this post was submitted on 03 Nov 2024
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Tap for spoilerThe bowling ball isn’t falling to the earth faster. The higher perceived acceleration is due to the earth falling toward the bowling ball.

(page 3) 39 comments
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[–] [email protected] 23 points 5 months ago (10 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.

[–] [email protected] 10 points 5 months 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

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[–] [email protected] 3 points 5 months ago (4 children)

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.

Tap for spoiler(In the example with fridge the static friction force cancels all other forces up to certain value and after that - motion)

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).

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[–] [email protected] 35 points 5 months ago* (last edited 5 months ago) (1 children)

This argument is deeply flawed when applying classical Newtonian physics. You have two issues:

  1. 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.
  2. 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.
[–] [email protected] 24 points 5 months ago* (last edited 5 months ago) (3 children)

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.

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[–] [email protected] 3 points 5 months ago (1 children)

Isn't "heavier" only used when describing weight and not mass?

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[–] [email protected] 1 points 5 months ago (2 children)

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?

[–] [email protected] 4 points 5 months ago* (last edited 5 months ago)

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.

[–] [email protected] 3 points 5 months ago (1 children)

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.

[–] [email protected] 3 points 5 months ago

Drat. Thanks 😂

[–] [email protected] 6 points 5 months ago* (last edited 5 months ago) (1 children)

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?

[–] [email protected] 5 points 5 months ago

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.

[–] [email protected] -2 points 5 months ago (1 children)

You can stuff your misogynist fatshaming where it would hurt the most too wtf is going on with lemmy lately?

[–] [email protected] 12 points 5 months ago (3 children)
[–] [email protected] 7 points 5 months ago (1 children)

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.

[–] [email protected] 12 points 5 months ago (1 children)
[–] [email protected] 9 points 5 months ago

yeeeeee thank you heart-sickle

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[–] [email protected] 7 points 5 months ago (1 children)

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

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[–] [email protected] 7 points 5 months ago* (last edited 5 months ago) (3 children)

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.

[–] [email protected] 8 points 5 months ago* (last edited 5 months ago)

10% of the earths mass

[–] [email protected] 4 points 5 months ago

One tenth the mass of the earth?

[–] [email protected] -2 points 5 months ago* (last edited 5 months ago) (1 children)

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.

[–] [email protected] 2 points 5 months ago* (last edited 5 months ago) (1 children)

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.

[–] [email protected] 3 points 5 months ago (1 children)

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.

[–] [email protected] 0 points 5 months ago (1 children)

I meant cross-section area, not surface area. Sorry. Edited my comment above.

[–] [email protected] 1 points 5 months ago (1 children)

An average bowling ball is 8.5 inches in diameter, giving it a cross sectional surface area of roughly 60 sq in. Restricting ourselves to feathers made by non-human animals, the longest feather measured was on a Yokohama chicken at 34 feet / 400+ inches. I can't find the width of the feather, but it's still likely it outdoes an average bowling ball.

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[–] [email protected] 6 points 5 months ago (3 children)

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?

[–] [email protected] 6 points 5 months ago

It won't cause the perception to differ because the difference is so small it's impossible to measure

[–] [email protected] 3 points 5 months ago* (last edited 5 months ago) (1 children)

~~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

[–] [email protected] 8 points 5 months ago (1 children)

Even in a perfect vacuum the bowling ball still falls faster. See my comment sibling to yours.

[–] [email protected] 3 points 5 months ago* (last edited 5 months ago)

Oh, interesting. That's a cool fact

Also, I very much misread the post lol

[–] [email protected] 22 points 5 months ago (1 children)

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.

[–] [email protected] 3 points 5 months ago (2 children)

But the question is which one falls faster, not which one pulls the earth faster.

Middle it is!

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[–] [email protected] 50 points 5 months ago (1 children)

So will the bowling ball gravitationally attract the earth to itself there by reach the earth an infinitesimally small amount?

[–] [email protected] 46 points 5 months ago (1 children)

Yes, the earth accelerates toward the ball faster than it does toward the feather.

[–] [email protected] 17 points 5 months ago (1 children)

Wouldn’t this be equally offset by the increase in inertia from their masses?

[–] [email protected] 35 points 5 months ago* (last edited 5 months ago) (2 children)

If your bowling ball is twice as massive, the force between it and earth will be twice as strong. But the ball’s mass will also be twice as large, so the ball’s acceleration will remain the same. This is why g=9.81m/s^2 is the same for every object on earth.

But the earth’s acceleration would not remain the same. The force doubles, but the mass of earth remains constant, so the acceleration of earth doubles.

[–] [email protected] 19 points 5 months ago* (last edited 5 months ago) (1 children)

I wonder how many frames per... picosecond you'd need to capture that on camera... And what zoom level you'd need to see it.

I think the roughness of the surface of the bowling ball would have a bigger impact on the time, in that the surface might be closer at some points if it were to rotate while falling.

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