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Graph of Kinetic Energy v. Displacement of a Falling Object

  1. Feb 13, 2008 #1
    [solved] Graph of Kinetic Energy v. Displacement of a Falling Object

    1. The problem statement, all variables and given/known data
    Draw and label a graph with energy for the y axis and displacement for the x axis of the kinetic energy and potential energy of an object in free-fall that started with a horizontal speed of 30 m/s from a height of 80 m.


    2. Relevant equations
    U=mgh
    k=1/2mv^2


    3. The attempt at a solution
    I drew a straight line with negative slope for potential energy because m and g are constants in U=mgh, so it should be a linear graph, as for kinetic energy, I am sitting on the fence on whether or not to draw a straight line or a curve The v^2 makes me want to draw a curve, however, if the the potential energy is a straight line and K = E - U, then shouldn't k be directly proportional to displacement as well?
     
    Last edited: Feb 13, 2008
  2. jcsd
  3. Feb 13, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Good thinking!

    Why not use a bit of kinematics to double check? What's the relationship between v (or v^2) and displacement for a falling object?
     
  4. Feb 13, 2008 #3
    ahh..

    v^2=v0^2+2a(x-x0)
    but since initial velocity in the y direction is 0
    v^2=-2g(x-x0)

    and since -2g is a constant, v^2 is directly proportional to displacement, and thus kinetic energy is directly proportional to displacement!

    Thanks Doc Al!
     
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