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Potential Energy as a function of x

  1. Nov 19, 2007 #1
    [SOLVED] Potential Energy as a function of x

    1. The problem statement, all variables and given/known data
    Take U = 5 at x = 0 and calculate potential energy as a function of x, corresponding to the force:
    [tex] 8e^{-2x}[/tex]


    2. Relevant equations
    [tex]W_{net} = U_i - U_f[/tex]
    [tex]W = \int_a^b F_x dx[/tex]



    3. The attempt at a solution

    [tex]\int 8e^{-2x} dx = -4e^{-2x} = W(x)[/tex]

    [tex]W(x) = -4e^{-2x} = U_i(x) - U_f(x)[/tex]
    [tex]U_f(x) = U_i(x) + 4e^{-2x}[/tex]
    [tex]U_f(x) = 5 + 4e^{-2x}[/tex]

    correct answer: U(x) = [tex]1 + 4e^{-2x}[/tex]

    Any ideas how i went wrong?
     
    Last edited: Nov 19, 2007
  2. jcsd
  3. Nov 19, 2007 #2
    You were working with definite integral, I guess. when you integrated 8exp(-2x), you should have put the limits (x = 0 and x = x).
     
  4. Nov 19, 2007 #3
    SOLVED

    [tex] W(x) = \int 8e^{-2x} = -4e^{-2x} + C[/tex] ( I forgot the C earlier)
    [tex]W(x) = U_i(x) - U_f(x)[/tex]
    [tex] -4e^{-2x} + C = 5 - U_f(x)[/tex]
    [tex]U_f(x) = 5 - 4e^{-2x} - C[/tex]

    SOLVE FOR C

    U(0) = 5 = 5 - 4(1) - C
    C = 4

    SOLVE FOR U(x)

    [tex]U_f(x) = 5 - 4e^{-2x} - 4[/tex]

    [tex]U_f(x) = 1 - 4e^{-2x}[/tex]
     
  5. Nov 19, 2007 #4
    I am going to try this way as well when I get back from eating. Cheers!
     
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