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Carnival ride : chair swings from cable attatched to overhang, spinning on axis

  1. Oct 25, 2012 #1
    1. The problem statement, all variables and given/known data

    The chair is 10 m from the rotating vertical axis. The solid overhang stretches 6 meters from the axis. (making 4 m from end of overhang to chair on the radial axis). The chair spins at a constant speed at 1 revolution per 10 seconds. Find the angle θ the cable makes with the vertical axis.

    2. Relevant equations

    ƩFr = mar = m(ω^2)r
    ƩFz = maz
    ƩFt = mat = 0 (constant speed)

    3. The attempt at a solution

    I have not had troubles with the equation, but I have had issues setting up the problem.

    I originally thought that I might be able to find θ if I analyzed the chair as if the cable was attached directly to the z axis. This would give me an angle let's call β. From here I could use trig to find θ. This is only true if the relationship between the situation where the cable is attached directly to the z axis and the situation where the cable is attached to the over hang looks like this:

    |-\
    |-β--\
    |-------\
    |----------\
    |-------------\
    |----------------\
    |________________\
    (sorry for the bad diagram. Its a triangle ignore the --)

    where the bottom side is length 10 and

    |-\
    |-θ-\
    |----\
    |-----\
    |------\
    |-------\
    |_______\

    Where this bottom line is 4 and the heights are equal.

    I doubt this is true. I would guess that the heights wouldn't be equal, and thus I would not be able to find θ this way.

    My question is how I would find this true angle, or more generally, how would I deal with any radial problem where a mass is hung by a rope from a spot a certain distance x away from the center of the circle.

    Thank you
     
  2. jcsd
  3. Oct 25, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi conorwood! :smile:
    i think β and θ are the same

    try solving the equations …

    you'll probably find that the radius of revolution is the only length that matters :wink:
     
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