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Homework Help: Periodic motion -- Potential as a function of a non-linear Force(x)

  1. Oct 26, 2015 #1
    1. The problem statement, all variables and given/known data
    Please see the attached.I don't know how to do (ai).

    potential function is the potential energy defined by f = -dV/dx
    e is the total energy of the system where
    e = KE + PE
    = (dx/dt)^2 /2 + V

    Note:m=1 because the particle has a unit mass
    If you integrate f,you get V(the PE),which is -9/x + 18/x^2 :

    2. Relevant equations

    3. The attempt at a solution
    I actually sketched the graph as given on the above website,clearly if e is positive then V must be negative,which is shown on the graph when x--->infinity,this is the answer to part (aii).But for a(i) I have no idea,because I haven't met a negative total mechanical energy before.
    What I thought is:
    KE + V = -e
    KE is always positive,leaving V = -e-KE,
    This means PE is always negative,but from (aii) I show that V is negative if x--->infinity.In fact,
    V = -9/x + 18/x^2 = (18-9x) / x^2.

    i.e. V<0 if x>2

    If this is the case then in V = -e-Ke we need to have x>2 all the time,which doesn't make sense.Moreover this is the answer to (aii),e>0

    Would greatly appreciate if someone can give me an idea what's going on


    Attached Files:

  2. jcsd
  3. Oct 26, 2015 #2


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    Staff: Mentor

    For a given negative energy e<0, where can the particle be? Can it move to infinity? If not, how does its motion have to look like, e. g. if its initial motion is in positive x-direction?
    True. Where is the problem?
  4. Oct 27, 2015 #3
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