From: niklas.holsti@tidorum.invalid   
      
   On 2021-12-23 12:13, JF Mezei wrote:   
   > On 2021-12-23 03:37, Niklas Holsti wrote:   
   >   
   >> No. Your "push" is a compression wave, or sound wave, that propagates at   
   >> the speed of sound in the pole.   
   >   
   > Why the speed of sound?   
      
      
   Because "sound" is compression-rarefaction waves, which is what your   
   "push" is.   
      
   If you then /keep/ pushing with a constant force for enough time, the   
   waves will eventually dampen out (after being reflected back and forth   
   in the pole) and average to a static compression profile, decreasing   
   smoothly from the pushed end to the far end of the pole, in proportion   
   to the pressure needed at each point to accelerate the section of the   
   pole beyond that point. (This pressure profile is equivalent to the   
   increase of pressure with depth in the oceans, or in the atmosphere, due   
   to the "force" of gravity.)   
      
   For a short pole of a stiff material -- say, a broomstick or a tent pole   
   -- that averaging happens quickly enough that it is not noticeable to   
   the person pushing on the pole, and the delay can be ignored for   
   practical purposes. But you are talking about a /very/ long pole.   
      
      
   > Isn't "speed of sound" the speed at which a   
   > accoustic wave propagages through atmosphere at 1atm?   
      
      
   That is the speed of sound in air at 1 atm (and some known temperature   
   and humidity).   
      
      
   > (and would thus be quite different from one trype of material to   
   > another?   
      
      
   I did say, the "speed of sound IN THE POLE". Yes, it is different for   
   different materials, increasing with stiffness.   
      
      
   > If I get a vibrator to the pole, the vibrations are perpendicular to the   
   > pole, and that accelerartion is "local" to where the vibrator touches,   
   > but may spread along portion of the pole at their own leasurely speed.   
   > But as thet are vibration, the back and forth cancels itself overall so   
   > 0 net acceleration.   
      
      
   The difference in the force profile of the "push" -- whether it is   
   unidirectional, or oscillating -- is irrelevant to the propagation speed.   
      
   Even your vibrator /starts/ by pushing (or pulling) in one direction,   
   which (by the faulty reasoning) should instantly accelerate the whole   
   pole in that direction, which does not happen.   
      
      
   > But when I push the pole linearly, it is expected the whole pole will   
   > move and accelerate in one direction.   
      
      
   Eventually it will, but initially the acceleration propagates at the   
   speed of sound in the pole. The far end does not move until the   
   compression wave reaches that end.   
      
      
   > And this is what bugs me. When I   
   > push it, how is acceleration calculated if the total mass is not   
   > accelerated at the time I impart the force?   
      
      
   Stop assuming that the pole is "incompressible", which is an unreal   
   assumption.   
      
   Better imagine that the pole is sliced like a salami into a series of   
   flat thin disks with short and light helical springs in between adjacent   
   disks. You push on the disk closest to you; that accelerates this disk   
   and compresses the spring between this disk and the next disk; the   
   spring then pushes and accelerates that next disk, and so on to the far   
   end of the pole.   
      
   Given the masses and other properties of the disks and springs, the   
   acceleration of each element can be calculated, and also the speed with   
   which the acceleration propagates from disk to disk. In reality, the   
   disks correspond to the atoms or molecules of the pole, and the springs   
   correspond to the inter-atom/inter-molecule forces.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)