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Potential energy vs x graph

  1. Oct 10, 2009 #1
    1. The problem statement, all variables and given/known data

    You are given the plot of a potential energy function U(x) versus x.

    http://bcs.whfreeman.com/WebPub/Physics/tiplerphysics6e_bridge/question_bank_images/7-8.png?3200

    1. For each point indicated, state whether the x component of the force associated with this function is positive (+), negative(−), or zero (0)), by matching the points with the corresponding sign.
    1. Zero
    2. Negative
    3. Positive

    A = ?
    B = ?
    C = ?
    D = ?
    E = ?
    F = ?



    2. At which point does the force have the greatest magnitude?


    3. Which point is a stable equilibrium point?



    2. Relevant equations



    3. The attempt at a solution

    I don't know how to start. Please help.
     
  2. jcsd
  3. Oct 11, 2009 #2
    For conservative fields, which is usually what we take potential energy for, F = -dU/dx
     
  4. Oct 11, 2009 #3
    I didn't understand what you said.
     
  5. Oct 11, 2009 #4
    The force is negative the rate of change of potential energy with respect to displacement. So you can evaluate it as negative the derivative of U with respect to x.
     
  6. Oct 11, 2009 #5
    You mean we have to convert this graph into it's derivative? And then what?
     
  7. Oct 11, 2009 #6
    Well...you don't really have to convert it to its derivative...you can just imagine the tangents at the different points. Since force is negative the derivative, if the tangent has a negative slope, then the force is positive, and so on. The case of stable equilibrium is essentially when you have a restoring force - meaning that if you move to the left (- displacement), then the force is to the right (+ direction) and vice versa.
     
  8. Oct 11, 2009 #7
    So

    A=2
    B=1
    C=3
    D=1
    E=2
    F=1

    2nd question, force having greatest magnitude is point C ?

    3rd question, is it point F ??
     
  9. Oct 11, 2009 #8

    ideasrule

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    Homework Helper

    All of those answers are correct except the last one. Why F? For a stable equilibrium, you need to find a point where decreasing x causes a positive force, so U has to have a negative slope on the let. Increasing x must cause a negative force, so U has to have positive slope on the right. There's only one point where this is true.
     
  10. Oct 11, 2009 #9
    Is it C then? Because it has a positive slope on the right and negative on the left.
     
  11. Oct 11, 2009 #10
  12. Oct 11, 2009 #11
    It is E! Isn't it?
     
  13. Oct 11, 2009 #12

    ideasrule

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    Homework Helper

    Actually, the slope is negative on both the left and the right. For E, the slope is positive on both left and right.

    Another way to think about this: if you need to add potential energy to move away from a certain x value, that x value is a stable equilibrium point.
     
  14. Oct 11, 2009 #13
  15. Oct 11, 2009 #14
    is it???
     
  16. Oct 11, 2009 #15
  17. Oct 11, 2009 #16
    Ohh! Okk thank you so much!! Thanks a lot! :)
     
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