Capiert

va=(vi+vf)/2=(0 m/s + 10 m/s)/2=5 m/s I guess (accelerated) average_speed (va) is the wrong name (for what I'm trying to say). What would you propose (for the accelerated average speed)? (average accelerated speed, =average_(accelerated)_speed?) Speed_difference v=vf-vi=10 m/s - 0 m/s=10 m/s.

(I agree, but it looks like I did NOT make it (=that mistake), & you (accidently) did. Y/N?) Units: meter * meter = meter_squared. Your ke=m*v*v*a is wrong, & my KE=m*v*va is correct. I do NOT know why you (want to) perpetuate an error. Do you (know why)? Do you NOT recognize the difference between both formulas (KE & ke)? Surely that error must be obvious (=trivial). ?

I agree that formula you typed is garbage, but don't you think you made a typo (error)? I typed KE=m*v*va. va (=average_speed), NOT v*a (=speed_difference multiplied by acceleration). But thanks for showing me my formula that you meant.

Not yet. Please (simply) show me that math you mean (which unites both conservation laws).

That's a mighty fascinating question Strange. Gravitational push (e.g. expanding matter theory=hypothesis) supports an accelerating expansion, & a steady state (=NO big bang*), & that black holes are an optical illusion (=the red shifts are observed as different speeds further from the universe's center). I see KE as a(n incomplete) distortion of Newton's (linear acceleration) mechanics. (E.g. How can you support both COE & COM (conservations of: energy & momentum), when the math doesn't work to unite them?) *I just can't maintain the religious belief that all this universe was magically created in an instant, (like someone had done it, abracadabra!) It's so rediculous (=absurd) to maintain the superstitious tendancies of our (midevil) ancestors (if you can pierce thru the(ir) psychology). Tradition is popular, so it'( wa)s kept (to sell the idea, e.g. books).

Vis_viva=2*KE is twice the kinetic energy KE=m*v*va of a mass m multiplied by (both) its ((linearly) accelerated) speed_difference v=vf-vi, & average_speed va=(vi+vf)/2, for the initial & final speeds vi, vf. -- (That (double KE) was) Something I call(ed) speed_energy SE=2*KE, (pronounced: see to key) to get rid of the 2 divider (way back when .., in my notes). I.e. Depetto's (1903) E=m*(c^2) looked like twice a KE formula. ("Wasn't that (rest mass energy) missing the half?") -- Gravesande (had) dropped various brass ball weights in clay mud, & found: The product of height h & weight Wt=g*m, produced identical impressions; & so he concluded (what I call, (& nobody else)) Leibnitz's "v's: v; va" was (=were) correct. -Pun. What a joke. (=Sidetrack (away) from Newton's correct momentum physics.) Now, 100's of years later, we've got a big problem with unknown (=dark) energy. I.e. Although we can show a linear height relation with speed_squared (apparently) supporting energy, physicists did not pin point their missing double mass 2*m (factor). E.g. dark (=unknown) mass. Summary: mom^2=m*E*(v/va), E=(mom^2)*(vf+vi)/((vf-vi)*2*m). 2017_07_29_1124_Gravesande’s_vis_viva_2017 07 29 1124 PS Wi.pdf

I suppose (=guess) a hovercraft's apron helps round_out (=generalize) th(os)e surface differences, a bit, (to an air_pressure cushion force), decreasing that factor 2 closer to 1. But the air_leak outward at the bottom means we could never have 1. Hover in a (seated) tube: I'd expect, a fan('s force, balanced & aimed downward) in a (sitting) vertical tube (with (the tube's) inner diameter slightly larger than the fan blade's diameter, & with the tube's bottom sealed (off) by the ground (it's seated on)), would have a better merit factor, & help get closer to the 48 W/kg (instead of 96 W/kg) due to the contained air's (almost strictly vertical (net)) bounce_back. I.e. less air_leak sideways, as redirection of force (to 90 degrees=) horizontal. The air_pressure P=F/A is obviously larger under the fan (for the (same) area A, in any direction inside the tube), to support the fan's weight.

I have not (yet) estimated surface friction from surface texture. (That's a big deal.)

From that I can interpret (=assume) for the -10 % power advantage (the following equivalents:) the initial_speed vi=-0.98 m/s is negative as a backwind (=air bounce_back, from the ground) in the power equation P=F*(v+2*vi), where the speed_difference v=8.82 m/s. Or, the average_speed va=4.41 m/s for the equation P=2*F*va where the force F=Wt weight (=m*g) of the helicopter (with pilot etc).

To get the math straight I meant the hover power (equation) P=F*(v+2*vi) has "twice" the initial speed vi which is usually ignored when assumed zero. Where the speed difference v=vf-vi is the final speed vf minus the initial speed vi. The standard power P~F*v is an approximation (instead of exact(ly including initial speed vi, too)).

My point is the factor "2". I couldn't figure out why the standard formula (without the 2) did NOT work (til now). "Double" the (helicopter) mass m is needed because of Newton's 3rd (law) sets an opposite mass (=the air) also in motion.

The reason I "had" thought the answer was 48 W/kg was because the power P=F*va is the force F (as weight Wt=m*g=1 kg*9.8 m/(s^2)=9.8 N) multiplied by the average speed va=(vi+vf)/2=(0 m/s + 9.8 m/s)/2=4.8 m/s (attained in 1 second starting with the initial speed vi=0 m/s & ending with the final speed vf=9.8 m/s added together & (then) divided by 2). But Janus has shown us that formula does NOT work & that we need double the mass (2*m=m+m) (that extra kg, is) for the opposite & equal reaction (of the air) when m is the mass of helicopter + (passengers + fuel + bagage, etc) (Newton's 3rd law). The correct formula for a(n ideal) helicopter" (hover power) using that method, with the same average speed va=4.8 ms, (& ignoring losses) would be P=2*F*va, or P=2*m*g*va.

Then may we continue there? I.e. The difference of charge density.

Well then I'm sorry but I do NOT know what Manticore meant by "charge gradient". I could find nothing on the topic.

I assume, a charge gradient can be the difference wrt distance (position) of (either) the surface_charge_density sigma=Q/A (or the volume_charge_density rho=Q/vol). Isn't the charge gradient maximum near the plates; & minimum in the middle between the 2 plates? Is not the (electric) potential maximum at each plate; but minimum in the middle (between both plates), because of opposite polarities? Is not the electric_potential zero in the middle as an equipotential? I.e. (both potentials are the) same amount, but opposite polarity. Does not positive potential cancel negative (potential) at the same position (of overlap)? (Otherwise, zero (=neutral) charge would never exist, anywhere. A discharged capacitor would NOT be possible! But we don't see that (impossible neutrality). Instead we see that things can be charged (up), & (can be) discharged. E.g. A thing is either charged, or not (=neutral). The (dielectric's) polarization in the middle of the capacitor is minimum (e.g. zero); but maximum nearest the plates (having the opposite polarity of a nearby plate).

The (capacitor's) plates are physically separated (naturally, no argument there); but the(ir) (positive & negative, as) "sum" of their surface_charges (sigma=+/- Q/A) at the "position" of the oil drop has a cancelation effect (=resulting total, which is less (than a single plate)).

[Ref Swansont's "no idea..". PS: How do I get "quote" "copy & paste" to work in Windows explorer too on this website, instead of iPad?] I equate the force is proportional to a (volume) charge_density "difference" (between (the charged oil_drop) q & the plates total (+ & -) affect, considering q has its own charge_density=cd). If the volume_charge_densities are different (between q & its position), then they (both q & its position's cd) will attempt to equalize causing charge_flow (i.e. the oil_drop will (be forced to) move). That is the motivating force, (that moves the (bound) mass (of the charge)), the mechanism why it works, =moves (the charged oil drop mass). (The charges attempt to equally space (& distance) from 1 another because they all repell.) The volume_charge_density's "cancelation effect" is just another way to express the (Gauss's law) surface_charge_density's cancelation effect, when positive & negative (surface_charge_densities sigma=Q/A) overlap (onto the same position). "Surface (charge_density)" is the (simplified) math theory (trick=technique, model), that (2D, charge per 2D area) means (=implies) the real (=physical, =3D) charge per volume (rho).

My question was aimed at the (net) force intensity (onto the charged oil drop q) wrt position in the middle between the 2 plates, based on the surface_charge_density (sigma=Q/A) of the 2 opposite polarity plates (e.g. +Q/A, & -Q/A). From what I see, that force is zero. The (net) surface_charge_density is zero in the middle between both plates. Thus little (=zero) affect. (Otherwise, apparently uncharged objects would appear to attract (& repel) other objects, without electrostatic( law)s. A form of gravitation, & anti_gravitation (e.g. levitation)?) I suppose you will maintain that the negative plate would repel a negative charged oil drop; & the positive plate would continue to attract that same drop (thus ignoring a ((volume)_charge_density rho=Q/vol) cancelation effect), so that a (constant) continuum of force exists (wrt position between the plates).

Millikan used a voltage applied to 2 plates that are spaced with air distance d. That is a simple capacitor (to me) C=Epsilon*A/d (with Area A & having an applied voltage). i.e. The (=his) capacitor was charged. Thus he used the electric field of a capacitor with the dielectric, air.

The force (applied to the (oil drop's) charge q) is directly proportional to the voltage V (=potential "difference"). & the middle (=in between the 2 plates) of any (functionable) capacitor, is always 0 V(olts, potential difference) no matter what voltage (below its limit(ing voltage (rating)), to avoid damage) is applied. Charged, or uncharged! (Thus is there NO (electrical) acceleration there?) The potential difference (=voltage) is V=E*d. The electric field E=V/d is the (potential difference=) voltage V divided by distance d, & the Coulomb's electric force F=q*E is the charge q multiplied by the electric field E (=Q/(Epsilon_o*Spherical_Area)=Q//(Epsilon_o*4*Pi*(r^2))). So the force F=q*V/d is the charge q multiplied by the (potential difference=) voltage V divided by the (charge's) distance d (e.g. away from the electric field's (source) charge Q. In that case (((it is) the distance) away from) a capacitor plate).

I'm asking about the oil drops(' accelerated) speed. (Is that speed linearly or non_linearly accelerated?) Are they (=those oil drops) non_linear(ly accelerated, wrt position, e.g. height)? If the(ir accelerating) force (F=m*a) is NOT linear wrt distance, then the(ir) acceleration (a=F/m) can NOT be (linear wrt distance) either. I apologize for the spelling typo, the title should read "Millikan's.." (not Milikan).

You assume the (Coulomb's) electric force is a "constant" wrt the distance d between the 2 capacitor plates (e.g. for linac acceleration). But how can that be? I.e. When the equipotential (e.g. the (surface_)charge_density (sigma=charge/area)) in the middle between the plates is zero! Due to a "bipolar" Gauss (surface_charge) law sum, each plate receives half the voltage V/2, but has opposite polarity (i.e. +V/2 & -V/2) so the sum is the total voltage V between the 2 plates, but zero (voltage) in the middle of the air dielectric. Surely a "non_linear" acceleration must exist (instead) wrt distance between the 2 plates because "zero potential" difference (at the dielectrric middle) has no driving force. (=Net (+/-) force equals zero!) Or does it? E.g. The force near the plates is maximum; but is minimum (=zero) in the middle (between the 2 plates).

Optical doppler shift should help indicate if c is NOT constant. Hasn't light's speed value been recorded differently throughout the years (decades) (e.g. CRC HoP&C=Handbook of Physics & Chemistry)? 1. But at St Andrew's University: Professor Bonnell's astronomy students (were given a task, that) measured a "semi_anual" doppler_shift of star light. Explaination: (overview) http://supportto.michelsonexperiment.com Bonnell's task sheet: (4 pages) https://www.st-andrews.ac.uk/~bds2/ltsn/planetary.rtf Anti_Thesis: 2. Maxwell predicted Michelson experiments would fail, because the (2 bidirectional) delays would match (on earth); & (he=Maxwell) suggested (1_way) extraterrestrial observations (e.g. of planets, moons, stars) would confirm earth's speed v affecting light's speed c. Michelson's mirrors (5 cm wide) were wide enough to maintain reflection inspite of the v/c deflection (ratio) (+/-2.2 cm at v~30 km/s, path length D~11 m; but "divided by 8" mirrors!) so (almost=virtually) perfect cancellation was guaranteed. The (light) beam path should have been ab1a1; NOT aba1 in his (=Michelson's, pg 335) Fig 2 1887 paper, due to Huygen's wave front principle. (I.e. Straight up, diagonally down; NOT diagonally up, diagonally down: for a 90 degree incident, & <90 degree reflection wrt the b mirror.) 3. The significance is enormous for relativity (if), because Einstein's SR is based on 2 simple assumptions: light_speed's constancy; & the Fitzgerald_Lorentz contraction used to maintain assuming constant c.

Don't you mean he then continued to explain following theories that do not work?E.g. The further different (ether) theories which disagree with SR; SR had no problem with the quasi_rigid ether theory, SR could deal with that (qret); but the other following ether theories could NOT (work with SR). I thought (we agreed) "photon" was NOT mentioned in that Einstein document.How then could he have done that? Btw. Isn't space*time a product derivable by multiplying the quotient (space/time) by time squared?-Joke. Yes, by the look of it now. Yes.

Yes. I agree. He usedQuasi_rigid (reading between the lines, solid, if) it was NOT liquid, & did NOT disagree with SR. A solid is a (rigid) frozen liquid. "When in the first half of the nineteenth century the far-reaching similarity was revealed which subsists between the properties of light and those of elastic waves in ponderable bodies, the ether hypothesis found fresh support. It appeared beyond question that light must be interpreted as a vibratory process in an elastic, inert medium filling up universal space. It also seemed to be a necessary consequence of the fact that light is capable of polarisation that this medium, the ether, must be of the nature of a solid body, because transverse waves are not possible in a fluid, but only in a solid. Thus the physicists were bound to arrive at the theory of the "quasi-rigid" luminiferous ether, the parts of which can carry out no movements relatively to one another except the small movements of deformation which correspond to light-waves. This theory - also called the theory of the stationary luminiferous ether - moreover found a strong support in an experiment which is also of fundamental importance in the special theory of relativity, the experiment of Fizeau, from which one was obliged to infer that the luminiferous ether does not take part in the movements of bodies. The phenomenon of aberration also favoured the theory of the quasi-rigid ether." He (=Einstein) did NOT say photons, I did. If we have a solid (=something rigid) & it is NOT matter, then (with what is left) I can assume we are dealing with something electromagnetic (like photons). Einstein describes matter as "condensations of the electromagnetic field". I suppose photons could also be seen so but move (=travel, away). Einstein denies that the ether particles move around, but that does NOT deny the particles themself. "Special relativity forbids us to assume the ether is made of (matter) particles observable through time, but the ether itself does NOT conflict with special relativity." --- 1920 https://wikilivres.ca/wiki/Äther_und_Relativitätstheorie Although the ether is irrelevant for SR (seeming as an empty hypothesis); "Allerdings erscheint die Ätherhypothese vom Standpunkte der speziellen Relativitätstheorie zunächst als eine leere Hypothese." it's NOT for GR. (Last paragraph:) "Zusammenfassend können wir sagen: Summarizing we can say: Nach der allgemeinen Relativitätstheorie According to GR ist der Raum mit physikalischen Qualitäten ausgestattet; space has physical qualities; es existiert also in diesem Sinne ein Äther. meaning an ether exists. Gemäß der allgemeinen Relativitätstheorie According to GR ist ein Raum ohne Äther undenkbar; a space without ether is unthinkable; denn in einem solchen gäbe es nicht nur keine Lichtfortpflanzung, because in such not only would light NOT travel, sondern auch keine Existenzmöglichkeit von Maßstäben und Uhren, but also no possibility of length & clocks, also auch keine räumlich-zeitlichen Entfernungen im Sinne der Physik. also meaning no space_time distances of physics. Dieser Äther darf aber nicht But this ether is not allowed mit der für ponderable Medien charakteristischen Eigenschaft ausgestattet gedacht werden, to be thought of as having ponderable medium's characterictics, aus durch die Zeit verfolgbaren Teilen zu bestehen; made of particles followable using time; der Bewegungsbegriff darf auf ihn nicht angewendet werden." the word motion is not allowed on it (=the ether). -- Ruffly Einstein is saying: Space has physical properties, so an ether exists (according to relativity). No ether is unthinkable (wrt GR), because without it (=ether) light would NOT travel; also length & clocks for space_time distances would NOT be possible in physics. This ether is not the same as a ponderable medium's properties, of particles that can be followed with time because the ether does not move. ("The word motion (=travelling) is not allowed to be used on the ether.") But as a solid of photons, vibration would be possible instead. The particles would not move away, for good (=ever). If you translate german word for word you can miss the meaning because a 1:1 corelation to english does not always exist. They (=the Germans, also) have cliches (=figures of speach). E.g. aus "durch" die Zeit verfolgbaren Teilen zu bestehen; made of particles followable "thru" (=by using) time; E.g. der "Bewegungsbegriff" darf auf ihn nicht angewendet werden." the "word motion" is not allowed on it (=the ether). Motion, travelling. Depends on how narrowly you want to look at it. It could be any motion at all, or else leaving. That's why he describes with several sentences, to build a picture so you can figure out what he is saying. E.g. Till it makes sense. SR doesn't allow the ether to be made of time followable particles; but that doesn't prevent an ether. That only prevents (assuming) that the ether' particles move (around). (=We can have an ether but it does not move.) Thus we can not say the ether is moving (e.g. away). "Das spezielle Relativitätsprinzip verbietet uns, SR prevents us den Äther als aus zeitlich verfolgbaren Teilchen bestehend anzunehmen, from assuming the ether is made of moving particles (e.g. like a gas) aber die Ätherhypothese an sich widerstreitet der speziellen Relativitätstheorie nicht. but the ether hypothesis does NOT contradict SR. Nur muß man sich davor hüten, We must only prevent dem Äther einen Bewegungszustand zuzusprechen." saying the ether is moving (around). Bewegungszustand=state of motion, e.g. translatory linear. (I agree that doesn't exclude vibration now adays; but back then(?) would he go so deep into all details (for an intro lecture), that we will ever know?) He also said (=estimated) our universe is finite; NOT infinite. ---