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Inelastic collision involving pulley

  1. May 1, 2013 #1
    Here is the problem I am trying

    Two blocks A and B of same mass M are connected with
    each other with an ideal string of length [itex]2l[/itex] passing over an
    ideal pulley. The block A is connected to a light pan C
    with an ideal string as shown in figure. A particle of mass
    [itex]\frac{M}{2}[/itex] is dropped on pan from height
    [itex]\frac{l}{2}[/itex] as shown. If
    collision between particle and pan is plastic, acceleration
    of B just after the collision is

    a) [itex]g[/itex]

    b) [itex]\frac{g}{9}[/itex]

    c) [itex]2g[/itex]

    d) none of above

    I have attached the snapshot of the problem. Now, I am thinking on the following lines. Since
    the pan is light, when the mass M/2 falls on it, the string attached to the pan will feel the jerk.
    And we can think of mass M/2 attached to the pan and accelerating downwards with acceleration g. Do you think this is a good starting point ? I am not sure if my reasoning is correct here...

    thanks
     

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  3. May 1, 2013 #2

    haruspex

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    You don't think the pan and attached masses will reduce the acceleration at all?
    Try doing the free body diagrams for the three masses when M/2 has reached the pan.
     
  4. May 2, 2013 #3
    I don't know if issacnewton is willing to continue the thread but I would like to understand how to solve this. How did the OP conclude that the acceleration of the pan is g, is this even correct? Basically, how should I approach this problem?
     
  5. May 2, 2013 #4
    Sorry for late reply. I thought that since falling mass is going to hit the pan, its acceleration would be g. Probably this is wrong.
     
  6. May 2, 2013 #5

    haruspex

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    It's g before it hits the pan of course, but that's not what we want to know.
    This is rather a curious problem. I don't know whether it intends to confuse by supplying irrelevant information, but it certainly does that.
    It asks for the accelerations just after hitting the pan, not the velocities. So here's a question: do the velocities immediately after impact affect the forces at that time? If not, the history doesn't matter: we can just look at the free body diagram after impact, and not even care that an impact occurred.
     
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