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Explosion problem with energy

  1. Oct 21, 2008 #1
    1. The problem statement, all variables and given/known data
    An explosion breaks an object into two pieces, one of which has 1.5 times the mass of the other. If 7300 J were released in the explosion, how much kinetic energy did each piece acquire?


    2. Relevant equations
    Po = P


    3. The attempt at a solution
    I don't even know how to start this...
     
  2. jcsd
  3. Oct 21, 2008 #2

    Fredrik

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    Use a coordinate system where the center of mass is at rest. Do you know the formula for kinetic energy? There's a conservation law you can use to determine what you should put into that formula. I don't want to tell you any more, because that would make it too easy.
     
  4. Oct 22, 2008 #3
    Well the only law I know of for Kinetic Energy would be KE=1/2 m(v^2) and that Initial KE = final KE...but I don't know how to use either of those in this situation because I have nothing for velocity, and I'm not even sure if that is relevant.
     
  5. Oct 22, 2008 #4
    Forget the rest of the question for the moment. Did you draw a before/after picture and label it with everything you know about the two pieces? Does it remind you of anything you've seen before?
     
  6. Oct 22, 2008 #5
    Yes I did, but it doesn't remind me of anything...all I know about them is that one has a mass of 1.5 m, and the other's mass is m. I guess you could say it looks sort of like a Free Body Diagram?
     
  7. Oct 23, 2008 #6
    OK, now try imagining time is "in reverse", like you're rewinding a video tape. So the "after" picture comes first, then the "before" picture. What does the video tape look like?

    Does that remind you of a type of problem you've solved before?
     
  8. Oct 23, 2008 #7

    Fredrik

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    Energy is not conserved here. The problem statement tells you how much the energy will increase. There is however something else that's conserved here, and that conservation law will tell you the velocity.
     
  9. Oct 24, 2008 #8

    Fredrik

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    Did you figure out what other conservation law I was talking about? (It won't tell you the velocities separately. It will just give you one as a function of the other). Did you realize that [itex]K_1+K_2=7800[/itex]?
     
  10. Oct 26, 2008 #9
    No, i did not realize that. How did you get that?
     
  11. Oct 27, 2008 #10

    Fredrik

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    Now that I think about it, the specification doesn't say that the 7800 J is the amount of energy that was converted into kinetic energy. Some of it could be heat, or kinetic energy of gas particles that are leftovers from the explosion. But if it is, we can't solve the problem. So I can only assume that the 7800 J is just the energy that was converted to kinetic energy.

    In the center of mass frame, the total kinetic energy before the explosion is 0. We interpret the problem specification as saying that the total kinetic energy increases by E=7800 J. That tells us that

    [tex]E=\frac 1 2 m_1v_1^2+\frac 1 2 m_2v_2^2[/tex].

    What you have to do is to use a conservation law to eliminate [itex]m_2[/itex] and [itex]v_2[/itex] from the equation (express the right-hand side as a function of [itex]m_1[/itex] and [itex]v_1[/itex] only).
     
  12. Oct 27, 2008 #11
    Alright, I think I see what you're saying...but the number 7800 seems to have come out of nowhere. Either you mean 7300N because thats what the problem says, or I will need help on how you found that number...
     
  13. Oct 31, 2008 #12

    Fredrik

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    Oops...you're right. I read the number wrong.
     
  14. Nov 2, 2008 #13
    Ok, no big, just making sure that I didn't miss something.
     
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