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Cylinder hitting inclined plane

  1. May 31, 2016 #1
    1. The problem statement, all variables and given/known data

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    2. Relevant equations


    3. The attempt at a solution

    To bring the cylinder to a stop both linear impulse and angular impulse would be required . Linear impulse would be provided by the normal force from the plane whereas the angular impulse has to be provided by the frictional torque . Assuming the inclined plane has friction , I think both options A) and C) should be correct .

    But this is incorrect answer .

    If the plane is assumed frictionless then I think it would not be possible to stop the cylinder from rotating irrespective of the angle of the plane .

    Any help is very much appreciated .

    Thanks
     

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  3. Jun 1, 2016 #2
    Could the plane be assumed frictionless?
     
  4. Jun 1, 2016 #3

    TSny

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    Sounds right.

    Can you make any statement about the direction of the net linear impulse felt by the cylinder when it meets the inclined plane?
     
  5. Jun 1, 2016 #4
    If angle of inclined plane is 90° , then linear impulse imparted by plane would be horizontal towards left . If angle of inclined plane is 120° , then linear impulse imparted by plane would make an angle 60° with the vertical .
     
  6. Jun 1, 2016 #5

    TSny

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    Are you referring to the net impulse or just the impulse due to the normal force from the incline? We agreed that friction must act.

    In order to suddenly bring the center of mass of the cylinder to rest, what must be the direction of the net impulse?
     
  7. Jun 1, 2016 #6
    Sorry . That was impulse due to normal only .
    Are you hinting that frictional torque in case of 90° could make the cylinder jump ?
     
  8. Jun 1, 2016 #7

    TSny

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    No, I was just concentrating on the direction that the net linear impulse must have in order to stop the linear motion of the cylinder's center of mass.
     
  9. Jun 1, 2016 #8
    I think we cannot get the direction of the net linear impulse due to friction and normal without knowing their magnitudes .

    But don't you think that frictional torque in case of 90 °could indeed make the cylinder move upwards ?
     
  10. Jun 1, 2016 #9

    TSny

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    How is the direction of the net impulse related to the direction of the change in linear momentum of the cylinder?

    Yes, I think that could happen.
     
  11. Jun 1, 2016 #10
    They should be in the same direction .

    But in case of 90° the net impulse imparted by the plane cannot be in the horizontal direction towards left ( which should be the direction of change of linear momentum of the cylinder ). So, 90° is not possible .

    Right ?
     
  12. Jun 1, 2016 #11

    TSny

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    I think that's right.
     
  13. Jun 1, 2016 #12
    Ok .

    But , do you agree that cylinder would definitely lose contact with the floor (move up) if angle is 90° ?
     
  14. Jun 1, 2016 #13

    TSny

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    I don't think the cylinder would necessarily leave the floor. Got to quit for tonight. I'll check back tomorrow.
     
  15. Jun 1, 2016 #14

    haruspex

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    if there is friction (and you have proved there must be) then yes.
    To clarify, that is net of all the impulses involved. Vibhor, what are all the potential impulses?
     
  16. Jun 1, 2016 #15
    No problem :smile:

    I think there would be a non zero component of net impulse in vertical direction (due to frictional torque ) which means the center of mass of the cylinder would definitely go up .

    Another thing I wanted to clarify is that , I think it is also possible that the cylinder might not stop if the angle is 120° ?? [I know the question is asking whether there is a chance for the cylinder to stop , which it has if angle is 120° , but not if it is 90 °]
     
  17. Jun 1, 2016 #16

    haruspex

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    It is possible, e.g. if there is insufficient friction. But suppose there is plenty of friction from the sloping surface. What could happen then?
     
  18. Jun 1, 2016 #17
    Ok . In post#13 TSny is of the opinion that cylinder would not necessarily leave the floor .
     
  19. Jun 1, 2016 #18
    It might roll with/without slipping backwards (towards left ) .
     
  20. Jun 1, 2016 #19

    haruspex

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    It must. In order to counter the rotational momentum, there must be an upward impulse from the ramp. There is nowhere for a downward impulse to come from, so there will be a net upward impulse.
    When the angle exceeds 90 degrees, the normal impulse from the ramp can provide the necessary downward impulse.
     
  21. Jun 1, 2016 #20
    What about post#18 ?
     
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