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Particle moving on a conical surface

  1. Dec 3, 2012 #1
    1. The problem statement, all variables and given/known data

    A particle moves under the action of gravity on a conical surface z^2 = 4(x^2+ y^2),
    z ≥ 0, where z is the vertical axis. For initial position r = (1, 0, 2) and initial velocity
    ṙ = (0, 2, 0) find the extremal values of z along the trajectory. Take g = 10.

    2. Relevant equations

    I really have not a clue how to type the equation on this site but have uploaded the work out on pdf. will appreciate if anyone can shed some light on this. thanks
     

    Attached Files:

    Last edited by a moderator: Dec 4, 2012
  2. jcsd
  3. Dec 3, 2012 #2

    TSny

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    Hello, Drajcoshi. Welcome to Physics Forums!

    I'm not following your set up of polar coordinates. Did you really want to set ##z = \rho##?

    I think you can solve this problem with just application of conservation laws. Besides energy, can you think of anything else that's conserved?
     
  4. Dec 3, 2012 #3
    At this point I am we'll confused, how would you do it? Really appreciate your help. I think I completely messed up the calculation.
     
  5. Dec 3, 2012 #4

    TSny

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    There's another quantity that's conserved (hint: it's the z-component of some vector quantity).

    With this quantity and energy you will be able to set up equations to determine max or min of z.
     
  6. Dec 4, 2012 #5
    alright, did more calcultion and stuck dont know how to find the max and min of z. I have included the calculation, could you check it for me? thanks

    https://www.dropbox.com/s/0qq6cyopw4d0bvj/photo.JPG
     
  7. Dec 4, 2012 #6

    TSny

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    OK, so you have that the z-component of angular momentum as well as the total energy is conserved.

    Try writing expressions for ##L_z## and ##E##. You are only concerned with points of max or min ##z## and the expression for ##L_z## will simplify at those points.
     
  8. Dec 4, 2012 #7
    this this correct? what happens next? sorry all this maths notation is so confusing since i am not a maths student. also dont know how to write using the equation editor.
     

    Attached Files:

    • Lz.doc
      Lz.doc
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  9. Dec 4, 2012 #8

    TSny

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    I'm not really following your notation. If you let ##v## represent the speed of the particle, how would you express ##E## in terms of ##v## and ##z##?

    Can you also express ##L_z## in terms of ##v## and ##z## at a point of maximum or minimum ##z##? (First express it in terms of ##v## and ##\rho## and then express ##\rho## in terms of ##z##.)
     
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