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A ball of mass m at rest at the coordinate origin exploded into three equal pieces?

  1. Apr 8, 2010 #1
    A ball of mass m at rest at the coordinate origin exploded into three equal pieces.
    At a certain instant, one piece is on the x-axis at x=40cm, and another is at x=20cm, y=-60cm. where is the third piece at that instant


    I don't have an idea how to solve it I tried many time but I don't reach an answer.

    I have to use Fex=Mac.m
     
  2. jcsd
  3. Apr 8, 2010 #2
    Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

    It is solved using conservation of momentum; or centre of mass considerations. (It amounts to the same thing)
    As there are no external forces acting, the centre of mass of the combined 3 fragments cannot have changed position, and must still be at the centre of the coordinate system.
    Alternatively, if you let the time interval = t, you can write down the x and y coordinates of the momentum of the 2 known fragments. (You have the distance travelled in that time from the coordinates. Velocity = distance/time)
    The total momentum of those two plus the unknown fragment must equal zero.

    I don't see how you can use F=ma here.
     
  4. Apr 8, 2010 #3
    Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

    My Physics teacher told me it solved by F=ma ..
     
  5. Apr 8, 2010 #4

    Borek

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    Staff: Mentor

    Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

    Sorry to hear that.

    Momentum conservation it is.
     
  6. Apr 8, 2010 #5
    Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

    Is the answer going to be -60i+60j ?
     
  7. Apr 8, 2010 #6
    Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

    What do i and j represent here? Are they unit cm vectors in the x and y directions?
    You would normally give the answer as x=-60cm and y=+60cm
    How have you calculated those values. You would need to show some working, not a guess.
     
  8. Apr 8, 2010 #7
    Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

    My Work :

    By Conservation of Momentum :

    Pi = Pf
    0= mv1 + mv2 + mv3

    Devid By 3m ..

    = v1 + v2 + v3
    = d1/3t + d2/3t + d3/3t

    Devide By 3t ..

    d3 = -( d1 + d2 )

    d3 = -( 40i + 20i - 60j )

    d3 = -40i - 20i + 60j

    d3 = -60i + 60j

    So x= -60
    and y = 60
     
  9. Apr 9, 2010 #8
    Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

    Up !
     
  10. Apr 9, 2010 #9
    Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

    Yes those answers are correct. (In centimeters)
     
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