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Momentum of pendulum after hitting it with bullet

  1. Apr 23, 2008 #1
    1. The problem statement, all variables and given/known data
    An 9 g bullet is fired into a 2.5 kg pendulum bob which is initially at rest and becomes embedded in the bob. The pendulum then rises a vertical distance of 6cm.
    What was the initial speed of the bullet? What will be the kinetic energy of the pendulum when the pendulum swings back to its lowest point?

    2. Relevant equations
    M1Vi+M2Vi=M1Vf+M2Vf


    3. The attempt at a solution
    For the first part how would i be able to find the final speed of the pendulum because to use vf^2=vi^2+2ax i would need to know the acceleration which is not given.

    For the second part wouldn't the KE be zero since the pendulum stops at it lowest point??

    thanx for the help.
     
  2. jcsd
  3. Apr 23, 2008 #2

    Doc Al

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    To find the initial speed of the bullet, treat this problem as having two parts:
    (1) The collision of bullet and pendulum. (What's conserved here?)
    (2) The swinging of pendulum+bullet after the collision. (What's conserved here?)
     
  4. Apr 23, 2008 #3
    Note that in problems like this, using the acceleration to find velocities (etc) is impossible because we don't know enough about the situation (i.e. the material characteristics) - and we don't need to.
     
  5. Apr 23, 2008 #4
    in the first one the total momentum's conserved but i would need to find the vf in order to use the equation and in the second one only total momentum is conserved the kinetic energy isnt since it would be a inelastic collision because they stick together.
     
  6. Apr 23, 2008 #5

    Doc Al

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    During the collision, momentum is conserved but mechanical energy is not. (As you correctly point out, the collision is inelastic.)

    After the collision, mechanical energy (but not momentum) is conserved.
     
  7. Apr 23, 2008 #6
    but i thought momentum is always conserved before and after the inelastic collision?
     
  8. Apr 23, 2008 #7

    Doc Al

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    Momentum is conserved during any collision, which means the momentum before and immediately after the collision will be the same. But the pendulum is suspended. As it swings, an external force (the tension in the string) acts and thus momentum is no longer conserved.
     
  9. Apr 23, 2008 #8
    i see but back to the question now i feel so lost... no clue on how to solve it.
     
  10. Apr 23, 2008 #9

    Doc Al

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    Hint: Work backwards. Start by finding the KE of the "pendulum + bullet" immediately after the collision.
     
  11. Apr 23, 2008 #10
    you cannot because you dont have the final velocity of the pendulum.
     
  12. Apr 23, 2008 #11

    Doc Al

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    What do you mean by "final"? After the pendulum rises, what must its speed be at the top of its swing?
     
  13. Apr 23, 2008 #12
    i thought it would be zero but than that would make the KE=0 which would not make sense
     
  14. Apr 23, 2008 #13

    Doc Al

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    Why would that not make sense?
     
  15. Apr 23, 2008 #14
    well idk but my teacher said its 1.5 J.. and since its like swinging back it would be that velocity not the velocity at its lowest point.. i think
     
  16. Apr 23, 2008 #15

    Doc Al

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    Not sure why you think it will have a non-zero speed at the top of its swing. If it had a non-zero speed it wouldn't be at the top--it would keep going higher! (It's like tossing a ball straight up in the air. What's the speed of the ball at the highest point? Zero of course.)

    Compare the total mechanical energy of the "pendulum + bullet" immediately after the collision to its total energy at the highest point of its swing.
     
  17. Apr 23, 2008 #16
    its not at the top o f its swing its at the lowest point so it will keep going.
     
  18. Apr 23, 2008 #17

    Doc Al

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    We seem to be talking in circles a bit. Distinguish three points in the life of the pendulum bob:

    (A) Before the bullet hits it.
    (B) Immediately after the bullet hits it. (At the lowest point of its swing.)
    (C) At the top of its swing.

    Point C is where the KE is zero. (Of course it's also zero before the bullet hits it, but who cares about that.)

    How much total energy does the pendulum have at point C? (Compared to point B.)
     
  19. Apr 23, 2008 #18
    actually i figured it out. i was making a really stupid mistake... thanx for the help!
     
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