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Centrifugal force on water in a glass

  1. Jan 28, 2017 #1
    1. The problem statement, all variables and given/known data
    There is a cyllindrical glass (r=0.05 m) full of water. It is rotating around its vertical geometric axis with 3 turns per second. How many centimetres higher is water at the rim than in the centre of the glass . Water rotates together with the glass.

    2. Relevant equations
    p=ρah
    ω=2πγ
    a=ω2r
    3. The attempt at a solution
    All I know is that the shape of water is parabolic. In the centre there is no additional pressure from rotation, the pressure on the glass is p=ρah, a=ω2r
    total pressure on any point is px + py (vectorial sumation)
     
  2. jcsd
  3. Jan 28, 2017 #2

    billy_joule

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    That's right. If we let the vertex be at (0,0) then you just need to find the Y value when X=0.05m.
    Start by drawing a free body diagram for a piece of water on the surface.
     
  4. Jan 28, 2017 #3
    probably is y=Cx2 ... but I do not know what is C, maybe a/g ... a=17.8 m/s^2, g=10 m/s^2 i do not know, honestly just guessing, as i do not know how to solve it
     
  5. Jan 28, 2017 #4

    billy_joule

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    Post your FBD and we'll see where you've gone wrong.
     
  6. Jan 29, 2017 #5
    I do not know what free body diagram is. Sorry. Please explain to me and I will try
     
  7. Jan 29, 2017 #6

    haruspex

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    Consider a small parcel of water at the surface, at some radius x. If the surface shape is described by y=f(x), what is the slope there? Draw a diagram of the parcel of water and the forces acting on it. Treat the rest of the water as a frictionless solid.
     
  8. Jan 29, 2017 #7
  9. Jan 29, 2017 #8

    haruspex

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    Ok. You left out a normal force, and you need to answer this question
    I.e., in terms of x and y.
     
  10. Jan 29, 2017 #9
    tanφ =ω2r / g
     
  11. Jan 29, 2017 #10
    and dy/dx = ω2r / g
    so: y= ω2r x /g ... for r=x I get y= ω2x2 /2g
     
  12. Jan 29, 2017 #11
    and I have y if i put r=x!
     
  13. Jan 29, 2017 #12

    haruspex

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    Right. So what answer do you get?
     
  14. Jan 29, 2017 #13
  15. Jan 29, 2017 #14

    haruspex

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    Using g=10m/s2, yes, but 4,5cm would be a bit closer.
    Well done.
     
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