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Pulley system problem.

  1. Sep 29, 2012 #1
    http://imgur.com/NMu80
    http://imgur.com/NMu80

    Hello!
    I have a problem to solve and im not quite sure how to.
    In the linked image i have the values of G, F and D given.
    F stays constant and right angled towards the lever.

    The bucket needs to go up 9 meters in 4 seconds.
    What is the smallest x can be for this to happen?

    I know how to find x if the system was standing still, or at constant speed.
    But it needs to move the bucket up 9 meters in 4 seconds.
    Since the only thing i can change is x i presume that the extra moment given by extra length of x, correlates to the speed it needs to have?
    Or can i look at this as a constant speed problem by saying that from the start of the movement, there was an average speed of 2.25 m/s?
    Which then would mean that the length of x is equal to what it would be if the system was standing still.
    As in
    G*(D/2)-F*x=0
    if using the center of the disc as the moment point.

    Im confused.
    Can i solve this simply through equilibrium analyzes or do i have to involve angular momentum or something like that?

    Sry if my english isnt the best. Its not my native language.
     
  2. jcsd
  3. Sep 29, 2012 #2

    gneill

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    Staff: Mentor

    Hello Hello2, Welcome to Physics Forums.

    Presumably 'x' is the length of a lever arm which will rotate the pulley? Are there masses specified for the items shown? Is it assumed that the force F will always act perpendicularly to the lever arm?
     
  4. Sep 29, 2012 #3
    Thanks for the welcome =)

    Yes, x is the length of the lever.
    I have the value of G, F and D
    D=200mm
    G=150N
    F=70N
    F stays constant and perpendicular to the lever during the movement.
     
  5. Sep 29, 2012 #4

    gneill

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    Staff: Mentor

    Okay, so suppose that the bucket ends up with a uniform acceleration (never mind how for the moment). What acceleration 'a' would be required to cover the specified distance in the given time?
     
  6. Sep 29, 2012 #5
    If the bucket has a uniform acceleration, then a=1.125 m/(s^2)
     
  7. Sep 29, 2012 #6

    gneill

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    Staff: Mentor

    Yes, very good. So, what upward force 'u' on the bucket is required to accomplish this? Remember, you have the weight of the bucket (G) and therefore its mass.
     
  8. Sep 29, 2012 #7
    Hm, am i right in saying that u=167.2N? using g=9.82 m/(s^2)
     
  9. Sep 29, 2012 #8
    So wait.. do i need to multiply u with the radius then and equal that to F*x
    So
    u*(D/2)=F*x
    and break out x from that?
    And look at it as having to be in equilibrium, only using the new force needed for that acceleration?
    Or am i just confusing things now?
     
  10. Sep 29, 2012 #9

    gneill

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    Staff: Mentor

    Sure, that looks fine.
    No, that's correct. The arm x and the radius of the pulley form a lever with a fulcrum about the pulley's pivot. So using the moments about the pivot to relate the forces is the right way to go.
     
  11. Sep 29, 2012 #10
    Yaay so then x=238.9 mm
    Unfortunately i dont have access to the answer right now but doing the same thing on a problem i do have the answer for, were i needed to find the radius instead of the lever arm length, i got the right answer.

    Its tempting to overcomplicate things (as in trying angular acceleration and such) when you havnt done these things too much yet.

    Thanks a lot Gneill! You were awesome help!
     
  12. Sep 29, 2012 #11
    So, this problem wasnt really done yet.
    I also need to find the reaction forces in the center of the disc.
    Call that point A, and i need to find Amax and Amin reaction forces.
    Would i be right in trying to find the answer using centripetal force? and combining that with G?
     
  13. Sep 29, 2012 #12

    gneill

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    Hmm. I think you'll want to look at the external forces acting on the system and see what reaction force at the pivot would keep the system pinned in place there. The force from the tension of the bucket rope is constant and directed vertically. The force from the lever arm starts out vertically too, but then changes direction. Presumably there will be points along its position that correspond to maxima and minima total force.
     
  14. Sep 29, 2012 #13
    ok.
    Do you mean something like in this picture?
    http://imgur.com/A4pX5
    http://imgur.com/A4pX5

    I only did those two cases because thats what would give Amax and Amin, if its the right way to go.
    But maybe i should use the force u, and not G like i wrote on there.
    And the moment doesnt affect the resulting force in A right? since it can't stop the moment from turning?
     
  15. Sep 29, 2012 #14

    gneill

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    Staff: Mentor

    The approach looks reasonable, but I would reconsider the total force applied by the rope with the bucket. It'll be accelerating, so the tension won't be just G.
     
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