From: fortunati.luigi@gmail.com   
      
   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?   
   >   
   > Of course you can't fall straight up and you can't fall sideways.   
   >   
   > In free fall you can only go in one direction (the vertical one) and in   
   > only one versus (downward).   
   >   
   > The elevator (in free fall) and everything inside it are forced to fall   
   > (always) vertically and (always) downwards.   
   >   
   > So there is a constraint.   
   >   
   > And, in free fall, can one move in a straight and uniform motion?   
   >   
   > No, in free fall the motion is always accelerated.   
   >   
   > The elevator (in free fall) and everything inside it are forced to   
   > always accelerate.   
   >   
   > So there is another constraint.   
   >   
   > So why call it "free fall" and not "forced fall"?   
   >   
   > Luigi Fortunati.   
   >   
   > [[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]]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)