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Equilibrium of frame with two masses

  1. Oct 7, 2013 #1
    1. The problem statement, all variables and given/known data
    I need to find the tension T, γ and β in part 2 of this question.
    The question is attached.

    2. Relevant equations
    First of all, the frame is a right angle triangle because (3L)^2 + (4L)^2 = (5L)^2
    take torque about the point O
    we got 2LF + mg(4Lcosγ) = Mg(3Lsinγ)
    from the balance of force, we got
    Tcosβ=(m+M)g + F cos γ
    Tsinβ = Fsinγ
    3. The attempt at a solution
    I have listed these 3 equations but I don't know how to solve them
    Please give me some help
     

    Attached Files:

  2. jcsd
  3. Oct 7, 2013 #2

    tiny-tim

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    Hi VHAHAHA! :smile:

    Hint: if there were only three forces, they would all have to go through the same point. :wink:
     
  4. Oct 7, 2013 #3
    But i think that there are 4 forces
     
  5. Oct 7, 2013 #4
    Do u mean that i have to combine 2 gravitational force into 1 combined force so that there is 3 force?
     
  6. Oct 8, 2013 #5

    tiny-tim

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    (just got up :zzz:)
    Yup! :biggrin:

    The two gravitaitonal forces are known, and they're easy to add …

    so go for it! :wink:
     
  7. Oct 8, 2013 #6
    the combined g force = (m+M)g
    how do go to the same point? i cant see any common point

    btw
    Why 3 force will meet at a point if it is at eqm.
    It there any proof? thanks
     
  8. Oct 8, 2013 #7

    tiny-tim

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    Just use the resultant. :smile:

    (It goes through the point where you'd have to put the fulcrum if you wanted to balance it)

    Suppose only two forces go through a point …

    then, if you take moments about that point, the moments of those two forces will be zero, and the moment of the third force won't! :wink:
     
  9. Oct 8, 2013 #8
    I don't understand
    If we see part 1
    T=(M+m)g
    but these 3 force don't have the common point
    they are parallel
     
  10. Oct 8, 2013 #9

    tiny-tim

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    ah, they have a common point "at infinity" :wink:

    alternatively, my argument only applied when …
    … and in part 1, two forces don't go through a point (except "at infinity")! :smile:
     
  11. Oct 8, 2013 #10
    Thank you.
    But i still don't understand
    There are 4 forces! How to use this rule in part 2 =
     
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