1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Graphing Potential and Kinetic Energy of an Oscillating Particle!

  1. May 28, 2009 #1
    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!
     
  2. jcsd
  3. May 28, 2009 #2
    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"
     
  4. May 29, 2009 #3

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Hint for potential energy graph: what is the potential energy of a mass that is at a height h?
     
  5. May 29, 2009 #4
    U = mgh?
     
  6. May 29, 2009 #5

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Yes. So if you had h(x), could you graph U(x)?
     
  7. May 29, 2009 #6
    yes of course!
     
  8. May 29, 2009 #7

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    As you said, the potential energy is mgh. All you need is to relate h to x, so you need the function h(x). If you know that, then you know th epotential energy as a function of x and you can plot that.

    Hint: read the question carefully.
     
  9. May 29, 2009 #8
    I'm so confused!
     
  10. May 29, 2009 #9

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The potential energy is equal to mg h.

    We need to know how the height h depends on the horizontal distance x of the ball. This given to you in the question.
     
  11. May 29, 2009 #10
    right! U = mgh
    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
     
  12. May 29, 2009 #11

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Good!
    It's indeed a parabola.
    Note that it does not increase exponentially. Exponential growth is when x is in the exponent.

    Now, for the kinetic energy, you need to express 1/2 mv^2 in tersms of x also. You already know the potential energy in terms of x. The trick is to use conservation of energy to
    relate kinetic energy to potential energy
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Graphing Potential and Kinetic Energy of an Oscillating Particle!
Loading...