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Sphere in a potential well

  1. Oct 26, 2011 #1

    ShayanJ

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    Imagine you put a sphere on a track which is part of a vertical circle.You expect the sphere to roll in a path like a pendulum.it should do it like a mass on an almost frictionless surface because the friction of the surface is rolling the sphere not stopping it and the air drag isn't very high.
    But in one of the Walter Lewin's MIT video lectures,He did such a thing but the period was less than what he predicted with conservation of energy and the sphere stopped rolling in a short time that I didn't expect.He didn't explain why that happens and the problem is I can't explain it and its killing me.really need some help.
    thanks
     
  2. jcsd
  3. Oct 26, 2011 #2
    It has to be some kind of dissipation of energy... you cannot make a perfectly frictionless surface..
     
  4. Oct 26, 2011 #3
    This is because of air resistance even if it is not very high .Also the surface is almost frictionless but not completely without friction
     
  5. Oct 26, 2011 #4

    ShayanJ

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    Yes I could think of that.But at first he asks students what's the reason and when they say friction,he says no.friction is not that much.
     
  6. Oct 27, 2011 #5
    if ball was sliding without rolling (this means that friction is trully zero since the torque from friction is what makes the ball rotate) then with simple conservation of energy the ball would continue forever. But due to the torque from friction some energy is converted to heat.
     
  7. Oct 27, 2011 #6

    ShayanJ

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    I think you meant:
    If ball was rolling without sliding.

    this is in contrast to your first sentence.

    In fact here we have two retarding forces:
    1)Air drag
    2)Because you can't have perfect rolling,there is just a little sliding and that intoduces a little friction.
    But as I said,Lewin said that friction is not the reason.
    The difference between Lewin's prediction of period and the real period was higher than an amount that could be possible due to such small frictions.
     
  8. Oct 27, 2011 #7
    I have not seen the video but I am fairly sure I know what he was trying to get the students to understand.

    If the sphere slides on the track you get one answer for the period, if it rolls you get a different period. The key is the conservation of energy. A sliding sphere just exchanges energy between gravitational potential energy and kinetic energy. A rolling sphere has to share the potential energy between kinetic energy and the energy of its own rotation due to its moment of inertia.

    The friction and hence the damping is also different between the sliding and rolling scenarios.

    Hope this helps.

    Regards

    Sam
     
  9. Oct 27, 2011 #8
    Ok seems i was wrong, only possible losses seem due to not perfect rolling as you said. Probably there is some other factor in the experiment which eludes our attention.
     
    Last edited: Oct 28, 2011
  10. Oct 29, 2011 #9

    ShayanJ

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    The point is the period formula differs by a factor of sqrt(10/7).
    also because the process of accelerating the ball takes more time because of rolling,I think in that time there is some sliding and so it stops sooner than an object sliding on an almost frictionless surface.
     
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