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Momentum in 2 Dimensions

  1. Apr 12, 2010 #1
    A radioactive nucleus of mass 5 × 10–26 kg is at rest and emits two neutrons,
    each of mass 1.6 × 10–27 kg, at right angles to each other. If both have speeds of
    360 m s–1, calculate the recoil speed of the nucleus.



    I named calculated the neutrons and named them p1 and p2.
    Since p1 = p2
    Therefore the momentum of both equals 1.8x10-26

    Using Pythagoras, I worked out the overall momentum to be 2.55x10-26

    I then used the formula m1v1 = m2v2 and worked out the velocity to be 509-510ms-1; I didn't bother working out the angle because that was already the wrong answer. The real answer is 17.39ms-1.

    What have I done wrong? Thanks in advance.
     
  2. jcsd
  3. Apr 12, 2010 #2

    rl.bhat

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    Therefore the momentum of both equals 1.8x10-26

    Using Pythagoras, I worked out the overall momentum to be 2.55x10-26

    Check these two calculations. They are wrong.
     
  4. Apr 12, 2010 #3
    It turns out I just got mixed up with the numbers and exponents. Thanks.

    Is my formula for this correct by the way (I'll count the two neutrons as one mass)?

    m1u1 + m2u2 = m2v2 + m2v2
     
  5. Apr 12, 2010 #4

    rl.bhat

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    The formula is correct. The left hand side is zero. After emission the mass of the nucleus is reduced by two times the mass of the neutrons.
     
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