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Physics: a bomb explodes into peices, find magnitude and direction of the third piece

  1. Nov 15, 2012 #1
    1. The Problem: A bomb at rest explodes, breaking into three pieces. Two of the pieces hace equal mass and fly off at 80° of each other with a speed of 100m/s. The tird peice has three times the mass of the other pieces. What is the magnitude and the direction of the third piece?

    2. Relevant equations
    potential energy equations for the x and y axis
    is have
    px: m0v0 = m1v1 +m2v2 +(3)m3v3
    py: m0v0 = m1v1 +m2v2 +(3)m3v3




    3. The attempt at a solution
    This is what i have so far, my confusion is that i was not given any direction and am not sure what i am suppose to put in for theta for m1 and m2 so that i can find v3 and theta3? thank you for any help in advance!

    px: 0 = m1v1cos(theta) +m2v2cos(theta) +(3)m3v3cos(theta)
    py: 0 = m1v1sin(theta) +m2v2sin(theta) +(3)m3v3sin(theta)

    px: 0 = m1(100)cos(theta) + m2(100)cos(theta) +(3)m3v3cos(theta)
    py: 0 = m1(100)sin(theta) + m2(100)sin(theta) +(3)m3v3sin(theta)


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



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 15, 2012 #2

    haruspex

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    Re: physics: a bomb explodes into peices, find magnitude and direction of the third p

    Clearly you need to specify a 'zero' direction then express your answer in relation to it. An obvious choice would be the line bisecting the trajectories of the two equal masses.
     
  4. Nov 15, 2012 #3
    Re: physics: a bomb explodes into peices, find magnitude and direction of the third p

    ok so iif i split it each angle would be 40 degrees in opposite directions giving me

    px: 0 = m1(100)cos(40) + m2(100)cos(40) +(3)m3v3cos(theta)
    py: 0 = m1(100)sin(40) + m2(100)sin(40) + (3)m3v3sin(theta)

    all the m1 and m2 would then cancel when i divide py by px giving me:
    .8355+ tan(theta) = 0
    so theta would be -39.8 degrees? i still think i am doing something wrong
     
  5. Nov 15, 2012 #4

    haruspex

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    Re: physics: a bomb explodes into peices, find magnitude and direction of the third p

    Check the signs in the second equation. m1 and m2 are not moving in the same direction.
     
  6. Nov 15, 2012 #5
    Re: physics: a bomb explodes into peices, find magnitude and direction of the third p

    if m2 is negative then they would end up being zero giving me 0 for theta and velocity, which doesn't make sense.
    px: 0 = m1(100)cos(40) - m2(100)cos(40) +(3)m3v3cos(theta)
    py: 0 = m1(100)sin(40) - m2(100)sin(40) + (3)m3v3sin(theta)

    0 + tan(theta) = 0
     
  7. Nov 15, 2012 #6

    haruspex

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    Re: physics: a bomb explodes into peices, find magnitude and direction of the third p

    What are all the solutions to that equation?
     
  8. Nov 16, 2012 #7
    Re: physics: a bomb explodes into peices, find magnitude and direction of the third p

    (inverse) tan 0 = 0 and therefore so does velocity
     
  9. Nov 16, 2012 #8
    Re: physics: a bomb explodes into peices, find magnitude and direction of the third p

    i suppose tan(180) = 0 also, but then velocity would still be 0
     
  10. Nov 16, 2012 #9

    haruspex

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    Re: physics: a bomb explodes into peices, find magnitude and direction of the third p

    Just noticed you corrected one equation but corrupted the other. You should have
    px: 0 = m1(100)cos(40) + m2(100)cos(40) +(3)m3v3cos(theta)
    py: 0 = m1(100)sin(40) - m2(100)sin(40) + (3)m3v3sin(theta)
    With theta = pi, you should get a nonzero solution for v3.
     
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