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Conservation of Momentum in Different Frames of Reference

  1. Mar 22, 2012 #1
    Hello All,

    The following may be a simple problem. But, your thoughts will be very much appreciated.

    1. The problem statement, all variables and given/known data

    Let's use a gun with mass m1 and a bullet m2. The bullet is fired in the positive direction with speed v2, and the gun recoils in the negative direction with speed v1.

    Because the momentum is conserved, m1v1 = m2v2.

    Hence, v2 can be calculated if m1, m2 and v1 are all known. In other words, v2 = m1v1 / m2. This calculation is from a stationary observer's frame of reference, outside the gun/bullet system.

    2. Relevant equations

    Now, I want to transform the same problem to the gun's frame of reference. (Hypothetically, it's an ant or a small person sitting at the muzzle observing the event!)

    In this new frame of reference, the bullet moves at the following final speed: vb, final = v2 - v1. The initial speed vinitial is zero, because the gun and the bullet are stationary. Therefore:

    m2 (v2 - v1) = (m1 + m2) vinitial = 0

    This means that v1 = v2.

    3. The attempt at a solution

    Clearly, the answer from the first frame should be equal to the answer in the second frame.

    Can someone please indicate to me where my working is incorrect?

    Thanks in advance.

    Quantised
     
    Last edited: Mar 22, 2012
  2. jcsd
  3. Mar 22, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    The problem is that your chosen frame of reference is not an inertial frame -- it will experience an acceleration while the gun is being fired, which means there will be some transient pseudo forces operating on all objects measured from that frame. Physical laws (like conservation of momentum) do not apply without modification to non-inertial frames of reference.
     
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