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Contraction of spring colliding with balls

  1. Aug 17, 2008 #1
    on a vertical spring (k=100n/m) there is a box with a mass of 5kg, a ball of 1kg is dropped into it from a height of 1m what is the maximum contraction of the spring if the collosion is plastic.

    i hope that my terminology is correct as i am not studying this in english and am translating

    what i did was find the velcocity of the colision, ie the velocity of the ball after falling 1m, came to 4.27[m/s]

    then using momentum and collision laws

    m1v1+m2v2=(m1+m2)U

    M1-the ball
    M2-the box

    m2v2=0(stationary object)

    U=m1v1/(m1+m2)
    U=(1*4.27)/6=0.7378[m/s]

    then what i did was, using energy i said the energy is conserved from after the impact till the springs maximum contraction so:

    E=0.5(m1+m2)U^2=0.5Kx^2
    3*0.7378^2=50x^2

    x=0.18m

    then onto that i added another0.49m which is the original contraction from the weight of the box, and i get
    x=0.67m

    but the answer in the book is 0.79m and i just cant see how they got it
     
  2. jcsd
  3. Aug 17, 2008 #2
    Re: collision

    Hello devinlevin!
    I would agree with your attack until your energy equation:E=0.5(m1+m2)U^2=0.5Kx^2
    3*0.7378^2=50x^2- specifically the left side.

    First try setting up a general equation, not plugging in numbers and tell me what you get.
     
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