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Conservation of momentum and wood ball problem

  1. Jun 27, 2007 #1
    A 20.0 kg wood ball hangs from a 1.50 m-long wire. The maximum tension the wire can withstand without breaking is 300 N. A 0.900 kg projectile traveling horizontally hits and embeds itself in the wood ball.
    What is the largest speed this projectile can have without causing the cable to break?

    What I have tried:

    I tried to use the tension formula (T = mv^2/r) along with the conservation of momentum formula.
    First I tried:
    v = sqrt(Tr/m) = sqrt(300*1.5/20) = 4.74
    and then m1v1 = m2v2 = mfvf
    so .9v = 20.9 *4.74 = 110.2 m/s which was wrong

    then I tried:
    v = sqrt(Tr/m) = sqrt(300*1.5/20.9) = 4.64
    so .9v = 20.9 * 4.64 = 107.8, which is also wrong

    Can anyone point out where I'm making a mistake? I think the theory is sound, but I cant figure out where I'm going wrong.
  2. jcsd
  3. Jun 27, 2007 #2
    The NET force is F=(mv^2)/r. The two forces acting on the hanging mass(es) are gravity and the tension in the wire. I cannot see that you've accounted for the former. Go back, draw a free-body diagram with the gravitational force included, and see where your thought leads you.

    Last edited: Jun 27, 2007
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