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Density integral

  1. May 3, 2009 #1
    1. The problem statement, all variables and given/known data

    The density of material at any point in a solid cylinder, y^2 + z^2 ≤ a^2, 0 ≤ x ≤ b is proportional to the distance of the point from the x-axis. Find the density. Use k as the proportionality constant.


    2. Relevant equations



    3. The attempt at a solution

    Can someone guide me here? is x here a?
     
  2. jcsd
  3. May 3, 2009 #2

    Defennder

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    No x isn't a. That's the parametric representation of a cylinder whose axis coincides with the x-axis. Now from what is given you should be able to tell that the equation describes a circle on the y-z plane. What then is the equation of any point within that circle? That, and using pythagoras theorem should give you the answer.
     
  4. May 3, 2009 #3
    how can I get the equation of any point within the circle?
     
  5. May 3, 2009 #4

    Defennder

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    Suppose the point is (x,y). What is distance from the centre to that point?
     
  6. May 3, 2009 #5
    the point (x,y) you mean here are you referring that to a point in the circle or.. if I visualize this correctly the cylinder is not standing on it's base.. right?
     
  7. May 3, 2009 #6

    Defennder

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    Well it depends on what you mean by "base". The base of the cylinder is the y-z plane. So from the conventional orientation of x-y-z plane it's lying on its curved side.
     
  8. May 3, 2009 #7
    Last edited by a moderator: May 4, 2017
  9. May 3, 2009 #8

    dx

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    The base should be centered at the origin, lying completely in the yz-plane.
     
  10. May 3, 2009 #9
    Last edited by a moderator: May 4, 2017
  11. May 3, 2009 #10

    dx

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    Like this:

    http://img22.imageshack.us/img22/5278/terip.jpg [Broken]
     
    Last edited by a moderator: May 4, 2017
  12. May 3, 2009 #11
    ok.. so now I need to find the equation within the circle... I am really confused how this can be achievedf
     
  13. May 3, 2009 #12

    dx

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    If the coordinates of a point are (x, y, z), what is the distance of this point from the x-axis?
     
  14. May 3, 2009 #13
    which part of the x-axis? the origin?
     
  15. May 3, 2009 #14

    dx

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    The shortest distance to the x-axis.
     
  16. May 4, 2009 #15
    is the answer just k(y^2+z^2)?
     
  17. May 4, 2009 #16

    dx

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    You forgot the square root. The density is k√(y² + z²). You might also want to mention that the density is 0 for √(y² + z²) > a.
     
  18. May 4, 2009 #17
    hmm.. yea I fogot the sqrt,, how can I express this in terms of r?
     
  19. May 4, 2009 #18
    Are you going to use polar/cylindrical coordinates? Use the polar coordinates (r,theta) for the yz plane instead of the usual xy plane.
     
  20. May 4, 2009 #19
    polar coordinates... how can I do that?
     
  21. May 4, 2009 #20
    ?

    :confused:
     
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