fictitious force is one that makes an accelerating frame seem like an inertial one. So why not just analyze in an inertial frame?

A non-zero angular speed does not imply the presence of a force, fictitious or real.

[John2020]

9 minutes ago, swansont said:

A fictitious force is one that makes an accelerating frame seem like an inertial one. So why not just analyze in an inertial frame?

I think this is what I did or not?

Could you help me answer the questions above?

Edited October 1, 2020 by John2020

[swansont]

Just now, John2020 said:

I think this is what I did or not?

Then there is no fictitious force. No force at all is required for what you’ve shown, if the mass moves at constant velocity.

[John2020]

8 minutes ago, swansont said:

Then there is no fictitious force. No force at all is required for what you’ve shown, if the mass moves at constant velocity.

I think you didn't notice that I explicitly wrote the change in angular velocity Δω is not zero that implies a varying momentum on mass m_T (Fig.1).

In case Δω = 0 then the mass m_T would have constant speed.

Edited October 1, 2020 by John2020

[swansont]

3 minutes ago, John2020 said:

I think you didn't notice that I explicitly wrote the change in angular velocity Δω is not zero that implies a varying momentum on mass m_T (Fig.1).

You’re right. (I think the page did not render properly)

There must be a real force causing this

[John2020]

6 minutes ago, swansont said:

There must be a real force causing this

I didn't draw it actually. It is a hidden couple (back side) that creates a varying torque that leads to a varying angular velocity.

I have to go to sleep. I will be very happy if you can help me find an answer on those two questions. See you tomorrow.

Edited October 1, 2020 by John2020

[swansont]

1 minute ago, John2020 said:

I didn't draw it actually. It is a hidden couple (back side) that creates a varying torque that leads to a varying angular velocity.

Well, you shouldn’t have hidden things (drawings are assumed to be faithful depictions), but why is there a question here? You have a torque. What’s the issue?

[John2020]

I mean to find an answer on the two questions a,b I mentioned on my first post.

Edited October 1, 2020 by John2020

[Ghideon]

Disclaimer: since there are hidden parts and not a clear what the system is and where its boundaries are there's room for error in my replies.

 

14 hours ago, John2020 said:

a) In Fig.1. is what is shown a Fictitious force?

When the mass mt (the blue box) is accelerated then mt is affected by a non Fictitious force. Is the location of the arrow indicating that mt is pushed, rather than pulled, by the black belt?

[John2020]

There are no hidden parts. Mass m_T moves just because of the accelerating belt (mass is coupled on the belt). The faded arrow indicates a non-real force.

Edited October 2, 2020 by John2020

[Ghideon]

54 minutes ago, John2020 said:

There are no hidden parts.

Ok. I may have misinterpreted:

15 hours ago, John2020 said:

It is a hidden couple

But it does not change my answer regarding the blue box. When the mass mt (the blue box) is accelerated then mt is affected by a non Fictitious force. 

 

 

[John2020]

15 minutes ago, Ghideon said:

But it does not change my answer regarding the blue box. When the mass mt (the blue box) is accelerated then mt is affected by a non Fictitious force. 

I think you are making a mistake here. A linear accelerating or rotating reference frame implies a non-inertial frame of reference that further implies the shown force should be a Fictitious (Inertial) Force or not?

[Ghideon]

24 minutes ago, John2020 said:

I think you are making a mistake here. A linear accelerating or rotating reference frame implies a non-inertial frame of reference that further implies the shown force should be a Fictitious (Inertial) Force or not?

I am initially looking at this from an engineering perspective; without enough understating of the scenario my reply will be incorrect. You have an arrow in a picture and it is not clear to me what it describes. What is the point of application of the force Fictitious in Fig1? What object is it acting upon? 

[John2020]

9 minutes ago, Ghideon said:

I am initially looking at this from an engineering perspective; without enough understating of the scenario my reply will be incorrect. You have an arrow in a picture and it is not clear to me what it describes. What is the point of application of the force Fictitious in Fig1? What object is it acting upon? 

1.The faded arrow is not a real force (I already mentioned this)
2.The m_T is coupled on the belt
3.The belt is being accelerated (see Δω≠0)
4.Due to (2) and (3) the mass m_T accelerates
5.Due to (4) the acceleration of mass m_T appears as being influenced by a Fictitious Force (Inertial)

Obviously, it was made clear we found the answer on (a).
So, what about (b)? Do you see any kind of reaction force to emerge/appear while mass m_T is being accelerated?

[Ghideon]

17 minutes ago, John2020 said:

The faded arrow is not a real force (I already mentioned this)

Then it does not accelerate the blue box. Ill try a different way of answering:

17 hours ago, John2020 said:

a) In Fig.1. is what is shown a Fictitious force?

If the force Ffictitious in Fig1 acts on the blue box then the force Ffictitious is not fictitious; the answer to a) is "no".

 

From one engineering point if view, as I have tried pointed out, the force is ambiguously drawn. The force seems to push the box which may not be a good way to explain the situation. A soft belt does not so much push the box, it will pull the box. As long as the box accelerates to the right there will be tension in the part of the belt to the right and possibly slack on the left side. Or there will be a varying degree of tension all along the belt; more to the right than to the left of the box. 

I'm not moving on to b) until a) is resolved. 

 

 

Edited October 2, 2020 by Ghideon
spelling&grammar

[John2020]

33 minutes ago, Ghideon said:

47 minutes ago, John2020 said:

The faded arrow is not a real force (I already mentioned this)

Then it does not accelerate the blue box. Ill try a different way of answering:

18 hours ago, John2020 said:

a) In Fig.1. is what is shown a Fictitious force?

If the force Ffictitious in Fig1 acts on the blue box then the force Ffictitious is not fictitious; the answer to a) is "no".

I didn't expect the drawing of an unreal force to be a problem. Anyway, the faded arrow is not a real force, it does not exist. Remove the label Fictitious and the faded arrow. 

I hope now it is clear. Forget (a) and (b) and focus on the following question:

While mass m_T is being accelerated, do emerge or appear any kind of reaction forces that may affect the rest of the system (isolated)?

Edited October 2, 2020 by John2020

[swansont]

3 hours ago, John2020 said:

There are no hidden parts. Mass m_T moves just because of the accelerating belt (mass is coupled on the belt). The faded arrow indicates a non-real force.

You agreed there is a torque, which is not shown.

The belt exerts a force on the mass. It is quite real.

1 hour ago, John2020 said:

I think you are making a mistake here. A linear accelerating or rotating reference frame implies a non-inertial frame of reference that further implies the shown force should be a Fictitious (Inertial) Force or not?

You don’t have to analyze this from an accelerating frame, and there’s no indication you have done so. Each of your two options would have different treatments, neither of which are present.

 

50 minutes ago, John2020 said:

I didn't expect the drawing of an unreal force to be a problem.

Not doing proper physics analysis is indeed a problem

50 minutes ago, John2020 said:

Anyway, the faded arrow is not a real force, it does not exist. Remove the label Fictitious and the faded arrow. 

Except it is, as the belt must exert a force on the mass if there is acceleration 

50 minutes ago, John2020 said:

I hope now it is clear. Forget (a) and (b) and focus on the following question:

While mass m_T is being accelerated, do emerge or appear any kind of reaction forces that may affect the rest of the system (isolated)?

The mass exerts a reaction force on the belt.

[Ghideon]

40 minutes ago, John2020 said:

I didn't expect the drawing of an unreal force to be a problem. Anyway, the faded arrow is not a real force, it does not exist. Remove the label Fictitious and the faded arrow. 

You say the force is unreal and you seem to claim the force affects and accelerates a mass. That is a problem. When you present and unclear description of a scenario to an engineer you will be asked for clarifications. 

 

37 minutes ago, John2020 said:

While mass m_T is being accelerated, do emerge or appear any kind of reaction forces that may affect the rest of the system (isolated)?

What is the system? Where are the boundaries? 

 

Side note; engineering point if view: Given the descriptions so far: when the belt is accelerating: yes there will be forces inside the belt drive system. Let's assume mass mt is large and acceleration is large. Due to internal forces belt may snap, the cogs on the wheels may slip or break, axels may bend etc. 

 

[John2020]

I make another attempt to make all these clear::

1.The boundaries of the system is the blue frame in Fig.1

2.Regarding the mass m_T when I sat coupled I mean it is one thing with the belt underneath (like being glued).

I will make a little bit later a new design in order to have everything in place (along with the couple that turns the gear).

58 minutes ago, swansont said:

Except it is, as the belt must exert a force on the mass if there is acceleration 

 Belt and mass m_T is one thing that way I present it, as one thing. It is like during the production of the belt we have melt belt material equal to mass m_T together with the belt part at that location. 

Edited October 2, 2020 by John2020

[swansont]

29 minutes ago, John2020 said:

Belt and mass m_T is one thing that way I present it, as one thing. It is like during the production of the belt we have place belt material eqauk to mass m_T.

Then treat them as a single object. You then can’t treat the mass as a separate object. Pick one or the other.

[John2020]

1 hour ago, swansont said:

Then treat them as a single object. You then can’t treat the mass as a separate object. Pick one or the other.

I think it was a bad idea this thread. Assuming the mass of the belt is negligible compare to m_T could we continue? IF not then close the thread.

[Ghideon]

 

2 hours ago, John2020 said:

1.The boundaries of the system is the blue frame in Fig.1

Thanks! I assume everything (engine, batteries etc) that is required to accelerate the wheel and hence the belt and mass, is inside the box. We can put the box in space if that is ok so that gravity can be neglected. 

 

3 hours ago, John2020 said:

While mass m_T is being accelerated, do emerge or appear any kind of reaction forces that may affect the rest of the system (isolated)?

The answer to your question is then: When the belt is started, during the acceleration there will be internal forces that affects other parts of the system. The forces are real forces. 

 

12 minutes ago, John2020 said:

 Assuming the mass of the belt is negligible compare to m_T could we continue?

Yes.