So we heard it again and again objects with
the same mass falls with the same
speed. If a drop a 1 kilogram bowling
ball it will hit the ground at the same
time as a 2 kilogram bowling ball. Or if i
a drop a hammer and a feather in vacuum
they will hit the ground at the same
time.
So do objects fall in the same speed no matter the mass? Well actually
not quite: you can argue that heavier
objects actually Falls faster than
lighter objects - the collision time is
faster. So what's going on? Well do you
remember this equation this is the force
of gravity between two objects of mass 1
and mass 2. It's just the masses times
the gravitational constant over the
distance squared. So if we drop the
hammer let's see what happens: First we
are looking at the force on the hammer
so let's switch the index to hammer. Next
pretend we are dropping the hammer just
a little bit above the radius of the
earth,so let's insert the radius of the
earth. We have the mass of the earth and
the mass of the hammer according to
Newton's second law the force on the
hammer is the acceleration on the hammer
times the mass of the hammer - 
so let's into that so we can see that.
the mass of the hammers cancels: goodbye.
And if you plug in the numbers well then
who gets 9.8 meters per second that's
the gravitational acceleration on earth.
nice nice nice nice nice.
But wait a minute couldn't we just do the same analysis for the earth?  Yep and the
result will look like this:  So we see the
acceleration on the earth depends on the
object we drop of course but it's so
weak it will take forever to accelerate
the ground up to the object we drop. I know
the palm tree will also follow the
ground it's just easy to see that the
ground is actually accelerating up.
I've simulated the hammer drop here in
red into the earth: blue. Far above into
the space it's just going to fall down
like always let's try that again but in
a frame of reference of the hammer but
what if we increase the Hammers
acceleration field? We just saw that the
how fast the earth will accelerate up to
the hammer depends on the mass of the
hammer.. So what if we instead of dropping
a hammer we drop a neutron star you know
a neutron star that's the corpse of
bigger stars after it burned out it has an
extreme density, and so if a neutron star
has a radius of 147 meters its mass will
be equivalent to the earth mass. So what
if we drop something that has the mass
of earth into the earth?  Well it will be
way faster than something like our one
kilogram hammer this will be the result
... and in the frame of the neutron star we
will see this: And compare that to the
hammer you can clearly see the collision
time is way faster for heavier objects.
And so it kind of falls faster doesn't
it? ... So just to clarify the bigger the
mass the more the earth will also fall
into the falling objects - causing a lower
collision time .. But for how much? Well
according to this equation by David Z
at physics exchange a hammer of 1
kilogram falling one meter will take
about this much time 0.45 seconds do you
know how long time have take to drop a
ham of 2 kilograms? well me neither
because I don't have enough decimal
values in Python to calculate this. But
if I dropped an object of 1 billion
Kilis instead of 1 kilo the collision
time will take this much time notice
here there's almost no difference in
collision time with the hammer but if I
drop the neutron star with the same mass
of the earth into the earth well 1
meter will only have a collision time of
0.3 19 seconds .. So yeah I know this is a
little bit annoying trying to redefine
falling but it's very interesting I
think so thanks for watching consider
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