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## OH Buoyancy!

There are 100's more of these -- many of them exact duplicates across numerous accounts which makes me suspicious... but on to the science.

So how does a force that pulls everything towards the center of the Earth manage to push lighter things up?

### tl;dr version of Archimedes' principle

Cut a small hole in the bottom of a bucket
Feed a string through, tie it to a small ball
Fill bucket with BBs
Pull string really hard
Observe that the BBs rise as the ball burrows down, displacing the BBs
Pulling the string applied greater FORCE to the Ball than the BBs

### A little bit more science G

First of all, the gravitational force on every molecule is F=m*'g' -- since 'g' is basically the same for all matter near Earth's surface this means that the F -- or FORCE, is proportional to the MASS of that object, times 'g' which is the effective acceleration of gravity at Earth's surface or roughly 9.8m/s².

This follows directly from the more general equation: F = G×m×m/r² where we know one of the masses is Earth (5.972 × 10²⁴ kg) and the distance [r] is 3959 miles (6371393 meters), which just leaves the familiar F=m*g from simple algebra:

F = G×m×m/r² = m×G×m/r²
-- so we can solve G×m/r²
F = m × [(6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²) × (5.972 × 10²⁴ kg)  / (6371393 m)²]
F = m × [9.818 m/s²]

So the force (F) pulling down each individual water molecule is actually extremely small, and the force is only slightly greater on an insect (rigid bodies share the force more than fluids so we can say the insect feels the combined force, as we do).  Sure, the total force over all the water molecules on Earth is a lot of Force combined - but that isn't what Gravity is doing in the scientific model -- that is only in the uneducated brains of Flat Earthers because they don't understand the difference between an acceleration (which is roughly the same for all objects) and the force (which is proportional to the mass of that object).

What often isn't stated clearly is that 'g' is not a constant but is a local value, a simplification.  Since 'r' is large even an airplane at 10km doesn't change the value much [9.788 m/s²].  You can watch this change in action in Wolfie6020's video.  So when you change the distance the value of 'g' changes, even here on Earth.

### Get on with it already

In a medium where the molecules are (fairly) free to move around, like water or the air (usually called a 'fluid'), everything is competing for that space at the bottom. This gives rise (pun!) to Archimedes' Principle which says that there is a force counter to the acceleration of gravity on a submerged object that is equal to the weight of the fluid displaced by the object.

In our bucket-of-BBs example the Ball displaced some volume (V) of the BBs, which also had some density (p), so the total mass displaced would be the volume (V) times the density (p).  But since we need weight we also have to multiply that times the acceleration, in this case the acceleration of gravity, or 'g'.

If you try to submerge a 24-inch beach ball in a pool you can feel just how tremendous that force can be, it would have a volume of about 31 1/3 gallons or 261.5 pounds [1163.2 N] of water displaced.

So putting that into mathematically terms is very straight-forward:

Buoyant Force = WeightDisplaced
Buoyant Force = MassDisplaced × accelerationOfGravity
Buoyant Force = (DensityofFluid × DisplacedVolume) × accelerationOfGravity

Also written: Bf = p × × g

If that Buoyant Force is greater than gravity then the thing will go up until this force is is equalized -- and it will go down so long as gravity is the greater force.

Imagine that you have a jar of water with a ping pong ball floating on the water. And you allow the Jar to free fall. What happens to the ball? If DENSITY alone explained the buoyant force then it should still float, but it doesn't - the buoyant force drops to zero because we have taken away the acceleration so 'g' becomes zero and p×V×0 = 0

And we know this acceleration changes things in other ways -- this is how a centrifuge works for example, it increases the acceleration factor which increases the buoyant force.

So my question to someone wishing to disprove this, do you have any compelling evidence that buoyancy works without an acceleration or that such an acceleration just happens to magically exist but isn't what we call 'gravity'?

Flat Earthers like to say that 'Gravity doesn't exist' and in a sense they are right.  At least in the sense that gravity works like no other force.  If I apply any other kind of force to my phone the accelerometers will register an acceleration.  But, if instead, I drop my phone and let it free fall, I can very clearly watch it accelerate towards the ground at 9.8m/s² (I needed my phone to film, so this is a ball, obviously):

while that same accelerometer will show as zero acceleration: Figure 1. iPhone 7 Plus in Free Fall from ~3.4s to 3.95s

This is why Einstein said that gravity doesn't exist and is instead the geometry of spacetime itself.

Meanwhile, my phone sitting on my desk is recording a 1G acceleration upwards because that is the force of the table pushing it up against gravity. So the entire WAY gravity works is different from every other force.

Here is another good video showing that 'density' doesn't do anything in free fall:

So that about wraps it up for this Flat Earth myth.

I welcome any proof that the felt force of gravity is not proportional to the mass.

You can scream 'flefuoyancy' all you want but that isn't evidence or proof.  You'd have to show me a fairly conclusive experiment that shows the well-documented, well-tested model is wrong.