martillo

Right for me too. By the way, I'm waiting for your treatment of the problem as we begun with your post: The subject for me is to analyze for if the Force Equation F = ma would hold or not for variable mass according to that your presented book, do you remember? I'm rereading it and seems the professor actually agrees with me! Is that right or am I taking it wrongly? Please explain with which equation the book agrees: with F = ma or with F = dp/dt for variable mass in the rocket. I'm a little confused... Now I see it clearly: DR. Cowan agrees with me that the equation used in the motion of rockets is F = ma = mdv/dt for variable mass! Excellent. I was worried about that. The claim of the thread still stands! I don't know what should we discuss then. Can you tell me now, I'm a little confused...

Thanks! I would appreciate your reasonings on the problem very much. Just for the case, I post here my derivation of the thrust based on the Force Equation as F = ma valid even for variable mass. I presented it at the OP but with a couple of stupid silly mistakes I have corrected in it: Rocket thrust force derivation The thrust equation of the rocket is derived here considering the approximation that the mass of the expelled fuel of the rocket is negligible compared with the mass of the mass of the rocket plus the mass of its contained fuel: Momentum and Force equations: p = mv, F = ma = mdv/dt dp/dt = mdv/dt + vdm/dt = F + vdm/dt Considerations: a) masses equations: m = mass of the rocket with its contained fuel me = mass of the expelled fuel m’ = m + me = constant = total mass of the system rocket with total fuel dm’/dt = dm/dt + dme/dt = 0 Then: dme/dt = -dm/dt b) velocities equations (one dimension): v = absolute velocity of the rocket ve = velocity of the expelled fuel in relation to the rocket assumed constant u = absolute velocity of the expelled fuel ve = v – u = constant dve/dt = dv/dt – du//dt = 0 Then: du/dt = dv/dt Derivation: Total momentum of the system rocket with total fuel: p’ = mv + meu dp’/dt = d(mv + meu)/dt = mdv/dt + v/dm/dt + medu/dt + u/dme/dt Considering: du/dt = dv/dt and dme/dt = -dm/dt dp’/dt = (m + me)dv/dt + (v-u)dm/dt As v – u = ve and considering me << m (m + me ≈ m) then: p’ ≈ mdv/dt + vedm/dt and as dp’/dt = 0 then: mdv/dt ≈ -vedm/dt Finally F = ma = mdv/dt ≈ -vedm/dt under the approximation me << m Then the rocket thrust force is: F ≈ -vedm/dt

Unfortunately I'm not able to analyze in terms of Lagrangians. That is Variational Calculus and as I said several times I have no expertise at all in this area. That's why I'm waiting for studiot's treatment of the problem now...

But you said to be considering the rocket as an open system with an external force applied to it... Right I edited it:

Just to clarify, what I agree here is that this is the equation currently being applied in the rocket motion. Here is used the Force Equation dp/dt = Fext. Is not my proposed equation, I claim that actually the equation should be: ma = mdv/dt = Fext and is not zero in the problem we analyze.

In the problem we are analyzing we have constant exhaust in velocity and mass, ve = constant and dme/dt = -dm/dt = constant. We have then a constant force F on the rocket which is the Thrust Force, F = -vedm/dt and the rocket have a constant acceleration continuously increasing its velocity v. To have constant velocity v no force would be applied except for the case of air resistance...

Is much more than that I think... A control in the rocket's motor on the quantity of exhausting (control of ve ) would be needed.

Seems straightforward to consider horizontal coordinate x and vertical coordinate z. Then it can be considered two equations, one in the x axis without gravity force involved and the other in the z axis with gravity included. The equation in the x axis is which we were considering in the entire thread and it has all Mathematical and Physical strictness I think. I agree although I don't think there's a problem with the x notation. Depends on the considered problem,. If the rocket is ready to launch then the origin is at the base of the rocket. If we consider just the rocket flying in the air from some instant then the origin would be the place of the rocket at that instant. I agree. I think it would be much better but I will try to follow your approach. I will point out if I see some problem with this at some time. Well, it will need a mobile exhausting system to control the direction of the flux of the exhaust and/or some mobile wings as some missiles have. I'm just looking forward for your announced treatment of the problem of the rocket...

I just disagree with your comment below of the equation because if the rocket is treated as an open system as you said at page 6 of the thread then Fext ≠ 0. Fext is equal to the force that the exhaust produce on the rocket Fext = -vedm/dt which is the Thrust Force.

I apologize. I read it to fast. I think I can agree in everything there. That's a problem I have while discussing with several ones at the same time, to read to fast. By the way we have discussed about some things may be time ago and I find you very knowledgeable and reasonable and have all my respect. I see now your approach is very similar to that we are having with studiot now. Your comments will be very important to me as always have been. From the combustion of the fuel. Energy is stored in the fuel. I totally agree with this I think...

I didn't ignored you at all. I answered you several times as you can see at page 8 of this thread. What arguments do you want me to take into consideration? I don't understand... I mean both pr and pe augments their magnitude (in absolutes values) with time while the rockets move. Right, a constant burn exhausting burnt fuel at constant velocity ve relative to the rocket and constant mass being expelled all the time (dme/dt = constant). I was making calculations. Please consider p = p0 at the start of the burn but p1 at the launching when the rocket starts to move. There's an interval of time between the start of burning and the start of the rocket's landing which is important to take into consideration. In this interval fuel mass is being expelled so pe augments in magnitude as the momentum of the total system p augments in magnitude from 0 to some p1 = pe1 . In this interval the momentum of the rocket remains pr = 0 since the rocket does not move (v = 0). At time t = 0 momentum p = p0 = 0.

No, I'm just saying I cannot proceed any more. It is not to yield to opinions. It is not about opinions, is to go on from what is right. We both cannot go on if we don't reach an agreement at this point. Good night.

You can't. The momentum of the total system of the rocket and the exhausted fuel includes all the mass exhausted from the initial state to the end. You cannot just discard all that mass already exhausted time ago in the conservation of momentum. If you don't agree with this I cannot proceed anymore. No, pr is not constant, is just pr = p0 - pe . Both increasing in time with the energy of the combustion of the fuel.

No but mB will be the total exhausted fuel all the time from the beginning to the end while dmB is a differential component of it in a differential element of time dt. You cannot relace one by the other in the equations. Is something wrong. Fine, I said: Proceed now as you want with p = some constant. Doesn't mind for me. I will consider: p = p0 for instance and pr + pe = p0 constant. Fine for you?

Until the moment the rocket begins to move we can consider the exhausted fuel as just wasted or used to heat the motor to a right temperature or something like that. I think we can well consider the moment of the total system (rocket + exhaust) as p=0 at the initial state as at any state. Or you don't want to analyze this way?

I'm confused with your approach and will take time to me analyze it but I will. Here is a mistake I think: in your ending relation does not appear mB. It should be: FB = dpB/dt = d/dt (mB (v-(v-ve)) = d/dt (mB (v - ue)) = mB(dv/dt - due/dt) + (v - ue)dmB/dt = mBdv/dt + (v - ue)dmB/dt Let me say if it is right for you. If you correct this may be we can go on.

May be I didn't express it correctly. Let me try again: If we consider the total system (the rocket and exhaust together) we have not only dp/dt = 0 but also p = 0. If we consider now rocket and exhaust separately, say pr and pe, then pr = -pe and so pr + pe = 0. Is not a conserved quantity unless it means zero. I think something is going wrong there... Let we see how it proceeds...

Well, for the total system (the rocket and exhaust together) we have dp/dt = 0, right? Thinking on...

As I could see Lee Smolin looking for a unification of Relativity with Quantum Physics. You are right that this not my approach of Physics from scratch at all. You decide...

If I would be wrong in something I would prefer to be corrected by you in it, not being just discarded...

That was said for the case presented by Genady of a melting ice moving at some constant velocity v. We were analyzing that how th principle of conservation of momentum applies.

You are right. They must be conserved for closed systems only without external forces or energies being applied to or delivered from it. It is just that it was the case we were analyzing, a closed system.

I like hyperphysics. It gives very concise, simple but precise and strict presentations of fundamental things in Physics. I analyzed many things with the help of it. But if you think it could change my approach that there is needed a profound review in Physics from the beginnings (say Newton laws) and that a new developing must surge from scratch then you are losing your time. That will come, in one way or another one, the point is if you are going to stay just waiting for it or if you are going to be a protagonist of it. I'm trying something, it looks a good approach although is just a start-point. Don't pretend me to have all resolved. Impossible. I'm presenting this start-point here in this forum to be analyzed with the total rationality I have seen things are treated here. I think we, here, could make a good progress. I would ask you now, just to consider what is proposed just for a while to analyze where it could go, just for a while...

No, no. Your comments are being very important to me. As you say they are being a contribution, an excellent contribution. It`s a misspelling, by discussing I meant interacting, interchanging ideas, with good criticism of course, just that. Which would be a better word for this?

I asked you to give me some time...