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A problem on concurrent forces in a plane.

  1. Dec 11, 2015 #1
    1. The problem statement, all variables and given/known data

    A ball rests in a trough as shown in figure. Determine the angle of tilt ##\theta## with the horizontal so that the reactive force at B will be one-third at A if all surfaces are perfectly smooth.

    2.Relevant equations

    Application of Lami's theorem and some algebra and geometry

    3.The attempt at a solution

    I tried to derive an relation between ## \theta ## and the Ratio between the reactions Ra and Rb ,so at ##\theta## =00 the ratio between the reactions is one and at a particular ##\theta## the ratio becomes 3. The relation goes like this ##f(\theta) = x\frac{Ra}{Rb} ## where ##x## is a constant
    This didn't lead me anywhere because there are too many unknowns.

    Another equation i can think of is ##\theta ##= x(Ra-Rb) so at ##\theta =0 ## , Ra =Rb at what ##\theta## will Ra=3Rb?? The required angle ##\theta= x(2Rb) ## and ##x= \frac{\theta}{2Rb}##

    I don't see this going anywhere either.
    Is this the right way to go ?
     

    Attached Files:

  2. jcsd
  3. Dec 11, 2015 #2

    SteamKing

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    I don't see why you can't draw a FBD of the ball and set up the normal forces on each contact surface using the conditions of static equilibrium.

    Remember, the angle θ must be incorporated into the angle of the trough measured w.r.t. the bottom of the wedge. When θ = 0, then these angles will both be 30° as indicated on the diagram.
     
  4. Dec 12, 2015 #3
    Thanks ,i took a little more time than expected to incorporate the angle since i had to imagine the thing to rotate ,i got the answer 16.13 degrees ,is there anyway to derive an equation like the one i mentioned ? i am just trying to find some alternative methods( if there are any).
     
  5. Dec 12, 2015 #4

    SteamKing

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    I doubt it, since the answer, I think, depends on the trigonometry of the situation, which is not linear.
     
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