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Homework Help: Advanced Momentum Question - need help

  1. May 15, 2006 #1
    Advanced Momentum Question -- need help

    The Question

    A bomb initially at rest on a smooth, horizontal surface explodes into 3 pieces. Two pieces fly across the surface at a 60 degree angle to each other: a 2.0 kg at 20 m/s and a 3.0 kg piece at 12 m/s. The 3rd pieces flys across the surface as well with a vector velocity of 30 m/s.

    --> make a hypothetical prediction based on the direction of the 3rd piece.

    assuming 100% conservation of momentum in both horizontal and veritcal directions, solve for the direction of the 3rd mass.

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    I made my cartesian plane, had the 2 bomb going [60 east of north] and [60 east of south] and the third somewhere in the NW direction.

    from here i am kind of lost, i was thinking to break each into there compentents?
     
  2. jcsd
  3. May 15, 2006 #2

    nrqed

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    Yes, the only way to proceed is to break the momenta into x and y components. Then impose that the sum of the x components of all 3 pieces is zero and same for the sum of the y components.
    Then isolate the x and y components of the piece moving at 30 m/s. You will get something of the form

    [tex] m v_x = A [/tex]
    [tex] m v_y = B [/tex]
    where A and B are some numbers. Then square both expressions and add them up. Using the fact that [itex] v_x^2 + v_y^2 = (30 m/s)^2 = 900 m^2/s^2 [/itex] you will find the mass. Then go back to one of the two equations above and find theta (using, say [itex] v_x = 30 m/s cos (\theta) [/itex]).

    Pat
     
  4. May 15, 2006 #3
    okay thank you very much i have this solved , i broke the horizontal and vertical up, then isolated for the m3 , then equated them to get rid of the m3.

    i got:

    -38 / 30cos(Theta) = -65.8 / 30sin(theta)

    cross multiplied and got 30 degress as my angle. :D
     
  5. May 15, 2006 #4

    nrqed

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    Ok..
    I am not sure how you defined your theta. Using v_x = 30 cos(theta) and v_y = 30 sin(theta) for the third mass would have led to a theta larger than 90 degrees, obviously. But You may have defined your theta to be North of West in which case 30 degrees seems plausible.

    I haven't checked your number but that may be right.
    Notice that you should *definitely* double check your answers for theta and the mass by plugging them back in your initial equations for momentum conservation along x and y and see that the total momentum is zero.

    Glad I could help.

    Regards

    Pat
     
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