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Rotational problem 2

  1. Jul 20, 2013 #1
    1. The problem statement, all variables and given/known data

    A 75 kg , 34 cm long rod hangs vertically on a frictionless , horizontal axle passing through its cener. A 15 g ball of clay traelling horizontally at 2.2m/s hits and sticks to the very bottom tip of the rod. To what maximum angle , measured from vertical , does the rod ( with the attached ball of clay ) rotate ?

    2. Relevant equations

    KE= 1/2 (m+M)V^2 , U= Mg(L-Lcosθ) , mvi=(m+M)(L/2-L/2cos)

    3. The attempt at a solution

    Energy is conserved , Ei=Ef. Ei= 1/2(m+M)v^2 , Ef = Mg(L-Lcosθ) +(m+M)(L/2-L/2cos) or should i consider K rot as well ?
     
  2. jcsd
  3. Jul 20, 2013 #2

    Simon Bridge

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    Start from before the collision - is the collision elastic?

    The kinetic energy left after the collision turns into gravitational potential energy right - so what would be the rotational KE when the rod reaches it's maximum angle?

    note: the rod is pivoted through it's center - how does it's grav PE change with angle?
     
  4. Jul 20, 2013 #3
    inelastic collision . Thats I am wondering the kinetic rotational energy is concluded and I am wondering the kinetic rotational energy is 1/2IW^2 and I = 1/2MR^2 + (M+m)R^2 ? how can I find angular velocity in this case ?
     
  5. Jul 20, 2013 #4

    Simon Bridge

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    You need to do conservation of angular momentum for the initial collision, use that ##\omega=v/r##
    So at the instant just before the collision, the mass m (given) is moving at speed u (given) a distance r (given) from the pivot (the rod has length 2r) then it's moment of inertia is ##I_m=mr^2## and it's momentum is ##L=(mr^2)(u/r)## ... afterwards: the instant after the collision, the mass m is moving with a (different) tangential velocity v, which gives angular velocity for both the mass and the rod (since they are turning at the same rate). Note: moment of inertial of the rod is not Mr^2. Look it up.

    The kinetic energy will be ##\frac{1}{2}I\omega^2##
     
    Last edited: Jul 20, 2013
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