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Oscillation (SHM)

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  1. May 3, 2016 #1
    1. The problem statement, all variables and given/known data
    Some sand is sprinkled onto the cone. The sand oscillates vertically with the frequency of the cone. The amplitude of oscillation of the cone is increased.
    At a particular amplitude of oscillation the sand begins to lose contact with the cone.
    By considering the forces acting on a grain of sand, explain why this happens.

    2. Relevant equations
    From mark scheme it says "Weight - contact force = m(w^2)x So as x increases, contact force decreases, sand loses contact with cone when contact force = 0"

    But I don't understand why it is m(w^2)x, not -m(w^2)x? as I thought they take upward as negative and losing contact only happens at maximum upward displacement position.

    3. The attempt at a solution
     
    Last edited: May 3, 2016
  2. jcsd
  3. May 3, 2016 #2
    pl. make out a diagram of oscillations and then mark out the forces acting on sand particle ;perhaps then you can gigure out the contact forces and required centrepetal/centrifugal force .
     
  4. May 3, 2016 #3
    Yes I did!
     
  5. May 4, 2016 #4
    then show it as attachment so that we can get to your problem
     
  6. May 4, 2016 #5
    _k8xiwHxV0bG9Qm2Ts8oD_m3dnq_2E2pyOJ2Xu78HfRZMMWe_zcAIIcCDmaJA?width=660&height=326&cropmode=none.jpg
     
    Last edited: May 4, 2016
  7. May 4, 2016 #6
    @mystreet123
    well the attachment fails to open -perhaps a template will be better so that it can easily open.
     
  8. May 4, 2016 #7
    Can you open it now?
     
  9. May 4, 2016 #8
    yes, thanks
     
  10. May 4, 2016 #9
    at some amplitude of oscillations of the cone the sand particles leaves the contact with surface

    suppose N is the contact force so N= mg - mw^2.x at any displacement x so when contact force is zero the wt will be balanced by the term on the right hand ;
    as i feel mg is down ward so mw^2 .x shoukd be upward.

    or think in terms of F(harmonic osc.) = F(Weight) -N
    what is wrong in the above picture of forces?
     
  11. May 4, 2016 #10
    But why I found N-mg = mw^2.x at highest position? if we take upward positive

    Because when I use this formula, as x increases, N also increases, instead of becoming zero
     
  12. May 4, 2016 #11
    in a harmonic oscillation the force which is always a restoring force acts opposite to the displacement

    F(osc)= -constantx displacement
    if displacement is +ve - force will be negative and just vice-versa
    if displacement from mean position is negative then force will be in opposite direction.
    will this clarify your picture?
     
  13. May 4, 2016 #12
    Yes understood thanks!
     
  14. May 4, 2016 #13
    in physics forum if you give thanks then just like the post
    we do not write explicitly
     
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