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Question about mechanics

  1. Apr 16, 2012 #1
  2. jcsd
  3. Apr 16, 2012 #2

    tiny-tim

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    welcome to pf!

    hi winichris! welcome to pf! :wink:

    show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
     
  4. Apr 16, 2012 #3
    Re: welcome to pf!

    My teacher taught some very easy notes.
    But he gave us this kind of so difficult problems.
    I dont have ideas about that.

    For Q1,
    velocity of mass m = 2a x (g/a)^0.5

    By conservation of momentum, m x 2a x (g/a)^0.5 = m x (velocity of ring)
    velocity of ring will be = 2a x (g/a)^0.5

    But I think this solution is wrong since by using conservation of energy:

    0.5 x m x (velocity of mass)^2 = 0.5 x m x (velocity of ring)^2 + mgh

    This will make h=0

    So can you help me to think of this question?
     
  5. Apr 16, 2012 #4

    tiny-tim

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    you need to start by finding expressions for the momentum and the energy at a general speed v (of the ring) and angle θ

    for horizontal momentum of the rod, you must use the velocity of the centre of mass of the rod

    for kinetic energy of the rod, you must add the rotational kinetic energy (using moment of inertia about the centre of mass) to the "translational" kinetic energy of the centre of mass

    start again! :smile:
     
  6. Apr 19, 2012 #5
    Re: ~~~~URGENT, Question about mechanics~~~~~~~

    When the mass is at its highest point, its velocity and angular velocity are both zero?
     
  7. Apr 19, 2012 #6

    tiny-tim

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    when the rod is at its greatest angle, its angular velocity is obviously zero

    but why would its ordinary velocity also be zero? :confused:
     
  8. Apr 20, 2012 #7
    Re: ~~~~URGENT, Question about mechanics~~~~~~~

    http://imageshack.us/photo/my-images/823/phy.png/
    When it is in the highest point, is the tangential velocity is zero? because v=rw, where w=0. (red blanket in the picture)

    As the whole system is moving to right, so there should be a radial velocity of the mass ??(blue blanket in the picture)

    But there is a question, there are 3 unknowns (angle theta, velocity of mass and velocity of ring) but there are only 2 equations.
    So whether the radial velocity of the mass is equal to initial velocity of the mass?

    Thanks a lot!
     
  9. Apr 20, 2012 #8

    tiny-tim

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    why are you using "radial" and "tangential"? there's no origin here (the ring is moving) :confused:
    no, there are only 2 unknowns … position of ring, and angle of rod
     
  10. Apr 20, 2012 #9
    Re: ~~~~URGENT, Question about mechanics~~~~~~~

    radial and tangential is for the rod (not the ring above).
    Because when it is at highest point, w=0, can i conclude that tangential velocity=0?

    Position of ring means velocity of ring?
     
  11. Apr 20, 2012 #10

    tiny-tim

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    yes of course :smile:
    you can use either
     
  12. Apr 20, 2012 #11
    Re: ~~~~URGENT, Question about mechanics~~~~~~~

    So with tangential velocity=0, the rod only consist of radial velocity.
    Is the radial velocity (blue blanket in the last photo) = initial velocity of rod ( radius x angular velocity)
     
  13. Apr 20, 2012 #12

    tiny-tim

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    can you please type your equations directly into the post, instead of photocopying them? :redface:

    and what is y? and remember that there's no mass at the free end of the rod
     
  14. Apr 20, 2012 #13
    Re: ~~~~URGENT, Question about mechanics~~~~~~~

    Let y be the radial velocity of the rod at highest point, x be the velocity of the ring when rod at highest point, v be initial velocity of the rod.
    v=rw=2a(g/a)^0.5, right?
    Will y and v be equal?

    Momentum: mv = my cos(theta) + mx
    Energy: 0.5mv^2 + 0.5Iw^2 = mg2a(1-cos theta) + 0.5mx^2 + 0.5my^2
     
  15. Apr 20, 2012 #14

    tiny-tim

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    the radial velocity is always 0 :confused:
    the rod doesn't have a velocity, it only has an angular velocity
    (try using the X2 button just above the Reply box :wink:)

    kinetic energy = 0.5mv2 for the ring + 0.5mv2 for the centre of mass of the rod + 0.5Iω2 for the rod

    (and at the top of the swing, ω = 0)
     
  16. Apr 20, 2012 #15
    Re: ~~~~URGENT, Question about mechanics~~~~~~~

    "when the rod is at its greatest angle, its angular velocity is obviously zero
    but why would its ordinary velocity also be zero? "<-- you said that the rod should have zero velocity before.
    Or maybe i misunderstand your meaning.
    So the ordinary velocity of the rod should be zero at highest point?
     
  17. Apr 20, 2012 #16

    tiny-tim

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    no, i said the opposite ...
     
  18. Apr 20, 2012 #17
    Re: ~~~~URGENT, Question about mechanics~~~~~~~

    Sorry i type wrongly.
    You say the rod does not have an ordinary velocity here..
     
  19. Apr 20, 2012 #18
    Re: ~~~~URGENT, Question about mechanics~~~~~~~

    Or maybe can you just tell me what will be the ordinary velocity of the rod when it is at highest point? thanks a lot, you are so helpful:)
     
  20. Apr 20, 2012 #19

    tiny-tim

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    the rod does not have an ordinary velocity, the rod has an angular velocity, and the centre of mass of the rod has an ordinary velocity

    at its highest point, the angular velocity is 0, and therefore the velocity of the centre of mass of the rod is the same as the velocity of the ring
     
  21. Apr 20, 2012 #20
    Re: ~~~~URGENT, Question about mechanics~~~~~~~

    At the highest point, the direction of the velocity of the center of rod is towards right or towards right upwards direction?

    If the direction is towards right,

    m(2aw) = m(velocity of ring) + m(velocity of center of mass of rod)
    As velocity of ring and velocity of center of mass of rod is same,
    so velocity of ring= aw

    right?
     
    Last edited: Apr 20, 2012
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