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Physics Question - ma = mg
T3sl4co1l:
IIRC, it's surprisingly not well understood why inertial mass equals gravitational mass, at least to high observational precision (which isn't all that high in the grand scheme of physicsthings, because gravity is difficult to measure).
The reason given by General Relativity, is that space itself is moving, accelerating towards gravitational wells. There was an excellent animation of this in a recent YT video, which of course I didn't bookmark, so if someone can remember it please put it here -- in any case, the fact that spacetime itself is curving in towards a mass, is equivalent and indistinguishable to inertial mass being accelerated.
What's weird about the picture is not that space is accelerating, but why we aren't when we stand on the Earth! Well, the answer is relative, of course -- since space is moving past us here on the surface at ~9.8 m/s^2, something must be accelerating us up through all of it. The force for that eternal acceleration is -- drumroll -- the force of your weight pushing you along, and so on down to the core of the Earth where all the force, from the entire mass of the planet, is bearing against itself; fortunately, planetary matter is not very compressible at these pressures (but it isn't resistant to shear, and so the Earth gets pulled into a sphere, more or less -- it reaches hydrostatic equilibrium).
So, obviously that weight exactly equals your inertial weight, because otherwise you'd be dragged along in space at 9.8 m/s^2 relative to the Earth's surface.
There are some weird ideas, like Mach effects, which I don't think have been disproven? Or perhaps they're equivalent after all, but we don't quite yet understand how. The deeper mystery is how to integrate General Relativity into the Standard Model, so that we have a complete understanding from the smallest quantum level to the scale of the entire universe. Perhaps then we will have a more complete explanation. That, however, will take some time it seems. :)
Also:
Purely from Newtonian mechanics, there is no answer, of course. Newton's laws can be derived from Relativity given suitable approximations (c --> infty), just as Relativity is an approximation of some as-yet-unknown better model, and so on (it's turtles all the way down, at least until we have a more convincing reason to believe otherwise).
Tim
thermistor-guy:
--- Quote from: bostonman on May 13, 2021, 03:03:47 am ---I'm trying to understand exactly why ma = mg.
I took physics, and, the concept of weighing myself on the scale and learning it's really our mass, I'm confused about ma = mg (this began after watching the Big Bang Theory).
...
--- End quote ---
I read your "ma=mg" as indicating inertial mass and gravitational mass are the same:
https://www.einstein-online.info/en/spotlight/inertial-and-gravitational-mass/
"Gravity"describes how bodies move through space-time, which is curved by large masses. If you treat gravity as a force, then it turns out that the acceleration of small bodies are the same regardless of mass. This is peculiar when you think about it.
Go to the gym. Lift a 10 kg mass, then a 20 kg mass with the same acceleration. The 20 kg weight takes more effort (force) on your part.
Drop the 10 kg and 20 kg weight from shoulder height to the gym floor. The two weights move through space-time, with the same acceleration. If you regard gravity as a force, then "gravity" must be exerting more force on the 20 kg weight - twice as much - as on the 10 kg, the same way you did during your lifts. This is odd.
Now imagine jumping out a window with the 10 kg weight and releasing it mid-air. You and the weight are travelling with the same acceleration through space-time. But you don't feel any force on you, you don't feel any pressure on your body, the way you do when you lift a weight, or go up in a fast elevator. Is gravity really a force, then? If it is, it's a strange kind of force where you don't feel any :-)
Interestingly, near the Earth, space-time is curved mostly by the Earth, but there is also a tiny effect due to the sun and moon. An extremely sensitive pendulum clock will detect it:
https://en.wikipedia.org/wiki/Shortt%E2%80%93Synchronome_clock
http://leapsecond.com/pend/pdf/1986-Mar-AH-Boucheron-Shortt.pdf
Physicists aside, we treat gravity as a force because it matches our everyday language, and makes sense of our everyday experience. But it is a misleading line of thought, according to General Relativity.
https://www.universetoday.com/108740/how-we-know-gravity-is-not-just-a-force/
T3sl4co1l:
--- Quote from: thermistor-guy on May 13, 2021, 04:38:07 am ---Physicists aside, we treat gravity as a force because it matches our everyday language, and makes sense of our everyday experience. But it is a misleading line of thought, according to General Relativity.
https://www.universetoday.com/108740/how-we-know-gravity-is-not-just-a-force/
--- End quote ---
And (not to be redundant as I haven't read the link to see if it happens to make this connection already..!) we have a similar case with "centrifugal force": the apparent force to the outside, is actually the rotating object pulling inward. The difference between centrifugal and centripetal is merely a coordinate transformation.
...And no Mr. Bond, I expect you to die.
Tim
Brumby:
I am consistently amazed at the tangents and minutiae that appear in response to such a simple question. Some have made good effort at trying to clarify while others have been anything but.
This, to me, is the best offering so far:
--- Quote from: AntiProtonBoy on May 13, 2021, 04:18:47 am ---Generic Newton's force formula:
F = m * a
Weight force on any planet (substitute a with gravitational acceleration):
Fplanet = m * gplanet
--- End quote ---
This is where a general formula benefits from subscripts to distinguish different scenarios.
For example:
gearth
gmoon
gmars
gpluto
goumuamua
All these values for g will be different - but they plug into equations the same way - giving results that are correct for their respective situations.
But then it is spoiled by this:
--- Quote ---Weight on any planet in kg:
weightplanet = m * gplanet / 9.81
--- End quote ---
For starters, kg is a unit of mass - not a weight. Secondly, what is that divide by 9.81 all about?
thermistor-guy:
--- Quote from: Brumby on May 13, 2021, 07:21:03 am ---I am consistently amazed at the tangents and minutiae that appear in response to such a simple question....
--- End quote ---
I don't regard it as a simple question. To me, the equivalence principle (inertial and gravitational masses are equivalent) is profound and mysterious.
Yeah we can do simple calculations, but lurking behind the "why" of those calculations lies something deep about the nature of reality. Since the OP has studied physics, I assumed the question was about more than simple calculation, and more about the "why". Looks like I've misunderstood.
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