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Finding Velocity of a ball hitting a ball hanging from a string

  1. Nov 16, 2008 #1
    1. The problem statement, all variables and given/known data
    A 20.0 ball is fired horizontally with initial speed Vi toward a 110 g ball that is hanging motionless from a 1.10 m -long string. The balls undergo a head-on, perfectly elastic collision, after which the 110 g ball swings out to a maximum angle theta = 50.0.

    What was Vi?

    2. Relevant equations

    call ball mass .02 kg = A
    call ball .11 kg = B
    Avai + Bvbi = Avaf + Bvbf

    Ki = Kf
    (1/2)Avai^2 + (1/2)Bvbi^2 = (1/2)Avaf^2 + (1/2)Bvbf^2

    vaf = (A - B)/(A + B) * vai

    3. The attempt at a solution

    vbi = 0 m/s
    Bvbi = 0

    Avai = -Avaf + Bvbf

    vai = (A + B)/(A - B) * vaf

    my problem is finding vaf, the final velocity of block A.

    the final height y = L(1 - cos(theta)) = 1.1(1 - cos(50)) = .393 m
  2. jcsd
  3. Nov 16, 2008 #2


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    Homework Helper

    You know the height the ball on the string went up to, so you know from conservation of energy and the m*g*h what the KE of the ball on the string was from the collision.

    mv2/2 = m*g*h
  4. Nov 16, 2008 #3

    So, I find vbf = sqrt((2*g*h)), masses cancel out.
    that gets me about 2.775 m/s

    Vai = Vbf*(A + B)/2*A
    which equals about 9.02 m/s.

    and algebraically plugging it back in to find vbf, I find that my answer is correct (at least for the previous work that I did).
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