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Linear momentum and collision

  1. Mar 8, 2009 #1
    1. The problem statement, all variables and given/known data

    A 5.00-g bullet moving with an initial speed of 400 m/s is fired into and passes through a 1.00-kg block, as in Figure P9.67. The block, initially at rest on a frictionless, horizontal surface, is connected to a spring of force constant 900 N/m. If the block moves 5.00 cm to the right after impact, find
    (a) the speed at which the bullet emerges from the block and
    (b) the mechanical energy converted into internal energy in the collision.

    2. Relevant equations

    conservation of momentum
    KE=1/2 mv2

    3. The attempt at a solution

    I solved part a, getting an answer of 100m/s for the speed at which the bullet emerges from the block. But I'm stuck at part b.
    I interpreted the question as: finding the mechanical energy tat was converted = change in mechanical energy = change in kinetic energy of the bullet = 1/2 m(vf -vi) = (1/2)(5/1000)(100-400)2 = 225J

    The correct answer should be 374J.

    Pls help, thanks! :)
     

    Attached Files:

  2. jcsd
  3. Mar 8, 2009 #2

    rl.bhat

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    Homework Helper

    What is the role played by the spring in this problem?
     
  4. Mar 8, 2009 #3

    lanedance

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    hi

    havenl't been through it all, but one thing that stands out is your last calc of cahnge in KE

    should be
    1/2 m(vf^2 -vi^2)

    NOT
    1/2 m(vf -vi)^@2as you've done in your calc
     
  5. Mar 9, 2009 #4
    oh shoot! I cant believe I made tt mistake again n again. :tongue2: Thanks for pointing it out!

    ok, i think i get it.

    change in KE of bullet = 1/2 m(vf2 -vi2)
    = (1/2)(5/1000)(1002-4002) = -375J

    change in KE of spring = (1/2)(1)(1.52 - 02) = 1.125J

    total change in KE = -375 + 1.125 = -373.875 = -374J (round up to 3sf)

    Is this correct? :)
     
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