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Can someone help me with Equilibirum?

  1. Apr 24, 2008 #1
    I don't understand how to do equilibrium problems. I don't know how to set them up and where to start. here is an example. Can anyone please help?

    1. The problem statement, all variables and given/known data

    A uniform thin rod of length 0.50m and mass 4.0 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.0g bullet traveling in the rotation plane is fired into one end of the bullet's path makes angle = 60.0 degrees with the rod. If the bullet lodges into the and the angular velocity of the rod is 10 rad/s immediately after the collision, what is the bullet's speed just before impact.


    2. Relevant equations

    1/2mv^2=1/2Iw^2
    I=1/12ML^2

    3. The attempt at a solution

    K-initial=K-final

    1/2mv^2=1/2Iw^2


    solve for v>>>>

    v=sq. root[Iw^2/m]

    v=sq. root[(1/12*ML^2)w^2/m]

    v=sq.root.[(1/12*4.003*.50^2)*10^2/.003]

    v=52.7m/s

    The answer is 1.3*10^3m/s.
     
  2. jcsd
  3. Apr 24, 2008 #2

    Hootenanny

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    Welcome to PF jinman,

    The collision isn't elastic and therefore kinetic energy isn't conserved. What is always conserved?
     
  4. Apr 24, 2008 #3

    Doc Al

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    This is not an equilibrium problem (not sure what you mean by that, anyway).

    I assume the bullet lodges itself in the rod, making this a perfectly inelastic collision. Kinetic energy is not conserved. But something else is. What?
     
  5. Apr 24, 2008 #4
    I don't know why i put Equilibrium. It must be momentum.

    P=P

    mv=Iw??
     
  6. Apr 24, 2008 #5

    Doc Al

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    Don't mix up linear momentum (p) with angular momentum (Iw). In this case, only one of them is conserved. Which one?
     
  7. Apr 24, 2008 #6
    I would say linear.

    m1v1=m2v2

    v1=m2(wr)/m1

    v1=4.003(10*.25)/ .003

    v1*sin 60=2888.91m/s???
     
  8. Apr 24, 2008 #7

    Doc Al

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    No, linear momentum is not conserved. I assume the rod is restrained by some fixed axis to only rotate about its center. That axis exerts a force on the rod, thus linear momentum is not conserved.
     
  9. Apr 24, 2008 #8
    Ok.

    I1w1=I2w2

    w1=I2w2/I1

    OK so I have to find the angular velocity of the bullet before the collision? How can i find the Inertia of the bullet?
     
  10. Apr 24, 2008 #9

    Doc Al

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