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Homework Help: Potential Energy Function

  1. Oct 2, 2008 #1
    A constant force Fx = 6N is in the +x direction.

    A) Find the potential energy function U(x) associated with this force if U(Xo) = 0.

    B) find a function U(x) such that U(4.0m) = 0

    C) Find a function U(x) such that U(6.0) = 14J

    I know that if PE is known then the F can be found by the derivative of the PE.
    I know that if F is known then the PE can be found by integrating the force.

    Since the force Fx is given to be 6N
    the integral of 6 = -6x + C
    Is that PE function for the force Fx?

    Im not sure what A means

    but is B 0 = -6(4) + C
    C = 24?

    and C is 14 = -6(6) + C
    C = 50

    Thanks for your help.
  2. jcsd
  3. Oct 2, 2008 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper

    You have correctly found the constant C, for parts B and C. So you should be able to write the full expression for U(x).

    Part A is done the same way.
  4. Oct 2, 2008 #3
    Thanks! I get it but I have 1 similar problem but I am confused from the context of the problem, if you could help, it be great.

    The force acting on an object is given by Fx = a/x^2. At x = 5.0m, the force is known to point int the -x direction and have a magnitude of 25N. Determine the potential energy associated with this force as a function of x, assuming we assign a reference value of -10J at x = 2.0m for potential energy.

    I know given the force I can take the integral to find the potential energy which is
    integral of a/x^2 since a is a constant I can take it out so it be negative
    integral of 1/x^2 dx = 1/x + C = a/x + C

    The problem is, they are giving me the other information of
    x = 5.0m
    force known to point in -x direction
    x = 2.0

    I do not know what to do with these info. I know they are important. Can someone guide me please, thanks so much.
  5. Oct 3, 2008 #4
  6. Oct 3, 2008 #5


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    Staff Emeritus
    Science Advisor
    Homework Helper

    You can use the given numbers to get a and C.

    For example,
    F = a/x^2
    You can find a, because you know that F = -25N when x = 5.0m

    Then use your equation for potential energy, and the information about the potential at x=2.0m, to find C.
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