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Linear Momentum and Energy

  1. Jan 5, 2012 #1
    1. The problem statement, all variables and given/known data

    A ballistic pendulum consisting of a heavy bob of mass M suspended form a fixed point by a thread of length l is at rest. A bullet of mass m and traveling horizontally at a speed v hits the bob and imbeds itself an the bob. As a result, the pendulum is deflected through a amaximum angle θ from the vertical. Show that

    v = (M+m)/m √(2gl(1-cos⁡〖θ)〗 )

    where g is the acceleration du to gravity ?

    2. Relevant equations



    3. The attempt at a solution
    i really blind with this questions, anyone please i need an answer how to solve it..thaanks :)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 5, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, as you suggest in your title, you can use "energy"- specifically, conservation of energy. (I don't believe you need conservation of momentum.)

    Initially, the mass Mis not moving so its kinetic energy is 0 and the mass m has speed v so its kinetic energy is [itex](1/2)mv^2[/itex]. We can take the potential energy to be 0 at the initial height of bullet and bob so the total energy is [itex](1/2)mv^2[/itex]. After impact, at the bob's highest point, both bullet and bob have 0 kinetic energy so the total energy is just the potential energy, (m+M)g h where h is the height the bob and bullet rise to. By conservation of energy, then, [itex](m+M)gh= (1/2)mv^2[/itex]. Solve that for v.
     
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