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Putty on a Pivoting Rod

  1. Apr 13, 2015 #1
    1. The problem statement, all variables and given/known data
    A piece of putty of mass m = 0.75 kg and velocity v = 2.5 m/s moves on a horizontal frictionless surface. It collides with and sticks to a rod of mass M = 2 kg and length L = 0.9 m which pivots about a fixed vertical axis at the opposite end of the rod as shown. What fraction of the initial kinetic energy of the putty is lost in this collision?

    2. Relevant equations
    KE = 1/2mv^2
    KE = 1/2Iw^2
    L=mvr
    L=Iw
    I=mL^2/3
    I=mr^2

    r=L (I'm using the pivot as the point of origin)

    3. The attempt at a solution
    Based on the wording, it's an inelastic collision, and the putty sticks to the rod.

    So, momentum is conserved:

    mvL = (mL^2/3+mL^2)w

    Using numbers, I found that w = 1.176 rad/s

    The initial KE is 1/2mv^2= 2.34

    The final KE is 1/2Iw^2= 0.79

    KElost/KEi=(KEi-KEf)/KEi = 0.66

    but the answer is wrong.
     
  2. jcsd
  3. Apr 13, 2015 #2
    Did the problem statement give any information regarding where the putty sticks to the rod? I see you assumed that it stuck to the end of the rod. If you guessed "wrong", that could be your source of error. Under this assumption I am also calculating a different value for the angular velocity post-collision.
     
    Last edited: Apr 13, 2015
  4. Apr 14, 2015 #3

    haruspex

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    If the mass is striking the end of the rod, that's too low. Are you confusing yourself by using 'm' for both masses in the equation?
     
  5. Apr 14, 2015 #4
    I don't believe I'm using the wrong ones.

    So working it over using the proper masses:

    2. Relevant equations
    KE = 1/2mv^2
    KE = 1/2Iw^2
    L=mvr
    L=Iw
    I=ML^2/3
    I=mr^2

    r=L (I'm using the pivot as the point of origin)

    mvL=(ML^2/3+mL^2)w

    w=mvL/(ML^2/3+mL^2) = 1.47059 rad/sec (I don't understand why it isn't the same, but whatever...)

    KEi = 1/2mv^2 = 2.34375 J

    KEf = 1/2(ML^2/3+mL^2)w^2 = 1.24081 J

    (KEi-KEf)/KEi = 0.470588 Which is correct.

    And looking through my calculator's log, I found exactly where I went wrong the first time. I accidentally used 2 as the velocity instead of 2.5. :| The stupid feelings.
     
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