2mo ago

ur dada so buff he falls significantly faster than g

136 comments

Stupid question, bowling balls don't fit through the vacuum's hose.
- Ur mom could suck it through

So will the bowling ball gravitationally attract the earth to itself there by reach the earth an infinitesimally small amount?
- Yes, the earth accelerates toward the ball faster than it does toward the feather.
  
  Wouldn’t this be equally offset by the increase in inertia from their masses?

This argument is deeply flawed when applying classical Newtonian physics. You have two issues:
Acceleration of a system is caused by a sum of forces or a net force, not individual forces. To claim that the Earth accelerates differently due to two different forces is an incorrect application of Newton's second law. If you drop a bowling and feather in a vacuum, then both the feather and the bowling ball will be pulling on the Earth simultaneously. The Earth's acceleration would be the same towards both the bowling ball and the feather, because we would consider both the force of the feather on the Earth and the force of the bowling ball on the Earth when calculating the acceleration of the Earth.
You present this notion that two different systems can accelerate at 9.81 m/s/s towards Earth according to an observer standing on the surface of Earth; but when you place an observer on either surface of the two systems, Earth is accelerating at a different rate. This is classically impossible. If two systems are accelerating at 9.81 m/s/s towards Earth, then Earth must be accelerating 9.81 m/s/s towards both systems too.
- Re your first point: I was imagining doing the two experiments separately. But even if you do them at the same time, as long as you don’t put the two objects right on top of each other, the earth’s acceleration would still be slanted toward the ball, making the ball hit the ground very very slightly sooner.
  Re your second point: The object would be accelerating in the direction of earth. The 9.81m/s/s is with respect to an inertial reference frame (say the center of mass frame). The earth is also accelerating in the direction of the object at some acceleration with respect to the inertial reference frame.
  
  If the earth would be accelerating towards you, then g would be less than 9.81.
  Think of free falling, where your experienced g would be 0.
  
  Even if you imagine doing them separately, the acceleration of the Earth cannot be calculated based on just a singular force unless you assume nothing else is exerting a force on the Earth during the process of the fall. For a realistic model, this is a bad assumption. The Earth is a massive system which interacts with a lot of different systems. The one tiny force exerted on it by either the feather or bowling ball has no measurable effect on the motion of Earth. This is not just a mass issue, it's the fact that Earth's free body diagram would be full of Force Vectors and only one of them would either be the feather or bowling ball as they fall.
  As for my second point, I understand your model and I am defining these references frames by talking about where an observer is located. An observer standing still on Earth would measure the acceleration of the feather or bowling ball to be 9.81 m/s/s. If we placed a camera on the feather or bowling ball during the fall, then it would also measure the acceleration of the Earth to be 9.81 m/s/s. There is no classical way that these two observers would disagree with each other in the magnitudes of the acceleration.
  Think of a simpler example. A person driving a car towards someone standing at a stop sign. If the car is moving 20 mph towards the pedestrian, then in the perspective of the car's driver, the pedestrian is moving 20 mph towards them. There is no classical way that these two speeds will be different.

Brian Cox shows ball and feathers falling together in vacuum: https://youtu.be/E43-CfukEgs
- The difference in relative acceleration implied by the meme is on the order of tens of yoctometres (10⁻²³ m) per second per second.
  It's a difference so small that it would be overshadowed by the fact that you're holding one object femtometres (10⁻¹⁵ m) higher or lower than the other in the gravitational field.
  Additional sources of error to consider at this scale might be the heat radiation from the surroundings providing radiation pressure on the object, the sloshing of Earth's core causing time-dependent variations in the gravitational field, the location-dependent variations in the Earth's gravitational field, and the difference in centrifugal (yes, centrifugal in this reference frame) force due to latitude differences of one micrometre, and also due to natural variations in the rate of Earth's rotation over time.
- I love it when scientists who know something to be true in theory get to see practical experiments like this. The jubilation on thier faces.

There’s too many words in this meme that’s making me dizzy from all your fancy science leechcraft, wizard.
I reject your reality and substitute my own: the feather falls faster. It’s more streamlined than the bowling ball, and thus it slips through the vacuum much faster and does hit the ground and stay on the ground, I think. The ball will bounce at least once, maybe even three times. On each bounce, parts of it probably break off, which change the weight. Thankfully those broken pieces won’t hurt anyone because they’re sucked up by the vacuum. Thus, rendering your dungeon wizard spells ineffective against me.
- This person sciences good

But what weighs more:
A ton of bowling balls or a ton of feathers? 🤔
- When you carry a ton of feathers, you also have to carry the weight of what you did to those poor birds...
  
  What about all the bowling cattle you had to castrate for those balls?
- That's a trick question. Feathers have lower density than bowling balls; a ton of feathers would have a larger volume compared to the same mass in bowling ball, thus the feathers are heavier
  
  Why does a larger volume mean the feathers are heavier?
  
  nice chatgpt roleplay
  
  Its a trick question because both weigh the same - a ton. The bag of feathers may take up more volume due to the lower density, but it'll still weigh the same as the bag of bowling balls.

This would make a good "What if?" for XKCD. In a frictionless vacuum with two spheres the mass of the earth and a bowling ball how far away do they need to start before the force acting on the earth sized mass contributes 1 Planck length to their closure before they come together? And the same question for a sphere with the mass of a feather.
- I actually thought the answer might be never, but a quick back of the envelope calculation suggests you can do this by dropping a ~1kg bowling ball from a height of 10^-11m. (Above the surface of the earth ofc)
  This is an extremely rough calculation, I'm basically just looking at how big a bunch of numbers are and pushing all that through some approximate formulae. I could easily be off by a few orders of magnitude and frankly I didn't take care to check I was even doing any of it correctly.
  10^-11m seems wrong, and it probably is. But that's still 1,000,000,000,000,000,000,000,000 times further than the earth moves in this situation. Which hey, fun What If style fact for you: that's about the same ratio of 1kg to the mass of the Earth at ~10²⁴kg.
  That makes perfect sense because the approximations I made are linear in mass, so the distance ratio should be given by the mass ratio.

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 • 10²⁴ 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.
- Uh... That's not how that works. The distance between two objects changes with acceleration a1-a2 where object 1 moves with acceleration a1 and object 2 a2 (numbers interchangeable). In the bowling ball's case a2 is the same but a1 is bigger in the negative direction so the result is that the bowling ball falls faster.
  
  Calculate the force between the earth and the bowling ball. It'll be G • (m(earth) • m(bowling ball)) / (r = distance between both mass centers)²
  Simplify. You're getting g • m(bowling ball).
  Now do the same for the feather. Again, the result is g • m(feather).
  Both times you end up with an acceleration of g. If you want to put it that way: The force between the earth and the bowling ball is m(bowling ball)/m(feather) times as high as the force between the earth and the feather, but the second mass also is m(bowling ball)/m(feather) times as high, resulting in the same acceleration g.
  Higher force on same mass results in stronger acceleration. Same force on higher mass results in lower acceleration. Higher force on equally higher mass results on equally high acceleration.
  I just asked my professor this exact thing (if the ball would get to the earth sooner because it accelerates the earth towards it) like two weeks ago and my previous message + this message was his explanation.
  PS: If you're looking at this from outside, the ball travels less distance before touching the ground (since the ground is slightly nearer due to pulling the earth more towards it), but also accelerates slower while accelerating the earth faster towards it. The feather gets accelerated faster towards the earth and travels a longer distance before touching the ground but doesn't accelerate the earth as fast towards it.
  But because we're not outside, we only care about the total acceleration (of the earth towards the object and the object towards the earth), and that's g. We don't notice if (fictional numbers) the earth travels 1m and the object travels 1m or if the earth stays in place and the object travels 2m, what matters for us is how long it takes an object 2m away from the earth to be 0m away from the earth.
- 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
  
  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.
- This is not correct, the force on the objects is the same sure, but the accelerations aren't so you can't calculate them both in one go like this.

Depends on the color of the feather and the ball.
There's a simple explanation.
- Exactly, red has way more up-quarks than blue
  
  Because light-blue weighs less than blue.

If anyone's wondering, I used to be a physicist and gravity was essentially my area of study, OP is right assuming an ideal system, and some of the counter arguments I've seen here are bizarre.
If this wasn't true, then gravity would be a constant acceleration all the time and everything would take the same amount of time to fall towards everything else (assuming constant starting distance).
You can introduce all the technicalities you want about how negligible the difference is between a bowling ball and a feather, and while you'd be right (well actually still wrong, this is an idealised case after all, you can still do the calculation and prove it to be true) you'd be missing the more interesting fact that OP has decided to share with you.
If you do the maths correctly, you should get a=G(m+M)/r^2 for the acceleration between the two, if m is the mass of the bowling ball or feather, you can see why increasing it would result in a larger acceleration. From there it's just a little integration to get the flight time. For the argument where the effect of the bowling ball/feather is negligible, that's apparent by making the approximation m+M≈M, but it is an approximation.
I could probably go ahead and work out what the corrections are under GR but I don't want to and they'd be pretty damn tiny.
- Physics books always say to assume the objects are points in doing calculations. Does the fact that the ball is thicker then the feather make a difference?
  
  Possibly?
  A bowling ball is more dense than a feather (I assume) and that's probably going to matter more than just the size. Things get messy when you start considering the actual mass distributions, and honestly the easiest way to do any calculations like that is to just break each object up into tiny point like masses that are all rigidly connected, and then calculate all the forces between all of those points on a computer.
  I full expect it just won't matter as much as the difference in masses.
- Quick intuition boost for the non-believers: What do things look like if you're standing on the surface of the bowling ball? Are feather and earth falling towards you at the same speed, or is there a difference?

Reading that spoiler, I hate scientists sometimes.
- For some reason on my client, it can't remove the spoiler (gives a network error). I'm assuming it says that since the ball has more mass, it has a higher attraction rate of its own gravity to Earth's, so does fall faster in a vacuum but so miniscule it would be hard to measure?
  
  "The bowling ball isn't falling to the earth faster. The higher perceived acceleration is due to the earth falling toward the bowling ball." is what the spoiler says

But ... Steel is heavier than feathers ...

“In our limited language that tries to describe reality and does so very poorly, how would you describe this situation that would literally never happen?”
- I'm pretty sure bowling balls and feathers fall all the time
  
  I think they mean the vacuum part.
  To which I'd add that we had astronauts perform this experimentally on the surface of the moon.

Obviously the bowling ball because it's more MASSIVE.
- Or dense?
  
  It's the mass that results in gravity, not the density. A giant cloud of gas will have the same gravitational effects as if it were compressed into its solid phase

uhmmm ackchshickzually, it's the space-time that's falling

the feather falling toward the earth will also be attracted to the bowling ball (which is on the earth)
doesnt offset, because the feather-ball attraction is not as large as the earth-ball. just wanted to say
- They are on opposite sides of the earth

Here’s a problem for y’all: how heavy does an object have to be to fall 10% faster than g? Just give an approximate answer.

So obviously I ended up in the middle of this bell curve. How would that cause the perception of the ball's acceleration to differ?
- When the earth pulls on an object with some F newtons of force, the object is also pulling on the earth with the same force. It’s just that the earth is so massive that its acceleration F/m will be tiny. Tiny is not zero though, so the earth is still accelerating toward the object. The heavier the object, the faster earth accelerates toward it.
  Both the bowling ball and the feather accelerates toward earth at the same g=9.81m/s^2, but the earth accelerates toward the bowling ball faster than it does toward the feather.
  
  But the question is which one falls faster, not which one pulls the earth faster.
  Middle it is!
- It won't cause the perception to differ because the difference is so small it's impossible to measure
- ~~The middle of the bell curve only works in a vacuum, and the top of the bell curve is true with wind resistance~~
  Edit: I misread the post
  
  Even in a perfect vacuum the bowling ball still falls faster. See my comment sibling to yours.

This may be a stupid question, but: assuming an object (the bowling ball) is created from materials found on Earth and that it remains within the gravity well of Earth from material procurement stage to the point where it is dropped, wouldn't the acceleration of the Earth towards the object be kind of a null considering the whole timeline of events? I mean, I get the distinction of higher mass objects technically causing the Earth to accelerate towards them faster if we're talking a feather vs a bowling ball that both originated somewhere else before encountering Earth's gravity well in a vacuum, it just seems kind of weird to consider Earth's acceleration towards objects that are originating and staying within its gravity well?
- I didn’t think about that! If the object was taken from earth then indeed the total acceleration between it and earth would be G M_total / r^2, regardless of the mass of the object.

Hum... What is your measurement error?

Isn't "heavier" only used when describing weight and not mass?
- It's almost analogous. A more massive object experiences a larger force caused by gravity, so assuming the gravity field stays the same, a larger mass is heavier.
  You're right that it's technically incorrect, especially when talking about something like moving the Earth with gravity.

No, it isn't. Because earth wouldn't fall towards the ball. Why?
Go to your frige right now and try to push it with one finger. It doesn't move does it? You may say "That's because of static friction!" And you would be correct. The force of static friction. Because the object moves in the direction of vector sum of all forces.

And adding microscopic attraction force towards the ball absolutely doesn't change the full vector sum of forces, that are applied to Earth constantly (which is probably pointed towards the sun).
- It does change the vector though. There's no (well barely any) friction in space. In fact pushing the fridge with one finger rather than pushing the fridge will move and rotate the earth at incomprehensibly small velocity for a short time.
  
  It does change the vector, yes, but to such a small amount that it does not become pointed at a ball.
  You can substitute static friction with a gravitational pull of the sun, and the result is going to be the same as in fridge example

Does this imply that if I am standing on an object moving at a constant speed in a straight line, and I am lifting and dropping a sufficiently massive object such that I’m causing the object in standing on to accelerate towards the object I’m dropping, that eventually I’ll slow or stop the object I’m standing on?
- Nope. The argument only works if you conjured the bowling ball and feather out of ~~thin air~~ vacuum. https://lemmy.world/comment/13237315 discusses what happens when the objects were lifted off earth.
  
  Drat. Thanks 😂
- For the sake of simplicity, let's say you have negligible mass, while the two masses, m1 and m2, have equal masses and sizes. Everything is moving at some velocity in a vacuum.
  When the two masses are touching, the Centre of Gravity is midway between their Centres of Mass, which in this scenario would mean it is where they touch.
  When you pick up m2, an equal and opposite force would push m1 away. Because they both have equal mass, both would end up the same distance away from the CoG. If you lifted m2 on your head, the CoG would be right at the middle of your height.
  For as long as you're holding m2, your body is resisting the force of attraction due to gravity between m1 and m2. When you drop m2, both it and m1 accelerate towards the CoG. When they meet, the energy you put into lifting m2 would be converted into heat in the collision. From an outside observer, while you were doing all that, the CoG was moving in a perfectly straight line with no change in velocity.
  Now, if you instead threw m2 away from m1 faster than its escape velocity, then that would change the velocity. If m1 and m2 weren't equal in mass and size, the CoG would still be moving in a straight line, but the distance m1 and m2 moves away from the CoG would be proportional to their masses.

You can stuff your misogynist fatshaming where it would hurt the most too wtf is going on with lemmy lately?
- fixed it sorry
  
  Oh wow, awesome! Was bracing for a whole host of anti-woke commentary but you genuinely seem to care about respecting others so I should point out that you only fixed the misogynist part and not the fatshaming part.
  
  lol. What had you said?

Bowling ball. Because wind resistance is a thing and the feather has higher surface area creating more drag, and there’s no such thing as a perfect vacuum.
- A feather has smaller cross-section area than a bowling ball. But drag acceleration is proportional to the cross-section area divided by the mass (and this quantity is indeed smaller for the bowling ball).
  Anyway the hypothetical scenario in this meme is a perfect vacuum. Check my other comments to see why it still works.
  
  A feather has smaller surface area than a bowling ball.
  Depends on the feather and the bowling ball. Even relatively small (by volume) feathers might outdo a bowling ball thanks to the numerous fine shapes they have.

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