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Physics Question - ma = mg
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Nominal Animal:

--- Quote from: RJHayward on June 25, 2021, 07:32:27 pm ---NOMINAL  ANIMAL for PRESIDENT
--- End quote ---
I was advised by the reptilians to tell you I politely decline, or else.
Nominal Animal:

--- Quote from: bostonman on June 27, 2021, 02:38:27 pm ---As for speed of lifting something, this actually also came from TBBT. Sheldon and the group were moving a time machine up the stairs and (I believe) Howard said why don't we push faster. Sheldon replied stating Work done doesn't matter how fast you push the object.

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Sheldon is correct that the time they take does not affect how much energy they need to transfer to the object to push it upwards in Earth's gravity field.

Sheldon is wrong in that the chemical energy required by human bodies to perform such energy transfers, definitely does depend on the rate at which the humans do it.
I don't know what that rate is at all, but provided an example model earlier.  It can be derived from basic principles, how muscle cells contract when given chemical energy, and so on.

So, it is correct – and the core of the joke is – if that one uses "work" strictly according to the physics definition, and completely ignores the human aspect of it.
Which is kinda at the root of all engineer/physicist jokes, I guess.

(I once had to walk out on a Physics 101 lecture, when the professor went "and as you can see, physics isn't as dry as one might think it to be, since 'bar' can be considered both an unit of pressure, as well as the place to relax after a hard days work", and the students dutifully emitted a respectful "laugh".  I love me dad jokes, and the layered nature of that joke (think about it), and loved the prof, but just couldn't handle the herd mentality.  I have hard time with canned laugh tracks, too.)


--- Quote from: bostonman on June 27, 2021, 02:38:27 pm ---That got me thinking because if I pick up a box 1m really fast, it feels like I've done far more work than if I lifted it slowly. Now if I lifted the same box 1m really fast ten times, I'd be out of breath whereas ten times slowly and I'd have far more energy at the end.

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I'm the opposite: I have ample power, but not much stamina.  (I think those are the terms, not sure.)

Anyway, it is a perfect example of what it means to be efficient at something.

If the object is at rest both in the beginning and in the end, it really does not care how long the lifting takes.  Its own total energy is changed by the exact same amount anyway (the physical work, i.e. m g h, given mass m, acceleration due to gravity g, and the vertical elevation h).

From the human or device causing the energy to be transferred to the object, "work" gives the minimum.  The less efficient we are at it, the more energy we'll waste.
Not using tools to optimize the energy expenditure is like asking friends to help move the object, but tell them to keep one hand behind their back.  Inefficient.

Giving the object more kinetic energy than necessary, or converting it repeatedly into waste heat (say, you lift the object one stair step at a time, lifting the object higher than the next step, then dropping it down), are just ways of doing it inefficiently.


--- Quote from: bostonman on June 27, 2021, 02:38:27 pm ---Excluding friction on the pulleys, wire resistance, etc.. I imagine the Work done by the motor to lift the box would be equal to the Work done by a human to lift the same box the same height.
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Yes.  It is easier, though, to think of Work from the perspective of the box: when being lifted upwards, measuring from standstill to standstill so ignoring kinetic energy transfers, the height determines exactly how much total energy the box gains.

From the perspective of humans doing the sweaty work, we can either be smart and make sure we spend the minimal energy – and we can do that without any external supplies of energy by using mechanical devices like pulleys –, or we can power through, ignoring the "waste" in chemical energy expenditure.

It is unfortunate that we don't have a separate word to describe the energy difference, since it is confusing.  (Then again, you wouldn't believe some of the physics misconceptions I've observed in graphic artists who have been taught with "interesting" definitions of "gravity", "volume", "depth", et cetera; perfectly valid and very useful in their own domain (in visual/graphic arts), but not at all valid in others, like physics.  Same problem, resulting in utterly hilarious misconceptions.)


--- Quote from: bostonman on June 27, 2021, 02:38:27 pm ---In other words, the calculation is identical, and I can safely say I burned X calories lifting the box ten times based off converting Joules (i.e. Work) into calories.
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Yes; exactly: because you transferred the energy ten times to the box, did not try to recover any of that energy, you can be sure that by doing it, your body burned at least the amount of chemical energy corresponding to the Work while doing it.
RJSV:
====.   Since ACCELERATION term is in an equation, therefore there must be movement present... ====

Erroneous because:. Newton started by saying "Let's examine a body in motion ( if I understood the help from Timfox).

   This thread, in 1740, could still encompass all the non-relativistic aspects of our discussion / friendly argument.
Perhaps one my faults is to focus too much on some blatant mis-statements:. But I needed clear examples to quote / make my point.
   Here is my main concern:
   There are equations involving an acceleration constant, where movement changes are described.
BUT, there are other equations where (an acceleration constant) is simply an expression of gravity-related physics, that is the strength of gravity (planet bulk) affects the outcome of a calculation.  You cannot expect an explicit 'change in movement' every time.
   Perhaps it was stupid of me to expect every post to be perfect, (and putting focus on the occasional mis-statements).  The example that bugged me was the post stating that 'MV' increased, therefore MASS increases with velocity increase. Uh, no, it is velocity that got bigger, to cause the parameter 'MV' to increase.
AND injecting relativistic effects into this discussion is just extra confusion, especially when the terms are similar, and often identical. (That being the use of the term 'mass increase'.

   So let me restate that:
    I read that 'MV' increased with speed, therefore the 'mass increased'.
    So sloppy, obviously SLOPPY MATH.
   The I read that at relativistic speeds the apparent mass DOES increase, probably having practical implications.
   BUT, and this is the even more crucial part, one reader takes that and runs back to (my) first complaint, that it's 'V' that caused 'MV' to increase, in a classical physics introspective. (He) takes the relativistic mass increase (valid), and runs back to the classical mode equation, implying that from a practical, everyday (non-relativistic) frame of view, the mass in 'MV' is wildly increased.... O.K. I added 'wildly' etc. to exaggerate my point.
  =========================================
   I recall someone I knew years back who used the term 'Lowest common denominator':. A phrase involving personal interactions among military folks.
   What he meant (I think) is that there is often a choice:
BUT: Do you force highest standards on everyone, or do you 'cave' to the ignorant, misbehaved (and maybe they are incapable of complying anyway.) ?
(Thanks Phil M.)
===========================================
Nom Animal:
   As for presidential bids, I've seen some great minds come out of FINLAND, there. You maybe too smart for that job.
Keep up the good work (helpfully debate).
P.S. I've seen other venues / political meetings where speakers actually had to PAY money, for their time at the microphone. Dave J. perhaps you could 'monitize' a longer thread, charging by the word...
(Just kidding)
Nominal Animal:

--- Quote from: RJHayward on June 27, 2021, 08:43:47 pm ---The example that bugged me was the post stating that 'MV' increased, therefore MASS increases with velocity increase. Uh, no, it is velocity that got bigger, to cause the parameter 'MV' to increase.
AND injecting relativistic effects into this discussion is just extra confusion, especially when the terms are similar, and often identical. (That being the use of the term 'mass increase'.
--- End quote ---
It is complicated, because whenever we talk about "bending spacetime", we must talk in relativistic terms; but at the same time, Newtonian physics and relativistic physics do and must agree at the simpler limit (zero velocity, uniform gravitational field, and so on), because system behaviour at simpler limit is measurable and physically verifiable.

No matter how fine the theory, it is only useful if it predicts behaviour physically observed.  That's why many think string theory is "just" math and not physics: it cannot really be used to model something physically measurable, so that its predictions could be compared against physical measurements.  That makes it "not physics" in the sense that physics describes how the universe behaves; maths folks (including string theorists) can work out the details and the tools, and philosophy folks can deal with the "why" part.

For example:

Mass does not bend space-time.  Energy does.

In relativistic physics, "mass" is rarely used.  Instead a quantity called "invariant mass" or "rest mass" is used; this is the mass of the object at rest, as if observed in a frame where the object is not moving.  The invariant mass is invariant, because it is the same quantity no matter what observational frame it is used in.

"Relativistic mass" is the term that best corresponds to what we call "mass" in non-relativistic, or Newtonian, physics.  It includes the space-time bending effects.

Because special relativity says that energy ≡ mass, (mass-energy equivalence, E=mc²), the above can sound like quibbling: I should not say mass does not bend space-time and energy does, because the two are equivalent.
But the above is not quibbling: it is worded so because 'mass' as a term is ambiguous.  In making that statement, I was thinking of the wrong kind of mass, you see.  See?

Simply put, we should avoid claiming mass bends space-time, because term 'mass' is ambiguous; we don't know whether it is used to refer to relativistic mass (which would be correct and match the classical physics definition of mass, but odd because physicists use 'mass' to refer to invariant or rest mass instead), or to invariant or rest mass (which usually 'mass' alone refers to when used in physics).  One interpretation is right but odd, the other is wrong but the more common use for the term.

A case in point: photons.

All electromagnetic radiation from gamma rays to infrared light consists of photons.  Photons are massless bosons: their invariant mass or rest mass is exactly zero (none of that "so tiny we can think of it as zero" stuff; plain and clear zero here), and any number of them can occupy the same state and space (until the energy density is high enough to cause certain interesting stuff to happen).  Bosons are the ones who like company, and fermions –– for example electrons being fermions –– are the ones who occupy their own quantum state, and exclude others from it.

In special relativity, the energy \$E\$ of an elementary particle is defined as
$$E = \sqrt{m_0^2 c^4 + p^2 c^2}$$
where \$m_0\$ is the invariant or rest mass, \$c\$ is the speed of light in vacuum, and \$p\$ is the linear momentum of the particle.  For particles with nonzero invariant mass, the linear momentum \$p\$ is
$$p = \gamma m_0 v = \frac{m_0 v c}{\sqrt{v^2 - c^2}}$$
where \$v\$ is the velocity of the particle, and \$\gamma\$ is the velocity-dependent Lorenz factor; I expanded that to get the nice simple expression on the right side, but note that usually it is kept contracted to \$\gamma\$ for brevity, so the right side expression may look unfamiliar to many.

Note that for small enough velocities, \$p = m_0 v\$.  The correction factor, Lorenz factor \$\gamma = 1 / \sqrt{1 - v^2 / c^2}\$, tells you the error you have for any given velocity if you use Newtonian physics instead of special relativity; see how only the \$p\$ term in total energy has anything to do with particle velocity?
The speed of sound in air is about 330 m/s, so about 0.0000011 of the speed of light.  At that speed, \$\gamma = 1.000000000000605\$, or less than one part in 1,000,000,000,000 over one.  Double-precision floating point numbers – those used for the vast majority of numerical computation on this planet outside financial stuff which uses decimal formats – have barely enough precision to describe that!

Also see how momentum is related to total energy (for elementary particles).  For collections of particles, we'd need to add their internal energy (stored in their structure, their interactions; including angular momentum).  In classical physics, we say kinetic energy \$K = m v^2 / 2\$, but it is important to understand how well that matches the relativistic energy.  If we use \$E(p) = \sqrt{p^2 c^2 + m_0^2 c^4}\$, then \$K = E(p) - E(0)\$.  Expanding the expression for \$K\$ using a Taylor series for small \$v\$ (around \$v = 0\$), we get \$K = m v^2 / 2 + 3 m v^4 / (8 c^2) + \dots\$.  Meaning, even the kinetic energy agrees *exactly* at zero velocity, and for larger velocities, just has relatively small additional terms.  Classical and relativistic physics agree at small velocities even here, as expected.

Photons have zero invariant or rest mass, and for them, linear momentum is
$$p = \frac{h}{\lambda}$$
where \$\lambda\$ is the wavelength of that photon.  Each photon has a single wavelength that only changes when it interacts with other stuff, transferring energy.  It does have other properties like polarization, but those do not affect or contribute to the total energy.  Thus, their total energy is
$$E = \frac{h c}{\lambda}$$

A mind-bending detail is that because the particle velocity depends on the observational frame used for the measurement, so does the total energy of the particle.

To un-bend ones mind, think of the Doppler effect: the wavelength of the light we observe does depend on our own velocity with respect to the light.  We still see it arriving at the speed of light in vacuum, but its energy is shifted.  Because photons, having no rest mass, zip everywhere at the speed of light.  (The velocity only drops when they interact with other stuff; exactly how that happens is quantum mechanics.  That is why we have a constant for it in vacuum, but it drops when zipping through matter.)

In sufficiently small regions, acceleration is indistinguishable from gravity.  Because of this, and the fact that Earths gravity well bends space around it, if we were to observe a single photon at a single moment of time (as measured by the position of that photon zipping along at the speed of light) from the surface of the Earth, and from an orbital space station, they would see the photon having different wavelengths.  Those two are different frames of reference, so there is nothing wrong in their observations differing (by exactly the relative difference of those two reference frames).  That is kinda-sorta one of the basic ideas of relativity.

Also, we have already experimentally proven that even photons themselves do bend space-time.  That tells us invariant mass or rest mass does not bend spacetime, because photons have none (again, not just "close enough to zero for all intents and purposes", but a clear and pure plain real zero), but we have observed them bending space-time.  And relativistic mass is even in principle indistinguishable from the energy, because of Einstein's mass-energy equivalence.  Thus, to avoid misconceptions, it is – I claim! – a good idea to think of *energy* as bending space-time, and relativistic mass being equivalent to energy per Einstein.  As a bonus, we don't have any issues with photons having zero invariant mass, because they are always zipping along at the speed of light (well, duh), and thus always have energy and thus relativistic mass; the zero invariant mass is just not practically relevant other than when working out the details using math.  And as a cherry on top, we easily slide into the habit of assuming 'mass' means 'invariant mass' (or rest mass), and instead of talking about 'relativistic mass' can talk about energy; energy being equivalent to mass, but as a term, not at risk of being confused with something else.

Compare to the thought pretzels one has to twist oneself into, if one insists mass is what bends space-time.  What 'mass', anyway?  No, I think that although you can argue that, that argument is not useful; you need to qualify it with 'invariant' or something else to be precise and not be accidentally misunderstood.
It's the same as when graphics artists talk about 'volume' or 'gravity' as an expression of an emotion evokable by visuals.  If everyone agrees on their definition, and nobody accidentally tries to infer anything about related stuff outside that very small domain, there is no problem.  So there is no technical problem in using those terms.  But, hilarity ensues when a graphics artist, genuinely puzzled, asks a physicist why they don't just use cut pastel tones to reduce gravity.

It is also okay to now realize that the Higgs boson so much talked about a few years ago, has really nothing to do with the bending of space-time, and everything to do with invariant or rest mass.  (Specifically, how "gauge bosons", those that carry the four fundamental forces we know of, have an invariant or rest mass of around 80 GeV/c², while it would be much easier to describe them if they had zero invariant or rest mass.)

See?  As in so many other things, if you just understand the terms correctly in their proper context, things just start falling into place.

They matter much more than just whether or not they are technically correct: they are crucial in building correct understanding in the first place, much beyond technical correctness or minute detail.
T3sl4co1l:
As a visceral example: shine enough light into a mirror box, and it becomes heavier.

Hmm, I forget if this can be understood in more classical terms -- would have to be something about Doppler effects on the radiation pressure, thus manifesting a difference as apparent mass? -- but all that General Relativity requires is that some energy is contained within an object (including rest-mass energy), and that's its effect on spacetime.

The idea of a kugelblitz, is to shine enough light, in from all sides, to a single common point, transmitting enough simultaneous energy to create a black hole.  The equations don't care what form of energy enters, only that enough does to create a singularity in spacetime.  What's inside that singularity?  Mass, energy?  Does it transform?  Moot question -- there's nothing at all at the singularity, it's a, well, singular point. :)  (I mean, as far as we know -- there has to be something quantum mechanical about that.  But it also can't matter because it's beyond the event horizon.)

Tim
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