[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Pressure == 0 at the center of a mass?!
Gene
Roberts
wrote:
[...]
> With gravity pulling away equally in all directions from the center of a
> planetoid there would be little or no weight and little or no pressure.
Seems like
a physics
problem!
I am
having
trouble
with this
idea of
zero
pressure
at
the center
of an
object. I
have no
problem
with zero
weight
and
unchanged
mass.
Firstly,
gravity
attracts,
or pulls
towards,
not
pulling
'away
equally
in all
directions'.
I would
say that
all parts
of the
object are
compressing
and
attracting
equally at
the
center, so
you fell
pressure
from all
the weight
in every
direction
above you.
I have
tried to
analyze
this with
thought
experiments
and all
come to
the same
conclusion,
please
enlighten
me in my
mistakes
in the
following
reasoning:
Suppose
you start
with a
homogeneous
sphere of
material
as the
only
mass in
the
universe.
Now carve
out an
element
from this
shaped
like ice
cream two
cones
formed by
rotating a
diameter
about an
angle.
Like this
gross
ascii
diagram:
-------
<-- these
are round
areas -
arcs on a
sphere
\
/ <-- the
angle here
is, say,
25 degrees
\
/
(but this
is
arbitrary)
\
/
* <---
center of
section
/ \
/
\
/
\ <-
bottom is
identical,
but
inverted
-------
I hope
that is
clear -
there are
two 3-D
ice cream
cones and
a '*' at
the
center.
Pray that
my word
wrap
doesn't
mess that
up.
Now comes
the
experiment.
Take one
half of
this cone.
Nothing
else
exists
in the
universe.
Now place
yourself,
and the
lens of
the
Peekskill
car,
at the
'*'.
You will
be
standing
on a sharp
point
feeling a
gravitational
force
that would
seem to
radiate as
if all the
mass
of the
cone were
positioned
at the
center of
mass of
that cone.
No doubt
the sharp
point
would
pierce
your skin
and you
would sink
a
bit under
your
weight.
The lens
might even
smash a
bit,
surely it
will
be
scratched.
Now
superimpose
the other
cone
opposite
you so you
are at the
'*' and
the cones
face each
other as
in the
original
diagram.
The two
equal
masses
pull you
equally
(and each
other) so
you feel
no net
weight,
but the
two points
are now
starting
to really
hurt a lot
more since
the two
cones are
attracting
each other
as well.
The lens
is now
shattered
and two
people
just
snatched
them away.
Here comes
a leap,
applying
superposition
(all I
remember
from
college
physics):
I see no
reason why
the effect
would
change
depending
on the
angle of
the cone
that we
started
with, so
let's make
the angle
180
degrees
and now
you are
quite
smashed,
but
weightless
at the
center of
a sphere.
The
pressure
isn't zero
at all but
increases
as the
angle
increases
and as the
diameter
(total
mass)
increases.
There's
nothing
but small
particles
of the
Peekskill
lens,
enough for
us all
to have a
crumb.
Of course
there's
levity
above, not
to offend,
but to
enlighten.
But still
I can't
see any
flaw in
the logic
even if
the lens
is
scratched.
References: