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Bullet pendulum problem w/ Calculus - AP Physics C

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  1. Nov 28, 2011 #1
    1. The problem statement, all variables and given/known data

    See problem here:
    http://i184.photobucket.com/albums/x153/spl10246/problem.png

    Solution:
    http://i184.photobucket.com/albums/x153/spl10246/solution1.png
    http://i184.photobucket.com/albums/x153/spl10246/solution2.png


    2. Relevant equations

    p = m * v
    K = .5 * m * v^2
    U = m * g * h
    a = dv/dt
    v = dx/dt

    3. The attempt at a solution

    I've gotten A and C fine, I'm still working to get B. D is the trouble part.

    F_net = m * a
    Only force acting is -bv

    m * a = -bv
    m * dv/dt = -bv

    dv/dt = -bv / m

    dv = -bv/m * dt

    dv/v = -b/m * dt



    At this point the published solution makes no sense to me at all. I am used to just putting an indefinite integral on both sides at this point. My confusion is about the bounds. Why is the left side v_0 to v?

    I understand the steps after setting up the integrals (including evaluating the integrals and using log properties and so on).
     
  2. jcsd
  3. Nov 28, 2011 #2
    Okay: I finally arrived at the right answer by just using indefinite integrals and including a constant of integration that I solved for. That got me v(t) = v_0 * e ^ (-bt/m)

    Then I did the same thing to get position from velocity, and used indefinite integrals again...
    I got position = m*v_0 / b * (1 - e^(-bt/m))

    Taking the limit as t-> infinity (b/c the block never fully stops, v(t) has no zeros but does a horizontal asymptote) yields m*v_0/b, which is the answer.
     
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