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Inelastic collision and Hook’s law

  1. May 11, 2009 #1
    1. The problem statement, all variables and given/known data
    a bullet of mass 0.005kg traveling at 120m/s hits a block at rest that falls and compresses a spring (k=99n/m) to a maximum compression of 0.121m what is the mass of the block? (solve using momentum)
    m1=0.005kg
    m2=?
    v1=120m/s
    v`=?
    k=99n/m
    x=0.121m

    2. Relevant equations
    m1v1=(m1+m2)v`

    Ee=Ek

    Et=Et`

    3. The attempt at a solution
    attempt one
    Ee=Ek
    1/2kx^2=1/2m1v^2
    v=squareroot((kx^2)/m1)
    v=17m/s
    m1v1=(m1+m2)v`
    0.005(120)= (0.005+ m2)17
    0.005(120)/17=(0.005+ m2)
    0.03529=(0.005+ m2)
    0.03529-0.005=m2
    0.030=m2

    I got it wrong and my teacher will not tell me the answer I can't see were i went wrong
     
  2. jcsd
  3. May 11, 2009 #2

    dx

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    Does the bullet stick to the block? If so, ½kx² should be equal to ½(m1 + m2)v² (instead of ½m1v²).
     
  4. May 11, 2009 #3
    yes the bullet sticks to the block and i am trying to figure out what m2 is so I am not sure how to incorporate ½(m1 + m2)v² (instead of ½m1v²).
     
    Last edited: May 11, 2009
  5. May 11, 2009 #4

    dx

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    Solve for v in terms of m1 and m2 and substitute it back in the momentum equation.
     
  6. May 11, 2009 #5
    v=squareroot((kx^2)/(m1+m2)

    m1v1=(m1+m2)v

    m1v1=(m1+m2)squareroot((kx^2)/(m1+m2)

    m1^2v1^2=m1+m2((kx^2)/(m1+m2))

    then the m1+m2 cancel iam sorry i not getting this i just can't see where iam going wrong

    Or did you mean
    m1v1=(m1+m2)v

    v=m1v1/(m1+m2) & v=squareroot((kx^2)/(m1+m2)
    so
    m1v1/(m1+m2)=squareroot((kx^2)/(m1+m2)

    (m1v1)^2/(m1+m2)^2 = (kx^2)/(m1+m2)

    (m1v1)^2/(m1+m2) = (kx^2) (brought m1+m2 over)

    (0.005*120)^2/(m1+m2) = 1.449459

    0.36=1.4 (m1+m2) (mutiplied both sides by (m1=+m2))

    0.36= 0.007247295 + 1.4m2

    0.352752705= 1.4m2
    0.2519=m2
    ???? is that it or did i mess up again
     
    Last edited: May 11, 2009
  7. May 11, 2009 #6

    dx

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    They don't cancel. One of the (m1 + m2)'s is under a square root.
     
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