Bender

P=F.v zero (output) power does not mean zero force. At the instant the thrust starts and v=0, the power will be zero. The "next instant", the rocket will have accelerated somewhat and the power is no longer zero. In other words, there is no length of time, however short, for which the average power is zero, but at the start itself, the momentary power is zero.

In the case of the rocket, the answer is provided by Swansont and others. There are several dependencies, one of which is the velocity. In practical systems, the power is usually not constant, especially the output power (output power = input power x efficiency). It is sometimes kept constant by a controller, e.g. in some electrical drives, but for practical reasons, the force (or torque) is limited at low speeds. For a universal motor, which can often be found in mixers and vacuum cleaners, the torque seemingly goes to infinity when the speed goes to zero. Of course, the electrical wires burn before that can happen (among other things; resistance of the wire becomes an issue).

Because I'm making a bunch of assumptions to get away from the rocket, which I interpret from the OP to be merely an example and detracts, as far as I can tell, from the real question. It is pretty obvious from the other replies in this thread that the OP is not interested in all the additional complications that come with the rocket. Look at the title of the thread: it is about the work equation, not about rocket propulsion. (also, I'm using output power, not input power)

The OP also assumes the force is constant. That's why he got 20 times the work. Obviously, both cannot be constant, but in the case of power being constant: F=P/v

I'll try to answer the OP as simply as I can. Therefore, I'm going to assume the rocket flies horizontal, has perfect efficiency and constant mass (in other words: it might as well be a car driving on a frictionless road in a vacuum). I have the impression that the rocket is overshadowing the essence of the question (although I could be wrong). If the force is constant, energy expenditure is not. It takes more work to accelerate from 10 m/s to 20 m/s then it takes to accelerate from 0 m/s to 10 m/s. Simply look at the formula for power: P=v F So, with constant force, the power (and thus work) increases with velocity.

If you happen to find one that is willing to listen ... .

If it falls apart in that situation, why not in others? Could you also address the other points in my previous post? (I think going back and forth about your so-called proofs is pointless, since you won't accept the arguments against it and I have run out of ways to rephrase them.)

If the wave functions do, in fact, collapse, and there are no hidden variables of any kind, this "program" is very unpredictable and chaotic. Even if the manyworlds interpretation is correct and wave functions do not collapse, the totality may be predictable and without mistake but the individual timeline we are aware of, is still equally unpredictable and chaotic.

I think it is important to note that the gradient isn't constant: there are periods with little evolution and periods more rapid evolution, depending on a variety of factors (including random luck). During "high gradient" periods, you'll have a high probability of "missing links", because the sample rate is not high enough to catch the small details.

Then why don't you? No it isn't, that's why one is called "demonstration" and the other is called "experiment". After which it has been carefully explained why the "proof" is invalid. Thank you for making my point for me. In these descriptions you have read, did they mention "taking the rough estimates of a demonstration out of context"? If it wasn't for Poe's law, I could only assume you are trolling at this point. I do your work for you, doing the calculations with your premisses in mind, and you won't even bother looking at them? I is possible you lack the skill, in which case you are welcome to ask for help. If I did make a mistake, it would be very helpfull if you could point it out. Let's try something different: ever heard of helicopters? Don't you think the engineers designing them would have noticed if their calculations completely failed to predict the behaviour of the helicopter? What about the engineers designing satelites and space probes. They should have been in for quite a surpise is their yo-yo de-spin device completely failed to perform or they didn't manage to target their satelites with the reaction wheels they designed. Except, you know, they didn't because it all worked fine. Perhaps you have heard of Kepler's laws of planetary motion? They are entirely consistent with conservation of angular momentum; in fact, the concept of conservation of angular momentum has its origin in Kepler's second law. Don't you think astronomers would, at some point in the last couple of centuries, have noticed something if they completely and utterly fail to predict planetary motion?

Besides, you really can't dismiss the derivation that easily. Sure, you dismiss the one based on conservation of angular momentum, since that is the subject of this speculative thread. The other derivation, however, is entirely and directly based on Newton's laws of motion. To dismiss it, you first need to dismiss Newton's laws.

We have two rigorous methods actually making a prediction, one heavily contested idea that has yet to provide any prediction, and no proper experimental results. Perhaps if I'm bored this evening, I'll adjust Levin's estimate to match your measurements exactly. If you do not even have a way to make predictions based on your idea, how can you even hope to confirm them experimentally? Do you really think you can go to a scientific journal with a wild idea, no predictions, no mathematical model and no experimental results?

Bycicle lights can strobe even without dimmer, because alternator produces alternating current, so when it goes through zero, and there is no cfpacitance in your light, it goes out at least twice every revolution. In very cheap lights, it is possible that it is off half the time, because LED's are polarised and conduct the current only in one direction.

Yes

Steel, aluminum, casting iron, stone... If you go for glass, I'd recommend pyrex. What shape does it need to have? What are other requirements?

In other words, because I don't accept it, your god does not exist?

Ok, it took me more time than I was hoping, but I had some fun with the mathematical derivation of the example of the rotating professor (or a any isolated system, really) mathematically without using angular momentum, only using Newton's laws of motion and basic geometry. What we have is a central, rotating object with unchanging moment of inertia [math]I[/math] and angular velocity [math]\omega[/math]. There are two equal and small masses ([math]m/2[/math] each) symmetrically attached to this object at radius [math]R[/math]. They can symmetrically move in and out, while their angular velocity is always equal to that of the central object. When the radius changes, the masses have an acceleration with two components, the first is a result of the angular acceleration [math]a_1=\alpha R[/math], the second is the coriolis acceleration caused by the radial speed [math]a_2=2 \omega dR/dt[/math] (a derivation of this can be found here), or combined: [math]a_t=\alpha R+2 \omega dR/dt[/math] (1) We need to find a relation between the linear acceleration of the masses and the angular acceleration of the central object. The force required to accelerate the masses is: [math]F_t = m/2 \cdot a_t[/math] The torque required to accelerate the central object is: [math]T = I \alpha[/math] This torque is a result of the reaction forces from the masses: [math]T=-2 F_t R = m a_t R[/math] Notice that the radial forces do not matter as they cancel out. Now combining the last two equations: [math]I \alpha = - m a_t R[/math] or [math]a_t=-\frac{I \alpha}{m R}[/math] Substituting in (1) [math]-\frac{I \alpha}{m R}=\alpha R+2 \omega dR/dt[/math] or [math]2 \omega R dR/dt=-(\frac{I} {m}+R^2) \alpha[/math] [math]2 \omega R dR/dt=-(\frac{I} {m}+R^2) \frac{d \omega} {dt}[/math] [math]2 \omega R dR=-(\frac{I} {m}+R^2) d \omega[/math] rearranging [math]\frac{1}{\omega} d \omega= - \frac{2 R}{(\frac{I} {m}+R^2)} dR[/math] (2) Now I'm going to do a substitution to facilitate the integration: [math]x=(\frac{I} {m}+R^2)[/math] [math]dx=2 R dR)[/math] putting this in (2) yields: [math]\frac{1}{\omega} d \omega= - \frac{1}{x} dx[/math] integrating between two radiuses: [math]\int_{\omega_1}^{\omega_2}\frac{1}{\omega} d \omega= - \int_{(\frac{I} {m}+R_1^2)}^{(\frac{I} {m}+R_2^2)}\frac{1}{x} dx[/math] almost there: [math]ln(\frac{\omega_2} {\omega_1})=ln(\frac{\frac{I} {m}+R_1^2} {\frac{I} {m}+R_2^2})[/math] note that the second natural logarithm was inverted because of the minus So at last, shifting a bit around, we have the answer, which is very generally applicable: [math]\omega_2=\omega_1 \frac{I+m R_1^2} {I+m R_2^2}[/math] Of course, we can do the same calculation using conservation of angular momentum [math]L_1=L_2[/math] [math]I_1 \omega_1 + m R_1 v_1=I_2 \omega_2 + m R_2 v_2[/math] replacing v [math]I_1 \omega_1 + m R_1^2 \omega_1=I_2 \omega_2 + m R_2^2 \omega_2[/math] [math]\omega_1 (I_1 + m R_1^2)=\omega_2 (I_2 + m R_2^2)[/math] [math]\omega_2=\omega_1 \frac{I+m R_1^2} {I+m R_2^2}[/math] That looks surprisingly familiar (not that surprising really ). It sure was a lot easier. You seem very fond of logical proof, here you have an actual logical proof.

You have a point.

Problem: I do not accept this, so we cannot proceed further.

Ship captains do not have their hand on the rudder. They map out the course ahead of time (motivation), and notice the ship going in the correct direction after the navigator turns the rudder.

Why can there be no tangential component? Please keep the discussion to isolated systems, such as the rotating professor, and not the mass on a string, which isn't isolated.

If the radius is reduced, the angular velocity of the outside mass will increase, and it will fly past the perpendicular position of where the string is attached to the central mass, resulting in a tangential component of the force in the string, which slows down the outside mass and causes a torque on the central mass.

I didn't say my statement was new or original .

On dimming of LEDs: they don't usually dim, because they operate at a much lower voltage, and therefore contain electronics to convert any input to the supply they need (there have been problems with LED lights being on even with the switch turned off, because of a small voltage caused by capacitive coupling between the wires). Dimmable LEDs contain additional electronics to implement e.g. PWM based on the input they receive, which is quite similar to how a traditional dimmer works.

1. no 2. what you want is a peristaltic valve: take a motor with an eccentric camshaft to open or close the hose, much easier and requires no power in on or off position 3. In the configuration you suggest, de-magnetizing one of the magnets will be required to open the valve 4. Configurations with only one magnet and a coil work much better, you could use e.g. a spring to pinch the hose and a coil to push the magnet into the spring, but see 2 5. Possibly. You need a pretty big coil to demagnetise a Neodymium magnet.