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Prooving a system will travel up to 180 degrees

  1. Mar 3, 2015 #1
    1. The problem statement, all variables and given/known data
    To prove that system will travel freely upto 180 degree
    m2 is counterweight and m1 is mass of pan (=3kg)
    i have attched the fbd or another link http://www.imagebam.com/image/54bb5a394377595
    2. Relevant equations
    m1(h + a sin θ) g x = m2 y h g
    m2 = 9.13 kg
    3. The attempt at a solution
    we are stuck at the following equation
    Pwg ≥( m1 x^2 + m2 y^2) sin2 θ / [ x(h-xsin2 θ)]
    LHS is weight of pan and arm and if LHS>RHS, system will rotate freely
    is this correct? can you pls explain it properly because it will clear my concepts.
    Thanks.
     

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  3. Mar 3, 2015 #2

    BvU

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    Hello, welcome to PF :smile:

    Could you clarify the problem statement a bit more? The diagram is difficult to read, I see no forces, what is what, what is the pivot point, what is a, what is P w (pr Pw ?), etc.
     
  4. Mar 3, 2015 #3
    a is the length of bearing housing(the middle block which is the reference axis) hence a sin θ is added to h for balancing. my issue is the second equation. i cannot understand the RHS side.LHS is simply the wt of pan and tray.(ρwg).
    can you help me with the equation on RHS
    ( m1 x^2 + m2 y^2) sin2 θ / [ x(h-xsin2 θ)]
    Thanks a lot for a warm welcome in this wonderful community.
     
  5. Mar 3, 2015 #4

    BvU

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    Still lost -- or rather not "in":

    The thing on the right is a pan. What is a pan ? The thing in the middle is a bearing housing. Interesting. Does it pivot around some axis ? What axis ?

    If the LHS was the weight of the pan and arm and now is the weight of the pan and tray, how come m1 doesn't feature in it ? What tray ?
    What is s ?

    What does the equation m1(h + a sin θ) g x = m2 y h g represent ? I see something in kg m3 /s2

    What is ##\theta## ? What's the blue horizontal line ? And the black sloping line just underneath ?

    THe fat black lines to L and R ? The thin black lines (where the h are mentionsed) ?

    What is dangling from the bearing housing ? Where is the reference point for a ?

    Are lengths measured in meters ?

    What has to rotate 180 degrees ? Doesn't it bum into the fat line on the left ?
     
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