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Kinetic Energy in an Explosion

  1. Mar 13, 2012 #1
    1. The problem statement, all variables and given/known data

    An explosive of mass M is initially at rest. It then explodes into two pieces and travels along a straight line. The small piece has mass M1, speed V1, and kinetic energy K1=(1/2)M1V12. The kinetic energy of the bigger mass would be in terms of K1 would be:

    2. Relevant equations

    K=(1/2)mv2

    3. The attempt at a solution

    I'm not sure how to proceed without a mass ratio. The answer is [M1/(M-M1)]K1
     
  2. jcsd
  3. Mar 13, 2012 #2

    phyzguy

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    If an object of mass M splits into two pieces, one of which has mass M1, then what is the mass of the other one? Doesn't this give you a mass ratio?
     
  4. Mar 17, 2012 #3
    Yes I figured that part out. So M-M1 is the mass of the other piece. I don't know how to factor this into an equation that relates the kinetic energy of the first piece.
     
  5. Mar 17, 2012 #4
    Oh I think I understand why the answer is the answer. Dividing the small mass by the big mass gives you the ratio, and then multiplying this by the small pieces Kinetic Energy gives you the fraction of kinetic energy that the big piece has. I think. Now how do I put that in equation form to show that?
     
  6. Mar 17, 2012 #5

    phyzguy

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    First you need to conserve momentum. Since the object is initially at rest, it has zero momentum. Since momentum is conserved, it still has zero total momentum after the explosion. Since you know the momentum of one piece, what is the momentum of the other piece? Once you've calculated its momentum, since you know its mass, you can calculate its velocity and then its kinetic energy.
     
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