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Homework Help: Pendulum question

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data

    A pendulum consists of mass M hanging at the bottom of a mass-less rod of length L with a frictionless pivot at its top. A bullet of mass m and velocity v collides with M and gets embedded. What is the smallest velocity v of the bullet sufficient to cause the pendulum with the bullet to clear the top of the arc.

    2. Relevant equations


    3. The attempt at a solution

    First I found out the velocity of the moving block.


    and [tex]KE_{bottom}=PE_{top}[/tex]


    plug in [tex]v'[/tex]


    cancel out [tex](m+M)[/tex]


    cross multiply


    divide by [tex]m^2[/tex]




    Last edited: Nov 3, 2009
  2. jcsd
  3. Nov 2, 2009 #2


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    Homework Helper

    At the top of the arc, the velocity of M is not equal to zero because it clears the top.
  4. Nov 2, 2009 #3
    but is it more or less correct?
  5. Nov 3, 2009 #4


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    Homework Helper

    The total energy at the top is
    (m + M)*2gL + 1/2*(m + M)*v"^2
    At the top acceleration v"^2/L = g. Or v"^2 = Lg. Sustitute this value in the above expression.
    One more mistake.
    Check the step from v^2 to v.
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