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(solved) Rotating ball flies certain height in the air

  1. Jan 26, 2013 #1
    1. The problem statement, all variables and given/known data

    (answer is h * 5 /7)

    2. Relevant equations
    gravitational potential energy = mgh
    kinetic energy = 1/2 mv2
    rotational kinetic energy of sphere = 2/5 mv2

    3. The attempt at a solution
    The gravitation potential energy at the beginning at the top is the same as the kinetic energy and rotational energy at the bottom

    mghi = 1/2 mv2 + 2/5 mv2 = 9/10 mv2

    We also know that the rotational kinetic energy at the apex of it's final height, plus the potential energy it achieves there, is equal to the initial potential energy

    mghi = mgh + 2/5 mv2
    h = hi - (2/5 v2)/g

    and from our first equation, we know
    mghi = 9/10 mv2
    4/9 ghi = 2/5 v2

    So combining those...
    h = hi - (4/9 ghi)/g
    h = 5/9 hi

    But that is not the answer.... So where did I go wrong?

    EDIT: The rotational kinetic energy is actually 1/5 mv2. Sorry, it makes sense
  2. jcsd
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