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Particle sliding down a sphere - When does it leave the sphere?

  1. Aug 21, 2015 #1
    1. The problem statement, all variables and given/known data
    A particle is placed on top of a smooth (frictionless) sphere of radius R. If the particle is slightly
    disturbed, at what point will it leave the sphere?

    2. Relevant equations
    Same as first question, just
    F = ma = ΣF_i

    3. The attempt at a solution
    Similarly, we want to know when the normal force of the sphere on the particle is overcome:
    F_norm = F_cent
    mg CosΘ = (mv2/r)
    CosΘ = y/R (where y is the height above the center of the sphere)

    So:
    y = v2/g

    Finding v2:
    Using conservation of energy, PE_initial = PE_final + KE_final
    mgR = mgy + mv2/2

    Solving for v2
    v2 = 2g(R-y)

    Placing into equation for y:
    y = 2g(R-y)/g = 2(R-y)

    Solving for y:
    y = (2/3) R

    Correct? Or am I making a horrible mistake?
     
  2. jcsd
  3. Aug 21, 2015 #2
    This is correct.
     
  4. Aug 21, 2015 #3

    ehild

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    Homework Helper
    Gold Member

    The title of the thread is "Ball rolling down a sphere". You solved the problem of a particle sliding down a sphere instead of a ball rolling down.
     
  5. Aug 21, 2015 #4
    You're right, if I could change the original post, I would, but there's no "Edit" button. Could be an account permissions issue...
     
  6. Aug 21, 2015 #5

    berkeman

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    Staff: Mentor

    I can fix it. So the title should read "particle" instead of "ball"?
     
  7. Aug 21, 2015 #6
    Yes, thank you, and an even better description would be "Particle sliding down a sphere" (instead of rolling)
     
  8. Aug 21, 2015 #7

    berkeman

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    Staff: Mentor

    Done! And thank you to @ehild -- I had the same question when I saw the thread and posted answer. :smile:
     
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