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Ballistic spring system

  1. Apr 20, 2008 #1
    1. The problem statement, all variables and given/known data

    You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block. The spring's maximum compression d is measured.

    Find an expression for the bullet's speed.
    Express your answer in terms of the variables m, M, k, d, and constant g.

    2. Relevant equations

    Ki + Ug + Usp = Kf + Ug + Usp

    3. The attempt at a solution

    I used conservation of momentum to find the final velocity of the bullet+block

    (m+M)vf=mvi + Mvi



    where vB is the initial speed of the bullet.

    Next, I used:
    Ki + Ug + Usp = Kf + Ug + Usp

    (1/2)mvi^2 + (1/2)kd^2 + Mgd = (1/2)mvf^2 + (1/2)kd^2 + Mgd
    0 + (1/2)kd^2 + 0 = (1/2)(m+M)[(m+M)^2*vB^2] + 0 + Mgd

    I found the answer to be:

    ((kd^2 - Mgd)(m+M))/m^2 = Vb

    but this was not correct...please help me.
  2. jcsd
  3. Apr 20, 2008 #2
    I got it...nevermind
  4. Dec 11, 2008 #3
    Could someone please explain this, I got the following, but it is not correct

    vB = (k*d^2(m + M))/m^2

    I figured it out, i was missing the square root. The answer is:

    vB = sqrt((k*d^2(m + M))/m^2)
    Last edited: Dec 11, 2008
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