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Momentum, enegy and collisions

  1. Mar 1, 2009 #1
    A proton (mass 1 u) moving at 7.80 x10^6m/s collides elastically and head-on with a second particle moving in the opposite direction at 2.40x10^6 m/s. After the collision, the proton is moving opposite to its initial direction at 6.60x10^6m/s. Find the mass and final velocity of the second particle. [Take the proton's initial velocity to be in the positive direction.]


    I tried using the conservation of momentum and kinetic energy to do this. I get this big mess that i cannot solve for.. Please show me how i would do this. i would like to learn to do these problems. thanks.
     
  2. jcsd
  3. Mar 1, 2009 #2

    LowlyPion

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    Re: momentum

    You should have 2 equations with 2 unknowns from each of the conservations.

    Make it simpler by dropping the powers of 10 and add it back as a factor at the end.

    Try writing out your equations here.
     
  4. Mar 2, 2009 #3
    Re: momentum

    so if we let m1 be the proton. we have..
    (7.8)-(m2)(2.4)=(-6.6)+m2v2
    (7.8^2)+m2(2.4^2)=(6.6^2)+m2(v2)^2

    m2 = [(7.8^2)-(6.6^2)]/[(v2)^2-(2.4^2)]

    and then when i plug it back in, i get a quadratic. that gives me a mass considerably larger than the other one.
     
  5. Mar 2, 2009 #4
    Re: momentum

    What do you mean considerably? If your maths is right then what stops the second particle being very large?

    The Bob
     
  6. Mar 2, 2009 #5
    Re: momentum

    my math is probably bad, that is why i was hoping someone could show me the math so i can see where i went wrong
     
  7. Mar 2, 2009 #6

    LowlyPion

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    Re: momentum

    OK. So you can say that

    m*(v + 2.4) = 14.4 from the first equation. And ...

    m*(V2 - 2.42) = 7.82 - 6.62

    Note that this factors easily into

    m*(V + 2.4)(V - 2.4) = 7.82 - 6.62

    But from the first equation you know m*(v + 2.4) = 14.4 So ...

    14.4*(V - 2.4) = 7.82 - 6.62

    Much easier than a quadratic to solve.

    EDIT: Sorry the 7.82 and 6.62 terms got translated incorrectly. I fixed them now.
     
    Last edited: Mar 2, 2009
  8. Mar 2, 2009 #7
    Re: momentum

    that is much easier and such.. and after working it out.. i did not get the right answer. the answer was 3.6 doing that gave me 1.2
     
  9. Mar 2, 2009 #8

    LowlyPion

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    Re: momentum

    Sorry. I apparently switched two terms inadvertently in typing it out. I just fixed it.
     
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