Re: Free fall

Luigi Fortunati il 14/03/2024 19:11:39 ha scritto:

In free fall, can you go anywhere freely or are there constraints that
prevent this?
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Of course you can't fall straight up and you can't fall sideways.
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In free fall you can only go in one direction (the vertical one) and in
only one versus (downward).
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The elevator (in free fall) and everything inside it are forced to fall
(always) vertically and (always) downwards.
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So there is a constraint.
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And, in free fall, can one move in a straight and uniform motion?
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No, in free fall the motion is always accelerated.
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The elevator (in free fall) and everything inside it are forced to
always accelerate.
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So there is another constraint.
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So why call it "free fall" and not "forced fall"?
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Luigi Fortunati.
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[[Mod. note -- The "free" in "free fall" means that no non-gravitational
forces are acting on the falling body.  It's a statement about what forces
are (not) acting on the body, not about the uniqueness or non-uniqueness
of the resulting motion.  -- jt]]

What makes gravitational forces different from non-gravitational
forces?

Luigi Fortunati

[[Mod. note -- That's a very good question!

From the perspective of Newtonian mechanics, we can operationally
define "mass" (more precisely, "inertial mass") via Newton's 2nd law
*without* involving gravitation at all.  That is, we can apply the same
force to different objects [e.g., attach an ideal spring to the objects,
and apply enough force to stretch or compress the spring by some
standard amount], measure the objects' accelerations with respect to
an inertial reference frame, and define
  m = F/a
for each body.

Now let's introduce an ambient gravitational field.  For example, we
could consider vertical motion in a given place near the Earth or some
other massive body.  If we ask what gravitational forces act on different
bodies, we find experimentally that these forces are all precisely
*proportional* to the bodies' inertial masses, i.e.,
  F_grav = g m
where g is the *same* for all bodies in a given ambient gravitational
field (e.g., in the same place near the Earth).  That is, the gravitational
force on a body with inertial mass 2 kg is (a) precisely twice that on
a body with inertial mass 1 kg, and (b) the *same* independent of the
composition of the body.  As an example of (b), let's suppose we have
3 test bodies, each with an inertial mass of 1 kg, but the 1st test body
is made of iron, the 2nd test body is made of bismuth, and the 3rd test
body is made of helium.  Experimentally, the gravitational forces acting
on these three test bodies (in the same ambient gravitational field,
e.g., in the same place near the Earth's surface) are all the *same*.

In contrast, for other types of forces we do *not* have proportionality
to inertial mass, nor do we have independence of composition.  For example,
if we have an ambient magnetic field, the magnetic forces acting on our
three test bodies will be (very) different.

Corresponding to the above difference in *forces*, if we apply apply
Newton's 2nd law to *motion* under gravitation vs other forces, we find
quite different results:

For motion under the influence of gravitation alone (i.e., motion
where there are no non-gravitational forces, i.e., what I've described
as "free fall"), we find
  a = F/m = gm/m = g
i.e., there is a *universal* free-fall gravitational acceleration,
independent of the free-falling body's mass or composition.  For example,
our iron, bismuth, and helium test bodies will all have the *same*
free-fall gravitational acceleration.

In contrast, for motion under the influence of non-gravitational forces,
there is *not* a universal acceleration.  For example, in the presence
of an ambient magnetic field, our iron, bismuth, and helium test bodies
will have (very) different accelerations.

It's the *universality* of free-fall acceleration (which, via Newton's
2nd law, is equivalent to the *proportionality* of force to inertial mass)
that distinguishes gravitational from non-gravitational forces, and that
motivates defining "free-fall" as the absence of non-gravitational
forces.
-- jt]]