Simple Harmonic Motion (Bullet fired into a block attached to spring)

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

    A 5g bullet is fired horizontally into a 0.50kg block of wood resting on a frictionless table. The block, which is attached to a horizontal spring, retains the bullet and moves forward, compressing the spring. The block-bullet system goes into SHM with a frequency of 9Hz and amplitude of 15cm.

    A) Determine the speed of the bullet


    2. Relevant equations

    Fs=-kx
    a=-(k/m)x
    PEs= .5kx2
    v=±[(k/m)(A2-x2)].5
    T=2π(m/k).5

    3. The attempt at a solution

    I wasn't sure how to even approach this but I think I need to determine the spring constant k using a form of T=2π(m/k).5.

    So:
    T=2π(m/k).5
    T2=4π2(m/k)
    T2=4π2(m/k)
    k=(4π2m)/(T2)
    k=(4π2(.5kg+.005kg))/(92)
    k=.24613kg/s2

    Then plug that into:
    v=±[(k/m)(A2-x2)].5
    v=±[(.24613/.505)(.152-02)].5
    v=.1047m/s

    I have NO IDEA if I am right or not. Anyone want to confirm or deny?
     
  2. jcsd
  3. ideasrule

    ideasrule 2,323
    Homework Helper

    The frequency is 9 Hz, not the period.
    That would be right if you used the right value of k. The equation comes from the conservation of energy, which says that 1/2*k(A^2-x^2)=1/2mv^2.
     
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