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 Originally Posted by OngBonga
The distinction between a ground that moves and doesn't move is actually critically important when we consider the COR of the ground in this scenario. If the ground is some immovable perfectly rigid object, it has a COR of 0. If it moves just a single Planck length due to gravitational interactions, and then back again when it bounces off the ball, it has a COR of 1.
I prefer the latter solution because an immovable object is one ideal assumption more than necessary. It's not even possible in a perfectly ideal universe, it's just a made up concept that has no meaning in physics.
I need to google if COR is a single-particle property, or a 2-body interaction property.
I feel like it's the latter, but can't commit.
Easiest to just ignore the complications and treat the ground as "unaccelerateable" which is also nonsense, but it gets us there.
E.g. if I'm to perform this experiment in my office, then the mass of the ball is a couple tenths of a kg, whereas the mass of the Earth is 6(10)^24 kg. My estimation that the motion of the Earth is 0, and the motion of the ball is all that matters is technically wrong, but I'd be unable to measure that wrongness using any reasonable measurement device.
Newton's 3rd law says that the force the Earth exerts on the ball is equal in magnitude and opposite in direction to the force the ball exerts on the Earth. Equal and opposite forces forming a 3rd law pair.
F = ma
so
F/m = a
The same F applying to 2 drastically different masses will yield accelerations differing by as many orders of magnitude.
If the ball bounces 1 m, the Earth's bounce in the opposite direction adds another ~10^-25 m to the bounce.
That'd take 10 billion of those to get to the diameter of a single proton (~10^-15 m).
So, in practice, we're technically wrong to not include the acceleration of the Earth, but just as practically, we'd be unable to measure that difference, even if we accounted for it with our math.
The upshot is that we can make our lives a lot easier by ignoring it in our math and still being right enough.
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