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Change in Kinetic Energy

  1. Dec 11, 2013 #1
    1. The problem statement, all variables and given/known data

    If the resultant force acting on a 2.0kg object is equal to (3i + 4j) N, what is the change in kinetic energy as the object moves from (7i -8j)m to (11i -5j)m


    2. Relevant equations

    w = Fd
    Ek = 1/2mv2

    3. The attempt at a solution

    I assumed that Ek = w so I tried to solve it by getting the change in displacement and then getting the dot product using the given force (did not use the mass at all)

    d= (11i -5j) - (7i -8j)
    = (4i +3j)

    w= (3i +4j)(4i + 3j)
    = (12i + 12j)

    |w| = 17 J

    ... this answer was totally wrong, as the answer should be 24 J.

    I can't really grasp the relationship with force and kinetic energy.. would appreciate some help. thank you.
     
  2. jcsd
  3. Dec 11, 2013 #2
    Your dot product is incorrect. Remember it's also called the scalar product, because it produces a scalar, not a vector.

    The dot product of two vectors, [a,b] and [c,d], is ac+bd, a simple number. In your case you have everything else correct.

    Gotta kick that habit of tacking i and j back on there after evaluating the dot product!

    You can also see how this is wonky because you're saying w, work, is a vector quantity, which energy is not!
     
  4. Dec 12, 2013 #3
    Ohhh!! thanks so much!! so i really didn't need the 2.0kg?
     
  5. Dec 12, 2013 #4
    No, you really don't. The force over the distance is the work done, or change in kinetic energy. If you have a very massive object, the change in kinetic energy would be the SAME, but the resulting velocity would be lower!
     
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