Newton's laws in variable mass systems

[pallidin]

Open to what?
We have defined parameters that demands external forces are eminently and immutably existent.
How is that "closed" at all?

 

[Dickfore]

Please chose one of the options below:

[1] Open mechanical systems exist;

[2] Open mechanical systems do not exist.

Read carefully before you chose.

 

[pallidin]

Please chose one of the options below:

[1] Open mechanical systems exist;

[2] Open mechanical systems do not exist.

Read carefully before you chose.

My answer, 2
Totally open mechanical systems are not physically possible.
Provide even one example of a totally open system.

 

[D H]

In classical physics and thermodynamics, systems can be isolated, closed, or open. An isolated system is truly isolated. It exchanges neither energy nor mass with its surroundings. The surroundings are completely irrelevant in the case of an isolated system. The surrounding environment is important for closed systems and open systems. A closed system exchanges energy but not mass with its surroundings. An open system exchanges energy and mass with its surroundings.

Isolated systems are nice for toy problems. The only true isolated system is the universe as a whole (maybe; I think the jury is still out even on that). Many systems are approximately isolated. The solar system, for example.

The solar system obviously is not truly isolated. It does interact gravitationally with nearby stars and the galaxies.The solar system is, in fact, an open system. Some of the solar wind does escape the solar system, and some of the interstellar medium crosses the heliopause into the solar system. So, how can the solar system be an open system and yet be accurately treated as an isolated system? Simple: The interactions are tiny. Those interactions can be safely ignored in many applications. Even the most accurate of the solar system ephemerides model do not model interactions with bodies outside of the solar system.

So the solar system illustrates one simple way to deal with the challenges presented by an open system: Pretend otherwise. A lot of physics involves knowing what simplifying assumptions could help with solving a problem and determining whether using those simplifying assumptions comprises the solution.

With a rocket ignoring the exhaust is not an option. The exhaust is an extremely important part of the dynamics of a rocket. (It is in a sense why the rocket goes.) The exhaust stream, however, is not important at all. What happens to the stuff in the exhaust stream once it is well past the shock boundary isn't going to impact what happens to the rocket one iota. Properly drawing the control surface that separates the system of interest from the surrounding environment is another one of those simplifying that physicists and engineers make.

 

[pallidin]

An isolated system is truly isolated. It exchanges neither energy nor mass with its surroundings.

While true in a theoretical sense, it is not possible in the real world at all.

 

[pallidin]

Can it be shown, for example, that a totally isolated system can exist at all?
I want some evidence. Give me even a small piece to chew on.
Any takers?

 

[D H]

So what is the argument? DickFore has been talking about open systems. A rocket, for example. Reread the definitions of isolated, closed, and open systems, and then answer Dick's question in post #72.

 

[Dickfore]

Jesus Christ! Will you choose a stance and stick to it?

 

[pallidin]

Jesus Christ! Will you choose a stance and stick to it?

What? There IS NO SUCH THING as a closed system(excepting the universe of course)
That's my stance from the beginning if you didn't notice.
Hello?

 

[D H]

No, your stance has been that an open system doesn't exist. That is what has Dick and I confused.

That said, there certainly are systems that are for all practical purposes closed or isolated. If the effects of some external interaction are orders of magnitude smaller than the effects from state uncertainties, measurement errors, etc., or orders of magnitude smaller than any physically meaning result, who cares? If all external interactions are dwarfed by uncertainties, errors, and significance, the system is for all practical purposes isolated.

 

[pallidin]

Can ANYONE show me even ONE pure example of an open-system?
No.
That's my point, and highly relevant to physics.

 

[D H]

?

Will you take a stance, please? And do stop using words like "totally open" and "pure example of an open system". That doesn't make sense.

 

[pallidin]

Well, then, allow me to rephrase.
Is there any experimental evidence which demonstrates that systems are totally isolated from another? Any at all? Please give evidence.

 

[D H]

I think your confusion is that you do not understand that open is the opposite of isolated. Reread the definitions in post #74, and if what I wrote doesn't make sense, use google.

To answer your question, yes, except for systems that are isolated by virtue of the expansion of space, all systems interact with one another to some extent. That said, no physicist is going to care about the gravitational effect of some extremely remote star on their Earthbound gravity experiment. The interaction is so incredibly tiny that it can be utterly ignored. It doesn't exist as far as the experiment is concerned.

Modeling a system as being isolated or closed is a useful abstraction -- when that abstraction is applicable.

 

[pallidin]

?

Will you take a stance, please? And do stop using words like "totally open" and "pure example of an open system". That doesn't make sense.

Oh, what is wrong with "totally open"?
That simply means open without boundaries.
And "pure example" is only asking for the truth, that's all.

 

[pallidin]

Modeling a system as being isolated or closed is a useful abstraction -- when that abstraction is applicable.

Upon which standard do you define the abstraction? Not easy, my friend.

 

[D H]

Oh, what is wrong with "totally open"?
That simply means open without boundaries.

What's wrong with your terminology is that it is in complete disagreement with the standard definition of an open system. A system without boundaries cannot be open. Think of your house. Open the doors and windows and air flows into and out of the house. The house with the open windows and doors is an open system. Close all the doors, close all the windows, seal all the cracks and the air flow pretty much stops. That's a closed system (approximately). It's still not an isolated system because heat flows between the inside and outside the house through the closed windows, the closed doors, the walls, the floor, and the ceiling.

 

[D H]

This link presents a nice short synopsis of open versus closed versus isolated: http://www.bluffton.edu/~bergerd/NSC_111/thermo2.html.

 

[pallidin]

I will retire for the evening and consider your thoughts.
Thank you.

 

[jostpuur]

lol, what ever you say. I don't want to quarrel and get a ban. If someone reads this thread and knows Physics, they will draw a conclusion for themselves.

A ridiculous thread. cjl and Dickfore clearly have lot stronger understanding of basic mechanics than D H

In the beginning cjl was trying to explain this:

Rocket motors do not change in thrust just because you attach them to a different vehicle. The force they generate is purely a function of their massflow and their exhaust velocity. Hence, vehicle mass and velocity are irrelevant.

D H disagrees. According to him the thrust must depend on the vehicle into which the rocket is attached. He justifies this by defending the importance of the concept of thrust.

Or maybe, aerospace engineers thinking that the thrust produced by a jet or a rocket is a meaningful quantity and testable quantity is just plain goofy. NOT.

Makes no sense! The thrust produced by a rocket must not exist, because it must exist?

 

[D H]

(Specifically, F = $\dot m$V_e for any rocket motor, in which $$\dot m$$ is the fuel mass flow rate, and V_e is the exhaust velocity)

That is correct only if you toss the definition of force as F=dp/dt and use m·dv/dt=F_ext+u·dm/dt in its place, where u is relative velocity of expelled material. Defining F_reaction≡u·dm/dt let's one simply use F=ma, even for a system with non-constant mass. This form is admittedly very useful as the basis for the equations of motion of a rocket. It is however absolutely useless for computing things like work precisely because it throws out the connection with the conservation laws.

It is this $\dot m$V_e term that this entire silly imbroglio is all about. Is it a force or is it something that happens to have units of force? The answer lies in how one interprets Newton's second law. Is force defined by F=dp/dt or F=ma? Different textbooks do use different definitions, and the two definitions definitely are not the same in the case of a variable mass system.

 

[Dickfore]

It is a force. It comes from the ejected particles who act on the reamining part of the rocket according to 3rd Newton's Law.

 

[D H]

Fine. Is this force the same in all frames?

Answering yes puts you in the F=ma camp.
Answering no puts you in the F=dp/dt camp.

 

[Dickfore]

Fine. Is this force the same in all frames?

Answering yes puts you in the F=ma camp.
Answering no puts you in the F=dp/dt camp.

Forces are Galilean invariants. This one is too. To see this, notice that both $\mathbf{u}$ and $\dot{m}$ are Galilean invariants. There are no camps. Your transformation formula for the force was incorrect.

 

[D H]

Then tell that to Marion, and Goldstein (or the authors who have taken over for them) and others as well.

And please do find the flaw in that derivation. HINT: it is not my derivation.

 

[Dickfore]

The "third camp", the one you said retreated from the discussion, was right. I guess they saw that they were dealing with obtuse opponents, so there was no point for them to propagate the discussion.

You (and I) derived something which is not Second Newton's Law. It simply gives the acceleration of the center of mass of a system with variable mass in terms of the external forces (real ones) acting on the particles that happen to consist the system at that instant and the momentum flux (according to the CM frame) that goes out and into the system. The equation happens to be of the form:

$$m(t) \, \mathbf{a}(t) = \sum{\mathbf{F}_{\mathrm{ext}}(t)} - \mathbf{\Pi}_{\mathrm{out}}(t) + \mathbf{\Pi}_{\mathrm{in}}(t)$$

However, this is NOT Second Newton's Law! It is an equation of motion. I don't even think Newton wrote down an equation of motion for a system with variable mass. I think this equation is derived by Meshchersky in the beginning of the XX century.

Furthermore, this equation tells us about the motion of the CM of the variable mass system. As an extreme example, a variable mass systme is a two-body system where one of the particles exits the (geometric) boundaries. It is obvious that the above equation is of little use in that case. The case where this equation is useful is where it makes sense to approximate the momentum flux $\mathbf{\Pi}$ as a continuous function of time and the object you are considering has a much bigger mass than the mass it exchanges. Also, it is convenient if the geometric boundaries of the object are actually rigid walls and the motion of the object is then that of a rigid body (with a variable mass fuel compartment). This is an abstraction of a 'rocket'.

As you mentioned very well, this equation is not sufficient to predict the motion of such a 'rocket'. One still needs the equation of motion for the rotation angles in relation to the external torques. As you noted, the problem is quite complicated in realistic situations.

 

[arildno]

DH's position is just silly.
It is unsurprising that he employs the logical fallacy ad authoritam

To take a case where it is utterly nonsensical to describe the momentum flux as a force, we can look at a fluid moving at constant (horizontal) velocity U, and choosing as our control volume that at t=0 starts out as a line segment of length 1, broadening into a rectangle, where one side remains stationary at the initial position of the line segment, the other vertical side moving with (horizontal) velocity V.
Letting d be the density of the fluid, the momentum containe in our control volume is simply U*V*d*t, with a rate of change U*V*d

In this case, the rate of change of momentum within our control volume cannot be ascribed as the effect of an acting force.
Forces act solely upon material particles, not upon arbitrarily chosen spatial regions*. The rate of change of moementum is solely due to flux of momentum, i.e, a quantity that has the same units as force, but is still wholly distinct from force.


Note:
Some use "momentum flux" to designate what I'd call "momentum flux density", i.e, the rate of momentum transfer per unit area(by means of momentum-carrying particles leaving the control volume).


*Remember that in the classical world time&space are dynamically inactive quantities, merely the empty box within which dynamics and the play of forces occur.

 

[D H]

My view might be silly, but it is the one most widely supported in literature.

Oh, and it is also useful.

 

[Dale]

Can a rocket, as opposed to the rocket + exhaust, be modeled with a Lagrangian?

 

[D H]

If it is going through a non-conservative medium (e.g., the atmosphere), no. If it has a control system that turns thrusters on and off, throttles them, gimbals them, or activates some other effector to keep the vehicle under control, no.

In short, the answer is no.

 

[Dickfore]

DH's position is just silly.
It is unsurprising that he employs the logical fallacy ad authoritam

To take a case where it is utterly nonsensical to describe the momentum flux as a force, we can look at a fluid moving at constant (horizontal) velocity U, and choosing as our control volume that at t=0 starts out as a line segment of length 1, broadening into a rectangle, where one side remains stationary at the initial position of the line segment, the other vertical side moving with (horizontal) velocity V.
Letting d be the density of the fluid, the momentum containe in our control volume is simply U*V*d*t, with a rate of change U*V*d

In this case, the rate of change of momentum within our control volume cannot be ascribed as the effect of an acting force.
Forces act solely upon material particles, not upon arbitrarily chosen spatial regions*. The rate of change of moementum is solely due to flux of momentum, i.e, a quantity that has the same units as force, but is still wholly distinct from force.


Note:
Some use "momentum flux" to designate what I'd call "momentum flux density", i.e, the rate of momentum transfer per unit area(by means of momentum-carrying particles leaving the control volume).


*Remember that in the classical world time&space are dynamically inactive quantities, merely the empty box within which dynamics and the play of forces occur.

I don't have the faintest idea what you are talking about.

 

[arildno]

My view might be silly, but it is the one most widely supported in literature.

Again, just meaningless appeal to authority

 

[stewartcs]

Again, just meaningless appeal to authority

That's actually not a meaningless appeal to authority.

If DH had used himself as the authority, then made a claim that his position was true because he said it was, then it would be a logical fallacy. However, since DH is referring to separate reputable sources (i.e. peer reviewed literature) it is not a logical fallacy.

If using reputable literature as an authoritative reference is a logical fallacy then no one on this site should be posting unless they have performed original research (implying they would be committing a logical fallacy).

However, with that being said, if DH is a "rocket scientist" then he may very well qualify as an expert on this subject and may indeed make authoritative claims without committing a logical fallacy.

CS

 

[Dickfore]

That's actually not a meaningless appeal to authority.

If DH had used himself as the authority, then made a claim that his position was true because he said it was, then it would be a logical fallacy. However, since DH is referring to separate reputable sources (i.e. peer reviewed literature) it is not a logical fallacy.

If using reputable literature as an authoritative reference is a logical fallacy then no one on this site should be posting unless they have performed original research (implying they would be committing a logical fallacy).

However, with that being said, if DH is a "rocket scientist" then he may very well qualify as an expert on this subject and may indeed make authoritative claims without committing a logical fallacy.

I have yet to see him provide a peer-reviewed Journal or a redacted textbook in which the equation:

$$\mathbf{F} = \mathbf{F}' + \dot{m} \, \mathbf{V}$$

is derived (see the beginning of post #14).

 

[D H]

I have yet to see him provide a peer-reviewed Journal or a redacted textbook in which the equation:

$$\mathbf{F} = \mathbf{F}' + \dot{m} \, \mathbf{V}$$

is derived (see the beginning of post #14).

You have been given a reference to exactly such a derivation twice in this thread. Here they are (both link to the same article):

Plastino & Muzzio, Celestial Mechanics and Dynamical Astronomy, 53:3 (1992) http://articles.adsabs.harvard.edu//full/1992CeMDA..53..227P/0000227.000.html.

This may be of use here:
http://articles.adsabs.harvard.edu//full/1992CeMDA..53..227P/0000227.000.html