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Normal Force between two concentric cylinders

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  1. Jan 23, 2017 #1
    1. The problem statement, all variables and given/known data
    a cylinder sits inside of another fixed cylinder without friction and an internal force acts on the cylinder as shown in the diagram. Draw the normal force vector and write down the force and moment equations.

    I drew in my normal vector to counteract the A force vector and wrote out the force and moment balance equations but when I did a check by plugging in numbers I got that the normal force causes a moment on the inner cylinder. What did I do wrong here?

    2. Relevant equations
    Force balance, moment balance

    In the picture the black dash is the thin outer cylinder
    upload_2017-1-23_13-49-16.png

    3. The attempt at a solution
    ∑Fx = 0, ∑Fy = Ay - Ny = 0, ∑Fz = Az - Nz = 0,
    ∑Mx = (Az * ya - Ay * za) + (Nz * r cosθ - Ny * r sinθ) = 0,
    ∑Mx = ( -Ay * za) + (Nz * r cosθ - Ny * r sinθ) = 0,
     
    Last edited: Jan 23, 2017
  2. jcsd
  3. Jan 23, 2017 #2

    haruspex

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    A normal force is one that is perpendicular to the plane of contact between two bodies. In this case it would be radial to the cylinders.
     
  4. Jan 23, 2017 #3
    so In that case it doesn't matter where the A force originate, just its angle? it would like this then?
    upload_2017-1-23_14-0-16.png
     
  5. Jan 23, 2017 #4

    haruspex

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    Yes, that's better.
    There is a a mistake n the relevant equations you posted. They made a certain assumption which might not apply here.
     
    Last edited: Jan 23, 2017
  6. Jan 23, 2017 #5
    since the outer cylinder is fixed the inner cylinder cant move so the forces should sum to zero, but it could rotate about x
     
  7. Jan 23, 2017 #6

    haruspex

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    Right.
    So what equations do you now have?
     
  8. Jan 23, 2017 #7
    There will be a moment about the x axis caused by the y component of the A force

    ∑Fx = 0, ∑Fy = Ay - Ny = 0, ∑Fz = Az - Nz = 0,
    ∑Mx = -Ay * za = 0
     
  9. Jan 23, 2017 #8

    haruspex

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    Yes, so why did you write this:

    ?

    For the linear forces, you need to get the x and y components of A in terms of A, θ, az and r.
     
  10. Jan 23, 2017 #9
    oops. I copy pasted and modified which led to me forgetting to take out the = 0.
     
  11. Jan 23, 2017 #10
    I have a question about this with friction. If you added friction between the two cylinders then there would be a tangential force acting at the point where the normal force touches to counteract the rolling of the cylinder but then the force balance wouldn't work out? How is this rectified?
    ∑Fn = A - N = 0, ∑Ft = -uN ~= 0,
    ∑Mx = -Ay * za + uN * r
    upload_2017-1-23_18-37-44.png
     

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  12. Jan 23, 2017 #11

    haruspex

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    You have assumed the normal force would continue to act along the same radius.
     
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