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Free body diagram for a sliding contact

  1. Nov 28, 2015 #1
    1. The problem statement, all variables and given/known data
    Component A is pushed vertically down with a known force F into component B. The angled surface of B is parallel to the angled surface of A. The contact between A and B is rough and so is the contact between B and the ground. The coefficients of friction are known and so is the weight of component B.

    Determine the angle at which component B is about to slide.

    2. Relevant equations
    See attached image.

    3. The attempt at a solution
    I've drawn the problem in frame 1. In frame 2 I've drawn a free body diagram of component B. In frame 3 I've resolved these forces into X and Y directions. I assume I then write equations for these two directions and determine the angle which makes the net force in the X direction equal zero.

    Could someone please advise if I've identified the forces correctly and if this approach is correct, thanks!
     

    Attached Files:

  2. jcsd
  3. Nov 28, 2015 #2

    haruspex

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    What stops component A moving left?
     
  4. Nov 28, 2015 #3
    In the system that this is from, component A is constrained such that it's only able to move in the Y axis.
     
  5. Nov 28, 2015 #4

    haruspex

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    So include a force for that. It is relevant.
     
  6. Nov 28, 2015 #5
    So that's going to be a normal force on the left side of A equal to the sum of all the resolved forces that are acting in the -X direction i.e. μ1Fcosθ sinθ, and I'll need to include this in the force balance?
     
  7. Nov 28, 2015 #6

    haruspex

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    Yes, it will provide the horizontal balance for A, but since it will affect the normal force between A and B do not assume it is equal to μ1Fcosθ sinθ.
     
  8. Nov 28, 2015 #7
    Hm, will there additionally be a Fcosθcosθ term to add to that? I've got this from the X direction reaction force at the interface between A and B.
     
  9. Nov 29, 2015 #8

    haruspex

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    I don't know how you are getting that. I don't think it is right.
    You can avoid having to worry about the horizontal force on block A if you just look at the balance of the vertical forces on it. What equation do you get for that?
     
  10. Nov 29, 2015 #9
    I've tried doing a force balance for block A first of all. I've written it out in terms of forces normal and parallel to the contact surface (rather than breaking these down into X and Y components.

    http://i.imgur.com/TL0g7fr.jpg

    If you think this looks somewhat correct I'll go on and do a free body diagram for B. :smile:
     
  11. Nov 29, 2015 #10

    haruspex

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    The free body diagram for A should not know anything about the friction between B and ground.
    Trust me, it will be a lot simpler if you just look at the vertical forces on A. Resolving normally and parallel to the surface with B will only add more unknowns and equations.
     
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