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Potential and kinetic energy

  1. Dec 17, 2008 #1
    1. The problem statement, all variables and given/known data
    The U of a 4kg object is given by U= 3x^2-x^3 for x smaller than or equal to 3. U is equal to 0 for all numbers larger than 3. If the total energy of the object is 12J what is its speed at 2 meters?


    2. Relevant equations
    K(x)=E-u(x) E=mechanical energy
    K(x)=1/2mv^2


    3. The attempt at a solution
    It seems like i would plug 2 into the u equation and get the value of U at that particular moment, then use the E, which would be 12??? and subtract the U from it.
    I ended up with the answer 2m/s but I could have sworn doing something with integrals for a problem similar to this so it seems like this would be too easy.

    Any advice?

    thanks
     
  2. jcsd
  3. Dec 17, 2008 #2
    No, your approach and answer are correct. In class, you may have used an integral to determine the function for the potential from a given function for the force...make any sense?

    Another idea is to graph your potential function U(x). Then draw the line for your energy, E = 12J. The difference between E and U(x) is the kinetic energy at position x. If E < U(x), then the object cannot be located at this position, since the kinetic energy would be of negative value.
     
  4. Dec 18, 2008 #3
    Thanks you very much Bufford,
    I remember when we used integrals now.
     
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