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Angular Acceleration and Projectile Motion

  1. May 23, 2009 #1
    1. The problem statement, all variables and given/known data

    An amusement park game, shown in the figure (see attachment), launches a marble toward a small cup. The marble is placed directly on top of a spring-loaded wheel and held with a clamp. When released, the wheel spins around clockwise at constant angular acceleration, opening the clamp and releasing the marble after making 11/12 revolution.

    What angular acceleration is needed for the ball to land in the cup?

    2. Relevant equations

    x1 = vcos(theta)t
    y1 = y(initial) + vsin(theta)t - 4.9t^2

    omega = v/r

    a = (omega(final)^2 - omega(initial)^2)/2(delta(theta))

    3. The attempt at a solution

    1) 11/12 of a revolution = 330 degrees, therefore it is launched at an angle of 30 degrees.
    2) It is shot from an initial height of rcos30 = 0.2*sqrt3/2 m
    3) It has a range of 1 + rsin30 = 1 + 0.2*1/2 = 1.1 m

    I know I'm supposed to find launch velocity from this data but how do I go about doing so?
     

    Attached Files:

  2. jcsd
  3. May 23, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Sounds good. (I assume that the cup is at the same height as the center of the wheel? Hard to tell from the diagram.)

    Set up the usual projectile motion equations for vertical and horizontal position as a function of time.
     
  4. Oct 8, 2009 #3
    I'm trying to do this same problem, but I don't know how. I was hoping I could figure it out with some online help, but I don't understand where you got all the equations and such.
     
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