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Homework Help: Dynamics Homework Problem

  1. Jan 31, 2010 #1
    1. The problem statement, all variables and given/known data
    A 3-lb collar can slide on a horizontal rod which is free to rotate about a vertical shaft. The collar is intially held at A by a cord attached to the shaft. A spring constant of 2 lb/ft is attached to the collar and to the shaft and is undeformed when the collar is at A. As the rod rotates at the rate ThetaDot=16 rad/s, the cord is cut and the collar moves out along the rod. Neglecting friction and mass of the rod, determine

    a)the radial and transverse components of the acceleration at A

    b)The acceleration of the collar relative to the rod at A

    c)the transverse component of the velocity of the collar at B


    2. Relevant equations



    3. The attempt at a solution
    I know the solution to the problem. The answers are
    a) Ar=0, Atheta=0

    b)1536 in./s^2

    c)32.0 in/s

    I don't feel like this is a difficult problem, but I am definitely missing a key concept. How can you determine these quantities without r as a function of time?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

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  3. Feb 1, 2010 #2

    tiny-tim

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    Hi negatifzeo! :smile:

    (have a theta: θ and an omega: ω and try using the X2 tag just above the Reply box :wink:)
    I suppose you're wondering how you can find r'' without knowing r(t)? :redface:

    It doesn't matter, because you can work it out from good ol' Newton's second law … Fradial = m(r'' - ω2r) :wink:
     
  4. Feb 1, 2010 #3
    The angular velocity is given. The mass is given. But we don't know the total force, do we? The total force is broken up into two components, "e-sub-r" and "e-sub-theta", which we do not know.
     
  5. Feb 1, 2010 #4

    tiny-tim

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    Hi negatifzeo! :smile:

    (what hapened to that θ i gave you? :redface:)
    You won't need the eθ component of the force.

    Try it for a) first. :smile:
     
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