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Speed of a bullet in ballistic spring system

  1. May 22, 2009 #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 bullet of mass 6.20 g is fired into a block of mass 2.10 kg. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is k=63.0 N/m. The opposite end of the spring is anchored to a wall. What was the speed of the bullet if the spring's maximum compression is 12.1 cm?

    2. Relevant equations
    pinitial=pfinal
    E=0.5*k*x2
    E= 0.5*m*v2
    3. The attempt at a solution
    m1= bullet and m2= block; v1= vbullet

    i first solved m1v1+m2v2= mtotal*vfinal for Vfinal..so that looked like vfinal= m1*v1/mtotal

    then i used the energy equations to get 0.5*k*x2= 0.5*m*v2
    in v2 i substituted m1*v1/mtotal
    and then tried to solve for v1 which is the speed of the bullet we are looking for ...and my hwk app. is telling me my answer is wrong...so i was wondering if i made a mistake in the workings somewhere..
     
  2. jcsd
  3. May 22, 2009 #2

    Doc Al

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    Staff: Mentor

    Your method looks fine. Provide your final equation for v in terms of m1 and m2.

    Also: Check that you haven't made an arithmetic error.
     
  4. May 22, 2009 #3
    this is how my equation looks like
    (k*x2)/mbullet= (m1*v1/mtotal)2

    [tex]\sqrt{}(k*x^2)/mbullet[/tex] *Mtotal/mbullet = vbullet2

    the square root only applies to the k*x2/mbullet

    does that look right ??
     
  5. May 23, 2009 #4

    Doc Al

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    Staff: Mentor

    That should be:
    (k*x2)/mtotal= (m1*v1/mtotal)2
     
  6. May 23, 2009 #5
    i got the right answer but was wondering why it wouldnt be mass of bullet that would be divided by the energy of spring>>??
     
  7. May 23, 2009 #6

    Doc Al

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    Staff: Mentor

    Because after the collision, the KE of the system is ½mtotalv2. The bullet and block are treated as one unit.
     
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