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Power as a function of height (gravity and spring involved)

  1. Nov 19, 2008 #1
    There is a "cannon" pointing downwards with a spring inside where an object is inside and compressed up 1 meter.

    mass of object = 50.0kg
    k = 49050

    height = 0 at bottom of cannon.

    Potential energy at start = mgh + 1/2kx^2
    Kinetic energy at end = 1/2mv^2

    I had to first solve for the object velocity as a function of height 'y' above the bottom of the cannon.

    This was: v(h) = sqrt(-981y^2 - 19.6y + 1001)

    The question now is to solve for the amount of power being put out as a function of height.

    We are given the answer of: p(h) = 49y * v(h), but I am to find this on my own.

    I know: P = w*t, w = change in kinetic energy

    The change in kinetic energy can be found pretty easily, but what do I do about time?
  2. jcsd
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