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Math Help - Momentum Problem

  1. #1
    Super Member craig's Avatar
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    Momentum Problem

    Bullet of mass 0.05 kg is fired from a gun with velocity 700 m/s, find the momentum of the gun immediately after it's fired?

    I used Momentum = mv = -35 kg m/s? - Here I'm taking the direction of the bullet as positive.

    If the gun is brought to rest in 1s by a horizontal force that rises uniformly from 0 to Z N, then falls uniformly back to 0 again, find the value of Z.

    No idea how to start this really. Was thinking to try and find the average acceleration and then use F = ma, however the acceleration isn't constant, so this wouldn't work would it?

    Would love it if someone could give me a little pointer on this?

    Thanks in advance
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  2. #2
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    Let f(t) represent the force on the gun. Then the impulse is equal to the change in momentum:

    \int _0 ^1 f(t) \cdot dt = 35 \frac{kg \cdot m}{s}

    Since the force increases and decreases uniformly,

    \int _0 ^{0.5} f(t) \cdot dt = \int _{0.5} ^1 f(t) \cdot dt = 17.5 \frac{kg \cdot m}{s}

    And f(t) is the equation of a line from 0 to 0.5: f(t) = kt + c

    But c = 0 since f(0) = 0,

    so solve \int _0 ^{0.5} kt \cdot dt = 17.5 for k.

    Then Z = 0.5k.
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  3. #3
    Super Member craig's Avatar
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    Again sorry for the late reply.

    Thanks a lot for your reply, would have never thought to do it this way.

    Solving the integral above you get \frac{k}{8} = 17.5, k = 140.

    Putting this back into the equation of the line, we get the value of Z to be 70?

    Thanks again for the help
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  4. #4
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    Yes, the value of Z is 70.
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  5. #5
    Super Member craig's Avatar
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    Thanks again, your a life saver!
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