this post was submitted on 03 Nov 2024

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270

ur dada so buff he falls significantly faster than g (mander.xyz)

submitted 2 weeks ago* (last edited 2 weeks ago) by [email protected] to c/[email protected]

137 comments fedilink hide all child comments

Tap for spoiler

The bowling ball isn’t falling to the earth faster. The higher perceived acceleration is due to the earth falling toward the bowling ball.

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[–] [email protected] 24 points 2 weeks ago (28 children)

Why your spoiler is wrong:

The gravitational force between two objects is G(m1 m2)/r²

G = ~6.67 • 10^-11 Nm²/kg²

m1 = Mass of the earth = ~5.972 • 10^24 kg

m2 = Mass of the second object, I'll use M to refer to this from now on

r = ~6378 • 10^3 m

Fg = 6.67 • 10^-11^ Nm²/kg² • 5.972 • 10^24^ kg • M / (6378 • 10^3 m)² = ~9.81 • M N/kg = 9.81 • M m kg / s² / kg = 9.81 • M m/s² = g • M

Since this is the acceleration that works between both masses, it already includes the mass of an iron ball having a stronger gravitational field than that of a feather.

So yes, they are, in fact, taking the same time to fall.

[–] red 10 points 2 weeks ago (18 children)

the fact that you got upvoted, you clearly said force on both objects is gM and the feather or ball will move with g BUT earth will move with gM/m1 which is more in case of ball, and no its not acceleration between mases, its the force experiencec by both mases so, fg=m1.a

[–] [email protected] 2 points 2 weeks ago* (last edited 2 weeks ago) (17 children)

BUT earth will move with gM/m1

No. Multiplication is associative, you can switch the masses around as you please, nowhere in the formula does it say "the greater mass" or "the smaller mass" you could just as well re-arrange the formula and come up with "earth moves with gm1/M". Last but not least there's only one force acting on both objects... and gM/m1 is neither a speed nor a force. G * 100kg / 20kg is 5G. Measured in Nm²/kg² which is the same we started with because the two kg cancel each other out.

They both fall towards their shared centre of gravity. It's this "the earth revolves around the sun" thing again, no it doesn't, they both revolve around their shared centre of gravity (which, yes, is within the sun but still makes it wobble). That centre is very far away from the ball and very close to the earth and both are moving at the same speed towards it (because acceleration doesn't depend on mass), blip to the next frame of the simulation now the centre of gravity moved towards the ball, next frame still closer to the ball, that is the reason both reach it at the same time, not because one is faster than the other.

...or so it would be, if the shared centre of gravity of ball and earth wouldn't lie within the earth so they don't actually both reach it, the earth is in the way, the rest of the acceleration is turned into static friction: Because they both are still falling even when in contact. But really that complication only exists because they have volumes which is why I factored it out from the rest of the reasoning.

[–] red -3 points 2 weeks ago* (last edited 2 weeks ago) (1 children)

all that is only brain-rot statements with no technical meaning. lemme make this completly clear

mf= mass of feather mb= mass of ball me= mass of earth ae=accelaration of earth fg=force experienced by both

now in case of feather

force on earth is what? yes thats fg =G.mf.me/r^2

now thats the net force on earth, now what is newtons law? me.ae=G.mf.me/r^2

we get ae=G.mf/r^2

similarly in case of ball ae=G.mb/r^2

and accelaration of earth is clearly more in case of ball, and yes this is accelaration in non inertial frame study newtons laws of motion again if you didnt know, so your second paragraph is utter nonsense

instead of nonsense brainrot statements like 'Multiplication is associative, you can switch the masses around as you please, nowhere in the formula does it say “the greater mass” or “the smaller mass” you could just as well re-arrange the formula and come up with “earth moves with gm1/M” tell me where in equations you think i am wrong

[–] [email protected] -1 points 2 weeks ago* (last edited 2 weeks ago) (1 children)

It's not nonsense when it makes people understand, buddy. And don't get all "oh be technical" on me when you say things like "earth will move with ". Something that's definitely something, but not m/s.

inertial frame

I was talking about time-steps when I said frame. Hence "simulation", and "one frame, then another, then another", referencing successive moments in time.

[–] red -3 points 2 weeks ago (1 children)

yet another brain rot reply, man i am done,

""earth will move with ". Something that's definitely something, but not m/s" you idiot i was talking about accelwration, if you need units just put in dementions of all the variables, thats trivial stuff you dont understand nlm at all.

second para is another non technical nonesense

[–] [email protected] 3 points 2 weeks ago (1 children)

you idiot i was talking about accelwration,

Then why did you say "move" instead of "accelerate". And the units don't match acceleration, either. Best I can tell it's some fraction of a term. If you want it to be an acceleration then you're missing a squared distance, and if you want it to be acceleration, why are both mass terms in there.

For someone who throws around things like "that's non-technical brainrot" damn is your prose fuzzy.

[–] red -1 points 2 weeks ago (1 children)

tell me how Gm/r^2 dosent match acceleration, the fact that i wasted my time on low iq person like you

[–] [email protected] 4 points 2 weeks ago* (last edited 2 weeks ago) (3 children)

That's not what you wrote, or at least not what I complained about. You wrote:

BUT earth will move with gM/m1

where it was previously established that m1 and M are masses, and I interpreted g to be G (Newton's gravitational constant) instead of g as in "gravitational acceleration caused by earth" because... well, I'm not actually sure. The whole thing is already a mess of capitalisation but more importantly then it'd be acceleration, not movement, worse, the specific properties of the earth are included twice (once in g, then in one of the mass terms).

the fact that i wasted my time on low iq person like you

Maybe you should spend less time on insulting people and more on communicating your thoughts clearly.

[–] red -2 points 2 weeks ago* (last edited 2 weeks ago) (1 children)

tell me how gM/m1 is not acceleration, what even is your point omg

[–] [email protected] 2 points 2 weeks ago* (last edited 2 weeks ago) (1 children)

You said it was movement, aka change in position over time, not acceleration, or you would have said "x will accelerate at", not "earth will move at". I already explained why it's questionable as a term of acceleration.

And this could've been over after a single comment of you saying "oh, yeah, misspoke". Your math in the comment after that misbegotten term checks out, that's not the issue here, it's your presentation that went all haywire.

[–] red 1 points 2 weeks ago (1 children)

literally trivil matter, i didnt even say movement, the point is your statements were still brain rot nonesense and your original comment is wrong and you dont really understand stuff

[–] [email protected] 1 points 2 weeks ago (1 children)

Clarity of presentation is never a trivial matter. You can be right all you like if you don't get it across then it will be for nought but inflating your own ego.

[–] [email protected] -1 points 2 weeks ago (1 children)

But you're not right?

You've very clearly shown that you are wrong and then said "I'm right because I understand my explanation more than the reality of the situation"

[–] [email protected] 1 points 2 weeks ago (1 children)

I understand and agree with red's math, and I said no such thing as you put into quotation marks there.

[–] [email protected] -2 points 2 weeks ago (1 children)

Yeh tbh my bad Im a couple drinks in. All I know is that the guy who thinks the bowling ball doesn't technically fall faster is wrong (no idea if that's you or not) any doubters look at this equation (F = G(m1m2)/R2 ) for a couple minutes and come back to me.

In solidarity with whoever thinks I'm wrong I'll downvote my own comments losers

[–] [email protected] 1 points 2 weeks ago (1 children)

As to "what's falling faster" my point is still that everything's falling at the same speed, because the only non-arbitrary reference point to measure things from is the centre of gravity of the whole system, earth, feather, ball, all of them together.

Well it may still be arbitrary, but at least it's not geocentric or feathercentric or ballcentric. All three can be unhappy with the choice which means it's fair.

Flip that reference point to the earth though and yes the ball is approaching ever so slightly faster than the feather (side note: is our earth spherical or are we at least making it an oblong?). Flip it to the ball and the feather is falling a lot slower towards it than the earth is. Which is probably how I should have started explaining this: The mass difference between feather and earth with respect to the ball is so massive that it actually makes quite a difference while between feather and ball wrt. earth it's negligible.

[–] [email protected] 1 points 2 weeks ago

Yeah man that wall of text and all is great. But like F = G(m1m2)/R2 is so much easier and quicker to read so I'm going with that

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