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Graphing potential & kinetic energy of an oscillating particle

  1. May 29, 2009 #1
    Graphing potential & kinetic energy of an oscillating particle!!!!

    1. A particle oscillates back and forth in a frictionless bowl whose height is given by h(x) = 0.22x2 where h and x are meters. (a) Show graphically how the potential and kinetic energies of the particle vary with x.



    2. I completed the (b) and (c) part of the problem, but I'm not sure as to how I graph to illustrate how the potential nad kinetic energies of the particle vary with x. Any assitance would be very much appreciated!



    3. I really don't even know where to start or how to start, and how I would label my axis, etc. So if anybody can lead me in the right direction, that would be really great, becuase I'm lost!

    I know that the particle has maximum kinetic energy at the bottom of the bowl in which h=0 and x=0 and that IF the maximum speed of the particle was 0.4ms-1, x=0.19 and -0.19 and h=0.008. Will this information help me in drawing the graph? Because this is what I had to determine for parts (b) and (c): "(b) Where does the particle have maximum kinetic energy? (c) If the maximum speed of the particle is 0.4 ms-1, find the x-coordinates at which the particle has maximum potential energy"

    And I also know that U = mgh and if you had an h(x), you can graph U(x)...but how? That I don't know! So please please please lend your assitance!!!
     
  2. jcsd
  3. May 29, 2009 #2
    Re: Graphing potential & kinetic energy of an oscillating particle!!!!

    h(x) = 0.22x2 (where x2 = x squared)
    As x increases in the postive and negative direction, h increases exponentially. For instance, here is a small table I constructed:
    x h
    -10 22
    -5 5.5
    -3 1.98
    0 0
    3 1.98
    5 5.5
    10 22
    *If plotted, it would look like a parabola
     
  4. May 30, 2009 #3
    Re: Graphing potential & kinetic energy of an oscillating particle!!!!

    Put the x axis, well, x, and the y axis, the energy (J).

    U know potential energy is: W_p(x) = mgh(x)=mg.0.22x^2
    Draw that graph, it's a parabola :D

    The sum of potential and kinetic energy is constant (I call it W), u should be able to find W using the information about the max speed. Then kinetic energy is:

    W_k(x) = W - W_p(x).

    Now it's even easier to draw the graph of W_k(x). It's the reflection of the graph of the W_p(x) through a horizontal line.

    Do some math to find some special point.
     
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