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Projectile hits rod hanging from pivot.

  1. Dec 7, 2013 #1
    1. The problem statement, all variables and given/known data
    A thin, uniform bar, 2, long and weighing 90N is hanging vertically from the ceiling by a frictionless pivot. It is struck by a small 3kg ball, 1.5m below the ceiling, initially travelling horizontally at 10 m/s. The ball rebounds in the opposite direction with a speed of 6 m/s.


    2. Relevant equations

    Lbefore = Lafter

    L = Iω

    Irod = [itex]\frac{1}{2}[/itex]MR2

    Ipoint = MR2

    3. The attempt at a solution

    At the point of impact the ball can be thought of as a particle in circular motion about the pivot with radius 1.5m and tangential velocity 10m/s.
    The change in velocity is 16m/s. So the effective change in the angular momentum of the ball is

    ΔLball = Iball Δωball = [itex]\frac{IballΔv}{Rball}[/itex]

    This is equal to the change in the angular momentum of the rod (opposite direction):

    ΔLrod = Irod Δωrod = [itex]\frac{IballΔv}{Rball}[/itex]

    Insert values for I and rearrange :

    Δωrod = (2*mball*rball*Δvball) / (mrod*rball2)

    This gives ω = 3.92 rad/s , the given answer is 5.88 rad/s.
     
    Last edited: Dec 7, 2013
  2. jcsd
  3. Dec 7, 2013 #2
    I obviously used the fraction syntax incorrectly, please let me know what I did wrong. Thanks
     
  4. Dec 8, 2013 #3

    ehild

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    The formula for the moment of inertia of the rod is not correct.


    ehild
     
  5. Dec 8, 2013 #4

    haruspex

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    itex gives up if you put non-itex codes like [s u b] inside. Use ^ for sup and _ for sub.
     
  6. Dec 8, 2013 #5

    ehild

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    As haruspex said, _ for sub, but enclose subscript between curly thingies {} :smile:

    [itex]ΔL_{ball} = I_{ball} Δω_{ball} = \frac{I_{ball}Δv}{R_{ball}}[/itex]

    written as

    ΔL_{ball} = I_{ball} Δω_{ball} = \frac{I_{ball}Δv}{R_{ball}}

    ehild
     
  7. Dec 8, 2013 #6
    Ah yes. I should stick to deriving the moments of inertia, my memory doesn't serve me well. Thanks.
     
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