1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Force and Potential Energy Graphs: Mastering Physics HW 11.39

  1. Apr 13, 2013 #1
    1. The problem statement, all variables and given/known data
    The figure below shows the force exerted on a particle that moves along the x-axis. Draw a graph of the particle's potential energy as a function of position from x=0 to x=1.1 . Let U be zero at x=0.


    2. Relevant equations
    F=-dU/dx


    3. The attempt at a solution
    I decided to divide the force graph into three separate graphs:

    From x=0 to x=.5: F(x)= 4x
    From x=.5 to x=1: F(x)= -4x + 4
    From x=1 to x=1.1: F(x)= 0

    I then integrated each equation, and multiplied them by -1, getting U(x)= -2x^2, U(x)= 2x^2 - 2 and U(x)= 0, respectively.

    When I try to graph these equations, only the first one and the last one, U(x)= -2x^2 - 2 and U(x)= 0, seem to give me the correct answer. Can someone help me figure out where I went wrong?
     

    Attached Files:

  2. jcsd
  3. Apr 13, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Your U(x) should be continuous. If you define U(0) to be 0 then U(1) isn't 0. Adjust your constants.
     
  4. Apr 14, 2013 #3
    Does that mean that U(x) would have to be an absolute value function?
     
  5. Apr 14, 2013 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    In each integral, you get an unknown constant. To figure out what the constant is for that integral, you have to plug in known values for U and x at the start of that range.
    I don't see how you got 2-2x2 by integrating -4x+4.
     
  6. Apr 14, 2013 #5
    It should read 2x^2 - 4x. My mistake.

    And I forgot all about solving for the constant first...whoops! I figured it out, though. Thanks! ^.^
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted