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Potential energy functions of a particle

  1. Mar 13, 2009 #1
    1. The problem statement, all variables and given/known data

    A single conservative force acting on a particle varies as Fvec = (-Ax + Bx4)i N, where A and B are constants and x is in meters. Accurately round coefficients to three significant figures.
    (a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (Use A, B, and x as appropriate.)

    (b) Find the change in potential energy and change in kinetic energy as the particle moves from x = 1.80 m to x = 3.40 m. (Use A, B, and x as appropriate.)

    2. Relevant equations

    w = f x d

    3. The attempt at a solution

    ive only attempted part a since i think i will need it to go on to part b.

    w = f x d
    f = (-Ax + Bx4)
    d = x

    PE = (-Ax + Bx^4)x = -Ax^2 + Bx^5
  2. jcsd
  3. Mar 13, 2009 #2


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    Since the force is continuously variable over the range of x isn't your U(x) the integral of the Force F(x) and not just the product of x and F(x)?
  4. Mar 13, 2009 #3
    oh yeah.. so should it be

    (-1/2)Ax^2 + (1/4)Bx^5 ?

    i'm not sure what form my final answer should be.
  5. Mar 13, 2009 #4


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    How about -1/2Ax2 + 1/5Bx5 instead?
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