From: richalivingston@gmail.com   
      
   On Monday, February 20, 2023 at 1:25:07 PM UTC-6, Luigi Fortunati wrote:   
   > Stefan Ram il 19/02/2023 16:01:21 ha scritto:   
   > > Luigi Fortunati  writes:   
   > >> What is the difference between the force accelerating the mass (F=ma)   
   > >> and the force deforming the mass (Hooke)?   
   > >   
   > > It's the same force, but applied to two different systems.   
   > >   
   > > One system is a point of mass "m" that is not held in position.   
   > > When we call "F" the force acting on it, then the acceleration   
   > > of the point is "a".   
   > I had never heard this one: does F=ma only apply to material points and   
   > not to bodies?   
   ...   
      
   You are making this more complex than it needs to be.  Rather than thinking of   
   two different kinds of force, you need to model the objects (masses).  F=ma   
   is best thought of as applying to point or rigid masses.  If the situation   
   requires modeling elasticity of the object, then it is modeled as an array of   
   point masses with springs (and maybe dampers) between the point masses.   
      
   Many situations do not require such detailed models of the objects, such as   
   planets orbiting outside the Roche limit.  However if you are impacting such   
   a planet with a rock, then you need the elastic model I just described.   
      
   One place where a slightly different model is required is a planet inside the   
   Roche limit, or when calculating tidal forces.  Then the gravitational   
   "force" must be applied to each point mass in the elastic model.  As this   
   "force" will be different for each point, those differences in gravitational   
   "force" will result is elastic deformation of the body.   
      
   Rich L.   
      
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