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Rifle shoots bullet into pendulum What am I doing wrong?

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    A 30g rifle bullet traveling 220 m/s buries itself in a 3.0kg pendulum hanging on a 2.1m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's maximum displacement.


    2. Relevant equations

    p=mv
    K=1/2mv^2
    Ug=mgy


    3. The attempt at a solution

    First, I found the momentum of the bullet:

    p=mv
    p=(0.03kg)(200m/s)
    p=6.6kg*m/s

    Then I found the velocity of the pendulum after the bullet hits it:

    (6.6kg*m/s)/(3.03kg)=2.18m/s

    After that I found the Kinetic Energy of the system just after the bullet hits the pendulum:
    KE=1/2mv^2
    KE=(1/2)(3.03)(2.18)^2
    KE=7.19J

    Then, because that Kinetic Energy transfers to Gravitational Potential Energy when the pendulum has reached its max height, I set the Kinetic Energy equal to Gravitational Potential Energy.

    Ug=mgy
    7.19J=(3.03kg)(9.80)(y)
    y=0.24m

    Using the length of the pendulum (2.1m) as the hypotenuse and (length of the pendulum - y=1.86m) as the y component, I used the Pythagorean Thereom to solve for the x component.

    a^2+b^2=c^2
    1.86^2+b^2=2.1^2
    b^2=2.1^2-1.86^2
    b=0.98m

    So I got the x component to be 0.98m and the y component to be 1.9m, but MasteringPhysics says I'm wrong. What did I do wrong?
     
  2. jcsd
  3. Oct 20, 2009 #2

    Doc Al

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    Staff: Mentor

    Your work looks fine to me.
     
  4. Oct 20, 2009 #3

    Andrew Mason

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    Homework Helper

    As Doc Al says, your approach is correct. However, displacement should be measured from its original rest position. That is probably why your answer is not jiving. Also, I get .97m for the x component.

    AM
     
  5. Oct 20, 2009 #4
    Did I not measure from the rest position? What would be the correct answer if I did? What exactly did I do wrong?
     
  6. Oct 20, 2009 #5

    Andrew Mason

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    Homework Helper

    You are using 1.9m for the change in y. The block does not change its y position by that amount. You found that it changes by .24 m.

    AM
     
  7. Oct 21, 2009 #6

    Doc Al

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    Staff: Mentor

    D'oh! Good catch, AM. (I wasn't paying attention. :redface:)
     
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