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Cannon Recoil?

  1. Sep 14, 2007 #1
    1. The problem statement, all variables and given/known data

    Imagine a cannon that is free to roll on wheels. Initially, both the cannon and cannonball are at rest. When the cannonball is fired, though, the momentum transferred to the cannonball comes at the expense of the cannon, so the cannonball and cannon end up with momenta having equal magnitudes but opposite directions. If this is so, why does the cannonball fly away at a large speed while the cannon recoils only very modestly? Explain your response.

    2. Relevant equations

    Law of Conservation of Momentum
    Newton's Third Law

    3. The attempt at a solution

    According to the law of conservation of momentum, the momentum of the canon would equal the momentum of the canonball. Since momentum is mv, the cannon's large mass would account for its smaller velocity/recoil, compared with the canonball's smaller mass and greater velocity. Is this right? What am I missing?
     
  2. jcsd
  3. Sep 14, 2007 #2
    I don't think you're missing anything. Your answer is correct. Except that where you said "the momentum of the canon would equal the momentum of the canonball" you should take care to note that they are in opposite direction and so momentum (a vector) is not equal, but only equal in magnitude.
     
    Last edited: Sep 14, 2007
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