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Elastic Collisions and Harmonic Motion

  1. Apr 11, 2008 #1
    1. The problem statement, all variables and given/known data
    A ball is dropped from a height of 10 meters onto a hard surface so that the collision at the surface may be assumed elastic. Under such conditions the motion of the ball is
    (A) simple harmonic with a period of about 1.4 s
    (B) simple harmonic with a period of about 2.8 s
    (C) simple harmonic with an amplitude of 5 m
    (D) periodic with a period of about 2.8 s but not simple harmonic
    (E) motion with constant momentum


    3. The attempt at a solution

    I would assume that since its an elastic collision, that it would engage in simple harmonic motion, but the answer is D so evidently that is not the case. Anyone care to explain?
     
  2. jcsd
  3. Apr 11, 2008 #2
    You must have a definition of Harmonic motion somewhere in you textbook.It really isn't hard to find out if that definition does apply.
     
  4. Apr 12, 2008 #3
    the acceleration is not directly proportional to the displacement but a constant acceleration (assume there is no air resistance)
    there is no equilibrium position between the extreme ends... (as well as force= 0)
    and the direction is downward besides at the pt where the ball rebounces....
    it is periodic motion, since the collision is elastic .i.e. energy(KE) is conserved.
    by s=ut+1/2at^2
    s=5t^2
    t = sqrt 2=1.41 , representing the time for "half motion"
    T=1.41*2=2.82 s
     
  5. Apr 12, 2008 #4
    so it isn't harmonic motion. The acceleration isn't constant when the ball bounces
    of course. If "movement with constant acceleration" was a question, I'd have to
    answer no.
     
  6. Apr 12, 2008 #5
    Indeed, these three factors are just provided you as explanations :)
     
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